{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2024-11-19T00:31:23.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2024-11-19T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":42778,"title":"GJam March 2016 IOW: Polynesiaglot Medium","description":"This Challenge is derived from GJam March 2016 Annual I/O for Polynesiaglot. This is a subset of small set 2. The max Qraw is 2^50 (\u003c1.1259e15) for C[1,50], V[1,50], L[1,15].\r\nThe GJam story goes that words are such that consonants are always followed by a vowel. Determine the number of possible words of length L using C consonants and V vowels. The final Q is to be modulo of the prime 1E9+7.\r\nInput: [C V L] , C[1,50], V[1,50], 1\u003c=L\u003c=15\r\nOutput: [Q] max Qraw is 2^50 (\u003c1.1259e15); Q=mod(Qraw,1E9+7)\r\nExamples: [C V L] [Q]\r\n[1 1 4] [5] {aaaa,aaba,abaa,baaa,baba}  invalid are {bbaa, aaab} \r\n[1 2 2] [6] {aa,ae,ba,be,ee,ea} invalid are {ab,eb,bb}\r\nGoogle Code Jam 2016 Open Qualifier: April 8, 2016\r\nTheory: This is a large value problem, on the order of (C+V)^L, thus brute force will not work. This is also a probability tree type problem. Tree calculations can be reduced to a linear in L evaluation. Inspection shows Q(1)=V, Q(2)=V^2, L=3 Q(3)=V^3+V*C*V+C*V^2 = V*Q(L-1)+V*C*Q(L-2)+C*Q(L-1). There are no Cs at the Q1 level since can not end in a C. Qnext=f(Q(-1),Q(-2)). Qfinal=Q+C*Q(-1)\r\nQ3    V          C\r\nQ2  V   C       V\r\nQ1 V   V       V\r\n\r\nThis medium challenge has eps(Qraw) \u003c0.25 so normal matlab doubles work. For the unbounded case a solution method is to convert this Challenge algorithm to Matlab BigInteger java calls. Solution sizes are on the order of (C+V)^L with the large case being C=50,V=50,L=500.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 522.625px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407.5px 261.312px; transform-origin: 407.5px 261.312px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 21px; text-align: left; transform-origin: 384.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThis Challenge is derived from\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"/#null\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eGJam March 2016 Annual I/O for Polynesiaglot\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. This is a subset of small set 2. The max Qraw is 2^50 (\u0026lt;1.1259e15) for C[1,50], V[1,50], L[1,15].\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 21px; text-align: left; transform-origin: 384.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThe GJam story goes that words are such that consonants are always followed by a vowel. Determine the number of possible words of length L using C consonants and V vowels. The final Q is to be modulo of the prime 1E9+7.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.5px; text-align: left; transform-origin: 384.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eInput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e [C V L] , C[1,50], V[1,50], 1\u0026lt;=L\u0026lt;=15\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.5px; text-align: left; transform-origin: 384.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eOutput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e [Q] max Qraw is 2^50 (\u0026lt;1.1259e15); Q=mod(Qraw,1E9+7)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.5px; text-align: left; transform-origin: 384.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExamples:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e [C V L] [Q]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 40.875px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404.5px 20.4375px; transform-origin: 404.5px 20.4375px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.666667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.666667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.666667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.666667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404.5px 10.2188px; text-wrap: nowrap; transform-origin: 404.5px 10.2188px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e[1 1 4] [5] {aaaa,aaba,abaa,baaa,baba}  invalid \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003eare {bbaa, aaab} \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.666667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.666667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.666667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.666667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404.5px 10.2188px; text-wrap: nowrap; transform-origin: 404.5px 10.2188px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e[1 2 2] [6] {aa,ae,ba,be,ee,ea} invalid \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003eare {ab,eb,bb}\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384.5px 10.5px; text-align: left; transform-origin: 384.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"/#null\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"font-weight: 700; \"\u003eGoogle Code Jam 2016 Open Qualifier: April 8, 2016\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 42px; text-align: left; transform-origin: 384.5px 42px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eTheory:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e This is a large value problem, on the order of (C+V)^L, thus brute force will not work. This is also a probability tree type problem. Tree calculations can be reduced to a linear in L evaluation. Inspection shows Q(1)=V, Q(2)=V^2, L=3 Q(3)=V^3+V*C*V+C*V^2 = V*Q(L-1)+V*C*Q(L-2)+C*Q(L-1). There are no Cs at the Q1 level since can not end in a C. Qnext=f(Q(-1),Q(-2)). Qfinal=Q+C*Q(-1)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 81.75px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404.5px 40.875px; transform-origin: 404.5px 40.875px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.666667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.666667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.666667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.666667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404.5px 10.2188px; text-wrap: nowrap; transform-origin: 404.5px 10.2188px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eQ3    \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003eV\u003c/span\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e          \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003eC\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.666667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.666667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.666667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.666667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404.5px 10.2188px; text-wrap: nowrap; transform-origin: 404.5px 10.2188px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eQ2  \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003eV\u003c/span\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e   \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003eC\u003c/span\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e       \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003eV\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.666667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.666667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.666667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.666667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404.5px 10.2188px; text-wrap: nowrap; transform-origin: 404.5px 10.2188px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eQ1 \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003eV\u003c/span\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e   \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003eV\u003c/span\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e       \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003eV\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.666667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.666667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.666667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.666667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404.5px 10.2188px; text-wrap: nowrap; transform-origin: 404.5px 10.2188px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384.5px 31.5px; text-align: left; transform-origin: 384.5px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThis medium challenge has eps(Qraw) \u0026lt;0.25 so normal matlab doubles work. For the unbounded case a solution method is to convert this Challenge algorithm to Matlab BigInteger java calls. Solution sizes are on the order of (C+V)^L with the large case being C=50,V=50,L=500.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function Q=Polyglot(m)\r\n% Q total words of length L using C consonants and V vowels\r\n% Q is modulo 1E9+7\r\n C=m(1); V=m(2);L=m(3); %\r\n Q=0;\r\n\r\nend","test_suite":"%%\r\ntic\r\nm=[2 8 15 ];\r\nv=Polyglot(m);\r\nvexp=[6938704 ];\r\nassert(isequal(vexp,v))\r\n%%\r\nm=[2 7 15 ];\r\nv=Polyglot(m);\r\nvexp=[853390015];\r\nassert(isequal(vexp,v))\r\n%%\r\nm=[2 2 2 ];\r\nv=Polyglot(m);\r\nvexp=[8];\r\nassert(isequal(vexp,v))\r\n%%\r\nm=[2 2 3 ];\r\nv=Polyglot(m);\r\nvexp=[24];\r\nassert(isequal(vexp,v))\r\n%%\r\nm=[2 2 15];\r\nv=Polyglot(m);\r\nvexp=[32342016 ];\r\nassert(isequal(vexp,v))\r\n%%\r\nm=[4 2 2];\r\nv=Polyglot(m);\r\nvexp=[12];\r\nassert(isequal(vexp,v))\r\n%%\r\nm=[4 2 3];\r\nv=Polyglot(m);\r\nvexp=[40];\r\nassert(isequal(vexp,v))\r\n%%\r\nm=[4 2 4];\r\nv=Polyglot(m);\r\nvexp=[176];\r\nassert(isequal(vexp,v))\r\n%%\r\nm=[44 2 15];\r\nv=Polyglot(m);\r\nvexp=[916593151];\r\nassert(isequal(vexp,v))\r\n%%\r\nm=[1 3 15];\r\nv=Polyglot(m);\r\nvexp=[397629405];\r\nassert(isequal(vexp,v))\r\n%%\r\nm=[2 3 15];\r\nv=Polyglot(m);\r\nvexp=[105078522];\r\nassert(isequal(vexp,v))\r\n%%\r\nm=[2 4 15];\r\nv=Polyglot(m);\r\nvexp=[133836675];\r\nassert(isequal(vexp,v))\r\n%%\r\nm=[2 8 15];\r\nv=Polyglot(m);\r\nvexp=[6938704];\r\nassert(isequal(vexp,v))\r\n%%\r\nm=[2 8 14];\r\nv=Polyglot(m);\r\nvexp=[624439943];\r\nassert(isequal(vexp,v))\r\n%%\r\nm=[50 50 2];\r\nv=Polyglot(m);\r\nvexp=[5000];\r\nassert(isequal(vexp,v))\r\n%%\r\nm=[50 50 3];\r\nv=Polyglot(m);\r\nvexp=[375000];\r\nassert(isequal(vexp,v))\r\n%%\r\nm=[50 50 7];\r\nv=Polyglot(m);\r\nvexp=[249885158];\r\nassert(isequal(vexp,v))\r\n%%\r\nm=[10 20 10];\r\nv=Polyglot(m);\r\nvexp=[998720967];\r\nassert(isequal(vexp,v))\r\n%%\r\nm=[5 10 13];\r\nv=Polyglot(m);\r\nvexp=[746816099];\r\nassert(isequal(vexp,v))\r\n%%\r\nm=[1 1 13 ];\r\nv=Polyglot(m);\r\nvexp=[377 ];\r\nassert(isequal(vexp,v))\r\n\r\n\r\ntoc\r\n","published":true,"deleted":false,"likes_count":8,"comments_count":1,"created_by":3097,"edited_by":7,"edited_at":"2023-07-14T16:27:46.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2016-03-19T18:33:48.000Z","updated_at":"2024-11-07T10:33:15.000Z","published_at":"2016-03-19T20:24:10.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis Challenge is derived from\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eGJam March 2016 Annual I/O for Polynesiaglot\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. This is a subset of small set 2. The max Qraw is 2^50 (\u0026lt;1.1259e15) for C[1,50], V[1,50], L[1,15].\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe GJam story goes that words are such that consonants are always followed by a vowel. Determine the number of possible words of length L using C consonants and V vowels. The final Q is to be modulo of the prime 1E9+7.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e [C V L] , C[1,50], V[1,50], 1\u0026lt;=L\u0026lt;=15\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e [Q] max Qraw is 2^50 (\u0026lt;1.1259e15); Q=mod(Qraw,1E9+7)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExamples:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e [C V L] [Q]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[[1 1 4] [5] {aaaa,aaba,abaa,baaa,baba}  invalid are {bbaa, aaab} \\n[1 2 2] [6] {aa,ae,ba,be,ee,ea} invalid are {ab,eb,bb}]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGoogle Code Jam 2016 Open Qualifier: April 8, 2016\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eTheory:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e This is a large value problem, on the order of (C+V)^L, thus brute force will not work. This is also a probability tree type problem. Tree calculations can be reduced to a linear in L evaluation. Inspection shows Q(1)=V, Q(2)=V^2, L=3 Q(3)=V^3+V*C*V+C*V^2 = V*Q(L-1)+V*C*Q(L-2)+C*Q(L-1). There are no Cs at the Q1 level since can not end in a C. Qnext=f(Q(-1),Q(-2)). Qfinal=Q+C*Q(-1)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[Q3    V          C\\nQ2  V   C       V\\nQ1 V   V       V\\n]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis medium challenge has eps(Qraw) \u0026lt;0.25 so normal matlab doubles work. For the unbounded case a solution method is to convert this Challenge algorithm to Matlab BigInteger java calls. Solution sizes are on the order of (C+V)^L with the large case being C=50,V=50,L=500.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":2390,"title":"Fair Scoring for Cody","description":"The length-based scoring system for Cody has a few well-known loopholes that allow clever programmers to hide complex code inside certain functions so that it doesn't register in the score.  This problem represents an attempt to generate a fairer Cody scoring function.  It doesn't try to replace the length-based criterion with something more elegant; merely to eliminate places where longer code can be hidden and remain undetected by the scoring function.\r\n\r\nI have included a few examples that I consider abusive to start with.  These are just my own opinions.  Please feel free to add your suggestions for others in the comments section for this problem, and I will add good ideas to the test suite when I have the time.  Thanks for playing!\r\n\r\n* regexp:  count number of nodes inside (?@cmd) and add to total\r\n* regexprep:  count number of nodes inside {$cmd} and add to total\r\n\r\nUsing this scoring function, it might even be possible to allow use of eval.\r\n\r\n* eval:  count number of nodes inside argument to be evaluated and add to total\r\n\r\nOther possibilities -- should str2num count the numbers inside its argument?  Suggestions welcome!  And if you support the idea of changing the scoring function along these lines, please 'like' this problem.  Thanks!\r\n\r\nSee also http://www.mathworks.com/matlabcentral/cody/problems/2033-poll-would-you-like-the-regexp-cmd-functionality-to-be-banned-in-cody","description_html":"\u003cp\u003eThe length-based scoring system for Cody has a few well-known loopholes that allow clever programmers to hide complex code inside certain functions so that it doesn't register in the score.  This problem represents an attempt to generate a fairer Cody scoring function.  It doesn't try to replace the length-based criterion with something more elegant; merely to eliminate places where longer code can be hidden and remain undetected by the scoring function.\u003c/p\u003e\u003cp\u003eI have included a few examples that I consider abusive to start with.  These are just my own opinions.  Please feel free to add your suggestions for others in the comments section for this problem, and I will add good ideas to the test suite when I have the time.  Thanks for playing!\u003c/p\u003e\u003cul\u003e\u003cli\u003eregexp:  count number of nodes inside (?@cmd) and add to total\u003c/li\u003e\u003cli\u003eregexprep:  count number of nodes inside {$cmd} and add to total\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eUsing this scoring function, it might even be possible to allow use of eval.\u003c/p\u003e\u003cul\u003e\u003cli\u003eeval:  count number of nodes inside argument to be evaluated and add to total\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eOther possibilities -- should str2num count the numbers inside its argument?  Suggestions welcome!  And if you support the idea of changing the scoring function along these lines, please 'like' this problem.  Thanks!\u003c/p\u003e\u003cp\u003eSee also \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/2033-poll-would-you-like-the-regexp-cmd-functionality-to-be-banned-in-cody\"\u003ehttp://www.mathworks.com/matlabcentral/cody/problems/2033-poll-would-you-like-the-regexp-cmd-functionality-to-be-banned-in-cody\u003c/a\u003e\u003c/p\u003e","function_template":"function y = fair_score(prog)\r\n  y = 0;\r\nend","test_suite":"%%\r\nnewline = char(10);\r\ns = ['function testStr2Num(s)' newline...\r\n'str2num(''1'')'];\r\ny_correct = 9;\r\nassert(isequal(fair_score(s),y_correct))\r\n\r\n%% should this be added?\r\n% newline = char(10);\r\n%s = ['function testStr2Num(s)' newline...\r\n%'str2num(''1 2 3'')'];\r\n%y_correct = 11;\r\n%assert(isequal(fair_score(s),y_correct))\r\n\r\n%%\r\nnewline = char(10);\r\ns = ['function testRegexp(s)' newline...\r\n'regexp(s,''(\\d)'');'];\r\ny_correct = 10;\r\nassert(isequal(fair_score(s),y_correct))\r\n\r\n%%\r\nnewline = char(10);\r\ns = ['function testRegexp(s)' newline...\r\n'regexp(s,''(.{2,}).?(??@fliplr($1))'');'];\r\ny_correct = 14;\r\nassert(isequal(fair_score(s),y_correct))\r\n\r\n%%\r\nnewline = char(10);\r\ns = ['function ans = testRegexprep(s)' newline...\r\n'regexprep(s,''(\\d)'',''A'');'];\r\ny_correct = 12;\r\nassert(isequal(fair_score(s),y_correct))\r\n\r\n%%\r\nnewline = char(10);\r\ns = ['function ans = cellSourceIndex(C)' newline...\r\n'str2num(regexprep(num2str(1:numel(C)),''(\\d)'',''${num2str(repmat(str2num($1),1,length(C{str2num($1)})))}''));'];\r\ny_correct = 36;\r\nassert(isequal(fair_score(s),y_correct))","published":true,"deleted":false,"likes_count":4,"comments_count":12,"created_by":3117,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":"2014-06-26T11:53:06.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2014-06-25T20:27:27.000Z","updated_at":"2024-11-13T11:22:05.000Z","published_at":"2014-06-25T21:05:13.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe length-based scoring system for Cody has a few well-known loopholes that allow clever programmers to hide complex code inside certain functions so that it doesn't register in the score. This problem represents an attempt to generate a fairer Cody scoring function. It doesn't try to replace the length-based criterion with something more elegant; merely to eliminate places where longer code can be hidden and remain undetected by the scoring function.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eI have included a few examples that I consider abusive to start with. These are just my own opinions. Please feel free to add your suggestions for others in the comments section for this problem, and I will add good ideas to the test suite when I have the time. Thanks for playing!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eregexp: count number of nodes inside (?@cmd) and add to total\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eregexprep: count number of nodes inside {$cmd} and add to total\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eUsing this scoring function, it might even be possible to allow use of eval.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eeval: count number of nodes inside argument to be evaluated and add to total\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOther possibilities -- should str2num count the numbers inside its argument? Suggestions welcome! And if you support the idea of changing the scoring function along these lines, please 'like' this problem. Thanks!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSee also\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/2033-poll-would-you-like-the-regexp-cmd-functionality-to-be-banned-in-cody\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ehttp://www.mathworks.com/matlabcentral/cody/problems/2033-poll-would-you-like-the-regexp-cmd-functionality-to-be-banned-in-cody\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":2907,"title":"Collaborative Fun : Nomination","description":"Series of problems have been presented in Cody aiming at collaborative fun. This problem is based on Alfonso's problem #2825 - Pay it Forward. This one encourages more directed collaboration.\r\n\r\nYou can solve this problem only if you are nominated by some other player. Once you are nominated, you can solve it by returning anything. You can nominate a player to solve this problem by returning his player ID.\r\n\r\nThis is not a hacking problem. You should hack only when you are not interested in collaboration.\r\n\r\nExample - I have nominated Alfonso by returning his player ID 1379371. (Since test suite of this problem uses codes from his problem, it is fair to nominate Alfonso)","description_html":"\u003cp\u003eSeries of problems have been presented in Cody aiming at collaborative fun. This problem is based on Alfonso's problem #2825 - Pay it Forward. This one encourages more directed collaboration.\u003c/p\u003e\u003cp\u003eYou can solve this problem only if you are nominated by some other player. Once you are nominated, you can solve it by returning anything. You can nominate a player to solve this problem by returning his player ID.\u003c/p\u003e\u003cp\u003eThis is not a hacking problem. You should hack only when you are not interested in collaboration.\u003c/p\u003e\u003cp\u003eExample - I have nominated Alfonso by returning his player ID 1379371. (Since test suite of this problem uses codes from his problem, it is fair to nominate Alfonso)\u003c/p\u003e","function_template":"function y = nomination(x)\r\n  y = ;\r\nend","test_suite":"lines=textread('nomination.m','%s');\r\nid_own=str2num(regexp(lines{end},'\\d+','match','once'));\r\n\r\nx=uint64(nomination());\r\n\r\nif x == uint64(id_own)\r\n    assignin('caller','score',-1);\r\n    error('Funny! You tried to nominate yourself!')\r\nend\r\n\r\nassignin('caller','score',x);\r\n\r\nproblem=2907;\r\nhtml=urlread(sprintf('http://www.mathworks.com/matlabcentral/cody/problems/%d/solutions?term=size:%d',problem,id_own));\r\nn=numel(regexpi(html,'solution \\d+'));\r\n\r\nif n \u003c 1\r\n    error('Sorry. You are nominated by none.');\r\nend\r\n\r\n\r\n%_______\r\n\r\nurl = sprintf('https://www.mathworks.com/matlabcentral/cody/players/%d',x);\r\nhtml = urlread(url);\r\n\r\nc = regexp(html,'h1.+h1','match');\r\nname = c{1}(4:end-4);\r\n\r\ns = sprintf('____________________\\n\\nYou have nominated %s !!!',name);\r\ndisp(s)","published":true,"deleted":false,"likes_count":3,"comments_count":6,"created_by":17203,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":"2015-02-01T12:49:00.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2015-01-31T09:55:23.000Z","updated_at":"2024-11-08T13:06:23.000Z","published_at":"2015-01-31T09:55:23.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSeries of problems have been presented in Cody aiming at collaborative fun. This problem is based on Alfonso's problem #2825 - Pay it Forward. This one encourages more directed collaboration.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou can solve this problem only if you are nominated by some other player. Once you are nominated, you can solve it by returning anything. You can nominate a player to solve this problem by returning his player ID.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis is not a hacking problem. You should hack only when you are not interested in collaboration.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample - I have nominated Alfonso by returning his player ID 1379371. (Since test suite of this problem uses codes from his problem, it is fair to nominate Alfonso)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":1752,"title":"Get me! v4   (Cody hacking challenge)","description":"The latest version of the anti-hack test-suite.\r\n","description_html":"\u003cp\u003eThe latest version of the anti-hack test-suite.\u003c/p\u003e","function_template":"function y = get_me()\r\n  y = 42;\r\nend","test_suite":"%%\r\n\r\n% Clean workspace\r\n\r\n!/bin/cp get_me.m safe\r\n!/bin/rm *.*\r\n!/bin/mv safe get_me.m\r\n!/bin/rm @*\r\n\r\n% Clean user's function from some known jailbreaking mechanisms\r\nfunctions = {'!','feval','str2func','regex','system','dos','unix','perl','java','fopen','write','save','setenv','path'};\r\n\r\nfid = fopen('get_me.m');\r\n  st = char(fread(fid)');\r\n  for n = 1:numel(functions)\r\n    st = regexprep(st, functions{n}, 'error(''No fancy functions!''); %', 'ignorecase');\r\n  end\r\nfclose(fid)\r\n\r\n% Force a function header, and comment first code's line (the supposedly users' function header)\r\nst = sprintf('function y = get_me()\\n%%%s', st);\r\n\r\nfid = fopen('get_me.m' , 'w');\r\n  fwrite(fid,st);\r\nfclose(fid)\r\n\r\n% Release the Kraken!\r\nget_me()\r\n\r\n% Try to cleanup the mess\r\n!/bin/cp get_me.m safe\r\n!/bin/rm *.*\r\n!/bin/mv safe get_me.m\r\n!/bin/rm @*\r\n\r\npath(pathdef) % undo any change on search path\r\n\r\nassert(isequal(ans,now))","published":true,"deleted":false,"likes_count":4,"comments_count":7,"created_by":3359,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":17,"test_suite_updated_at":"2013-07-26T15:59:47.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2013-07-26T15:00:58.000Z","updated_at":"2024-11-13T12:17:55.000Z","published_at":"2013-07-26T15:00:58.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe latest version of the anti-hack test-suite.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":1875,"title":"GJam: 2013 China Event: Cannon Angle","description":"This Challenge is derived from \u003chttp://code.google.com/codejam/contest/2933486/dashboard#s=p1 GJam 2013 China Captain Hammer\u003e. The problem is modified to fit within Cody dimensions.\r\n\r\nThe Challenge is to return the lower angle of a cannon given a target distance and an initial cannonball velocity. Gravity is a constant at 9.8m/sec^2, A valid solution is assured. (Error tolerance 2e-6).\r\n\r\n*Input:* [v d]  Velocity and Distance in meters.\r\n\r\n*Output:* theta  in units of degrees with an accuracy of 2e-6\r\n\r\n\r\n*Competition Summary:*  Best Time of 8 minutes,  755/1070 completed\r\n\r\nThe winner completed all three GJam China Challenges in 26 minutes with second at 43 minutes.\r\n","description_html":"\u003cp\u003eThis Challenge is derived from \u003ca href = \"http://code.google.com/codejam/contest/2933486/dashboard#s=p1\"\u003eGJam 2013 China Captain Hammer\u003c/a\u003e. The problem is modified to fit within Cody dimensions.\u003c/p\u003e\u003cp\u003eThe Challenge is to return the lower angle of a cannon given a target distance and an initial cannonball velocity. Gravity is a constant at 9.8m/sec^2, A valid solution is assured. (Error tolerance 2e-6).\u003c/p\u003e\u003cp\u003e\u003cb\u003eInput:\u003c/b\u003e [v d]  Velocity and Distance in meters.\u003c/p\u003e\u003cp\u003e\u003cb\u003eOutput:\u003c/b\u003e theta  in units of degrees with an accuracy of 2e-6\u003c/p\u003e\u003cp\u003e\u003cb\u003eCompetition Summary:\u003c/b\u003e  Best Time of 8 minutes,  755/1070 completed\u003c/p\u003e\u003cp\u003eThe winner completed all three GJam China Challenges in 26 minutes with second at 43 minutes.\u003c/p\u003e","function_template":"function theta=Cannon(v,d)\r\n  theta=0;\r\nend","test_suite":"%%\r\ntic\r\nvd=[249 6326 ];\r\nexp=44.5948575;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[77 41 ];\r\nexp=1.9429163;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[28 11 ];\r\nexp=3.9516039;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[105 21 ];\r\nexp=0.5347917;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[147 51 ];\r\nexp=0.6626633;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 3210 ];\r\nexp=10.2293872;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[219 61 ];\r\nexp=0.3570850;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[240 41 ];\r\nexp=0.1998405;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[179 3269 ];\r\nexp=44.5041154;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 3480 ];\r\nexp=11.1338133;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[102 81 ];\r\nexp=2.1878908;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[121 51 ];\r\nexp=0.9781434;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[138 31 ];\r\nexp=0.4570257;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[210 4500 ];\r\nexp=45.0000000;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[192 3761 ];\r\nexp=44.4745779;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[37 41 ];\r\nexp=8.5337735;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[32 41 ];\r\nexp=11.5514232;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[199 81 ];\r\nexp=0.5742839;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 3360 ];\r\nexp=10.7304643;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[233 71 ];\r\nexp=0.3671784;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[266 81 ];\r\nexp=0.3214027;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[27 21 ];\r\nexp=8.1988972;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[279 21 ];\r\nexp=0.0757408;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 5230 ];\r\nexp=17.3572961;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[279 51 ];\r\nexp=0.1839431;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[218 21 ];\r\nexp=0.1240585;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 7690 ];\r\nexp=28.4309587;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[89 31 ];\r\nexp=1.0990234;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[141 2028 ];\r\nexp=44.2618026;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[178 81 ];\r\nexp=0.7178094;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[132 71 ];\r\nexp=1.1443126;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 690 ];\r\nexp=2.1544417;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 6970 ];\r\nexp=24.6861041;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[41 1 ];\r\nexp=0.1670142;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[123 21 ];\r\nexp=0.3897097;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[48 61 ];\r\nexp=7.5190650;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[77 81 ];\r\nexp=3.8470546;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[152 71 ];\r\nexp=0.8628902;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[267 11 ];\r\nexp=0.0433201;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[164 21 ];\r\nexp=0.2192071;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 4310 ];\r\nexp=13.9947943;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[256 71 ];\r\nexp=0.3041622;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[192 41 ];\r\nexp=0.3122545;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 7110 ];\r\nexp=25.3662790;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[98 31 ];\r\nexp=0.9063600;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[286 21 ];\r\nexp=0.0720786;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[44 91 ];\r\nexp=13.7142226;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 8360 ];\r\nexp=32.7741901;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 5060 ];\r\nexp=16.7170592;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[194 81 ];\r\nexp=0.6042720;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[96 61 ];\r\nexp=1.8595639;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[190 1 ];\r\nexp=0.0077770;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[237 51 ];\r\nexp=0.2549165;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[52 31 ];\r\nexp=3.2254600;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[250 71 ];\r\nexp=0.3189378;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[29 61 ];\r\nexp=22.6508544;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 4030 ];\r\nexp=13.0143792;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[39 31 ];\r\nexp=5.7607904;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[62 61 ];\r\nexp=4.4733355;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[246 61 ];\r\nexp=0.2829993;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[86 51 ];\r\nexp=1.9374169;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[252 91 ];\r\nexp=0.4023216;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[275 11 ];\r\nexp=0.0408363;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[49 81 ];\r\nexp=9.6529702;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[127 11 ];\r\nexp=0.1914728;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[223 61 ];\r\nexp=0.3443890;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[160 21 ];\r\nexp=0.2303047;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[196 31 ];\r\nexp=0.2265546;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[55 91 ];\r\nexp=8.5730698;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[110 1234 ];\r\nexp=44.0395169;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[274 61 ];\r\nexp=0.2281140;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 6800 ];\r\nexp=23.8846446;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 3310 ];\r\nexp=10.5630642;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[44 31 ];\r\nexp=4.5141266;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[295 1 ];\r\nexp=0.0032261;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[64 11 ];\r\nexp=0.7540525;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[240 21 ];\r\nexp=0.1023567;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[91 21 ];\r\nexp=0.7120327;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 1870 ];\r\nexp=5.8744286;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 1730 ];\r\nexp=5.4290641;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[259 51 ];\r\nexp=0.2134486;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[51 91 ];\r\nexp=10.0258563;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 4200 ];\r\nexp=13.6075829;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[262 81 ];\r\nexp=0.3312919;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[74 81 ];\r\nexp=4.1674764;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[88 81 ];\r\nexp=2.9417237;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[255 91 ];\r\nexp=0.3929103;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[72 41 ];\r\nexp=2.2226617;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 7900 ];\r\nexp=29.6707716;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 1620 ];\r\nexp=5.0800699;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[253 71 ];\r\nexp=0.3114186;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[265 91 ];\r\nexp=0.3638145;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[248 1 ];\r\nexp=0.0045647;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 6090 ];\r\nexp=20.7696393;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[158 71 ];\r\nexp=0.7985813;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 2170 ];\r\nexp=6.8338053;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 1500 ];\r\nexp=4.7002140;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[163 31 ];\r\nexp=0.3275780;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[139 31 ];\r\nexp=0.4504729;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[271 21 ];\r\nexp=0.0802786;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[113 41 ];\r\nexp=0.9016072;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[156 81 ];\r\nexp=0.9346125;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[100 61 ];\r\nexp=1.7135925;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[85 91 ];\r\nexp=3.5451226;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[43 61 ];\r\nexp=9.4316060;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[57 61 ];\r\nexp=5.3012744;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[136 61 ];\r\nexp=0.9260755;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 5200 ];\r\nexp=17.2436039;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[159 71 ];\r\nexp=0.7885653;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[86 61 ];\r\nexp=2.3180653;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 8140 ];\r\nexp=31.2094004;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 5190 ];\r\nexp=17.2057754;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[259 6845 ];\r\nexp=45.0000000;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 6570 ];\r\nexp=22.8379951;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[285 71 ];\r\nexp=0.2454102;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 6460 ];\r\nexp=22.3511092;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[75 573 ];\r\nexp=43.3260450;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[46 41 ];\r\nexp=5.4730826;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[52 21 ];\r\nexp=2.1824862;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 5950 ];\r\nexp=20.1913108;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[68 91 ];\r\nexp=5.5599659;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[64 21 ];\r\nexp=1.4399949;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[36 11 ];\r\nexp=2.3856596;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[134 21 ];\r\nexp=0.3283507;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[9 1 ];\r\nexp=3.4745532;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[143 31 ];\r\nexp=0.4256222;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[116 91 ];\r\nexp=1.9000393;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[23 41 ];\r\nexp=24.7121091;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 8390 ];\r\nexp=33.0022766;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[200 51 ];\r\nexp=0.3579647;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[66 91 ];\r\nexp=5.9068209;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[203 21 ];\r\nexp=0.1430697;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 230 ];\r\nexp=0.7175455;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 7250 ];\r\nexp=26.0668121;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[81 71 ];\r\nexp=3.0438586;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[184 91 ];\r\nexp=0.7547006;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[273 41 ];\r\nexp=0.1544470;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[224 91 ];\r\nexp=0.5091983;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[25 1 ];\r\nexp=0.4492173;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[243 51 ];\r\nexp=0.2424831;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 4920 ];\r\nexp=16.1968290;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 840 ];\r\nexp=2.6239945;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 2740 ];\r\nexp=8.6794304;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[49 91 ];\r\nexp=10.9018740;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[244 81 ];\r\nexp=0.3819768;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[197 31 ];\r\nexp=0.2242603;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[186 31 ];\r\nexp=0.2515707;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[278 71 ];\r\nexp=0.2579249;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[258 1 ];\r\nexp=0.0042177;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 2990 ];\r\nexp=9.5002916;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[10 1 ];\r\nexp=2.8120066;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 7390 ];\r\nexp=26.7901102;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 430 ];\r\nexp=1.3418485;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[46 215 ];\r\nexp=42.3568299;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 6250 ];\r\nexp=21.4435357;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[109 1 ];\r\nexp=0.0236301;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[152 31 ];\r\nexp=0.3767088;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[290 41 ];\r\nexp=0.1368700;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[277 21 ];\r\nexp=0.0768385;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[136 81 ];\r\nexp=1.2298703;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 910 ];\r\nexp=2.8433535;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[224 21 ];\r\nexp=0.1175014;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 2440 ];\r\nexp=7.7039453;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[119 71 ];\r\nexp=1.4081796;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[20 31 ];\r\nexp=24.7100694;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 5120 ];\r\nexp=16.9419243;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 1940 ];\r\nexp=6.0976449;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[119 1445 ];\r\nexp=45.0000000;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[255 6635 ];\r\nexp=44.7753101;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 280 ];\r\nexp=0.8735777;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[219 41 ];\r\nexp=0.2400045;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[262 61 ];\r\nexp=0.2494890;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 970 ];\r\nexp=3.0315083;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 7720 ];\r\nexp=28.6029416;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[189 31 ];\r\nexp=0.2436475;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[110 51 ];\r\nexp=1.1836603;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[298 61 ];\r\nexp=0.1928498;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[231 5445 ];\r\nexp=44.9999996;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[69 81 ];\r\nexp=4.7988649;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[107 11 ];\r\nexp=0.2697430;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[114 21 ];\r\nexp=0.4536767;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[47 225 ];\r\nexp=43.2757298;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[17 1 ];\r\nexp=0.9716372;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[130 81 ];\r\nexp=1.3460985;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 4630 ];\r\nexp=15.1376561;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[121 91 ];\r\nexp=1.7460565;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[82 41 ];\r\nexp=1.7129065;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[199 31 ];\r\nexp=0.2197751;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[93 71 ];\r\nexp=2.3071761;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 5540 ];\r\nexp=18.5513095;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[126 41 ];\r\nexp=0.7251166;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 4260 ];\r\nexp=13.8184496;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 440 ];\r\nexp=1.3730779;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 3130 ];\r\nexp=9.9634881;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[145 61 ];\r\nexp=0.8146500;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 1170 ];\r\nexp=3.6596870;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[200 4081 ];\r\nexp=44.4955953;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[271 41 ];\r\nexp=0.1567351;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 1490 ];\r\nexp=4.6685979;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[291 21 ];\r\nexp=0.0696230;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[139 51 ];\r\nexp=0.7411528;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[53 51 ];\r\nexp=5.1245500;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[42 71 ];\r\nexp=11.6156650;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[243 91 ];\r\nexp=0.4326773;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 4430 ];\r\nexp=14.4204070;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[210 11 ];\r\nexp=0.0700282;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[112 61 ];\r\nexp=1.3657683;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[219 31 ];\r\nexp=0.1814659;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 4910 ];\r\nexp=16.1599009;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[44 11 ];\r\nexp=1.5959920;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[192 11 ];\r\nexp=0.0837741;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[276 71 ];\r\nexp=0.2616766;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[75 91 ];\r\nexp=4.5611459;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[166 21 ];\r\nexp=0.2139567;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[195 41 ];\r\nexp=0.3027202;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[116 81 ];\r\nexp=1.6909858;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[282 8114 ];\r\nexp=44.6253583;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[37 11 ];\r\nexp=2.2581760;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 1910 ];\r\nexp=6.0019356;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[182 1 ];\r\nexp=0.0084757;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[176 21 ];\r\nexp=0.1903338;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[120 1 ];\r\nexp=0.0194965;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 1320 ];\r\nexp=4.1319681;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[298 9061 ];\r\nexp=44.6614758;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 7700 ];\r\nexp=28.4881098;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[79 636 ];\r\nexp=43.5312934;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 5280 ];\r\nexp=17.5474818;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[227 31 ];\r\nexp=0.1689006;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[275 41 ];\r\nexp=0.1522086;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[171 1 ];\r\nexp=0.0096012;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[229 91 ];\r\nexp=0.4872031;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[200 1 ];\r\nexp=0.0070187;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[147 41 ];\r\nexp=0.5327126;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[169 31 ];\r\nexp=0.3047300;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[133 41 ];\r\nexp=0.6507837;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 1150 ];\r\nexp=3.5967945;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[147 1 ];\r\nexp=0.0129922;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[144 51 ];\r\nexp=0.6905672;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[30 51 ];\r\nexp=16.8668385;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[217 4805 ];\r\nexp=45.0000000;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[131 1 ];\r\nexp=0.0163597;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[58 41 ];\r\nexp=3.4299252;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[116 61 ];\r\nexp=1.2731382;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[43 1 ];\r\nexp=0.1518392;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[167 21 ];\r\nexp=0.2114020;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[295 31 ];\r\nexp=0.1000086;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[217 51 ];\r\nexp=0.3040728;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 7220 ];\r\nexp=25.9148699;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[25 51 ];\r\nexp=26.5497777;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 3620 ];\r\nexp=11.6073520;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[67 31 ];\r\nexp=1.9402732;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 31 ];\r\nexp=0.0967027;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 8610 ];\r\nexp=34.8206771;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[81 91 ];\r\nexp=3.9060385;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[57 31 ];\r\nexp=2.6826598;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 180 ];\r\nexp=0.5615346;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[73 81 ];\r\nexp=4.2832883;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[201 21 ];\r\nexp=0.1459311;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[68 11 ];\r\nexp=0.6679330;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[159 51 ];\r\nexp=0.5663996;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[204 1 ];\r\nexp=0.0067462;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[189 81 ];\r\nexp=0.6366722;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 590 ];\r\nexp=1.8417362;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[149 61 ];\r\nexp=0.7714868;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 8980 ];\r\nexp=38.9553303;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[216 11 ];\r\nexp=0.0661918;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[119 91 ];\r\nexp=1.8053178;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[125 81 ];\r\nexp=1.4560313;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 6750 ];\r\nexp=23.6536081;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 790 ];\r\nexp=2.4674046;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 4520 ];\r\nexp=14.7419107;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 6830 ];\r\nexp=24.0242561;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[94 51 ];\r\nexp=1.6213062;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[75 21 ];\r\nexp=1.0483648;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 5630 ];\r\nexp=18.9049816;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[86 71 ];\r\nexp=2.6991243;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[43 31 ];\r\nexp=4.7284323;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[193 31 ];\r\nexp=0.2336526;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[259 31 ];\r\nexp=0.1297425;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[287 21 ];\r\nexp=0.0715772;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 6870 ];\r\nexp=24.2115915;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[57 41 ];\r\nexp=3.5519442;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[239 11 ];\r\nexp=0.0540650;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[192 71 ];\r\nexp=0.5407548;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 8470 ];\r\nexp=33.6315148;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[77 61 ];\r\nexp=2.8933815;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[105 1125 ];\r\nexp=45.0000000;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 9183 ];\r\nexp=44.6530547;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 7170 ];\r\nexp=25.6638839;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 5560 ];\r\nexp=18.6296154;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 980 ];\r\nexp=3.0628800;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[145 91 ];\r\nexp=1.2154985;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 5820 ];\r\nexp=19.6630507;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[32 61 ];\r\nexp=17.8587444;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 5270 ];\r\nexp=17.5093740;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[237 31 ];\r\nexp=0.1549479;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[168 1 ];\r\nexp=0.0099472;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[41 71 ];\r\nexp=12.2256701;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[207 11 ];\r\nexp=0.0720728;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[250 61 ];\r\nexp=0.2740155;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 51 ];\r\nexp=0.1590921;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[161 51 ];\r\nexp=0.5524132;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[265 1 ];\r\nexp=0.0039979;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[246 21 ];\r\nexp=0.0974246;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[195 61 ];\r\nexp=0.4503988;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[160 2612 ];\r\nexp=44.6077195;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 6150 ];\r\nexp=21.0206716;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[83 21 ];\r\nexp=0.8559461;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[160 61 ];\r\nexp=0.6690338;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[156 61 ];\r\nexp=0.7037899;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[162 1 ];\r\nexp=0.0106977;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[166 61 ];\r\nexp=0.6215362;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[107 51 ];\r\nexp=1.2510059;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[215 41 ];\r\nexp=0.2490182;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[212 91 ];\r\nexp=0.5684822;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[84 61 ];\r\nexp=2.4300259;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 6630 ];\r\nexp=23.1071658;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[119 61 ];\r\nexp=1.2097168;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[7 1 ];\r\nexp=5.7684795;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 6730 ];\r\nexp=23.5617578;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 2860 ];\r\nexp=9.0724806;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[274 21 ];\r\nexp=0.0785303;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 1510 ];\r\nexp=4.7318359;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[42 21 ];\r\nexp=3.3498826;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 5220 ];\r\nexp=17.3193640;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 8670 ];\r\nexp=35.3730578;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[18 31 ];\r\nexp=34.8306447;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 8540 ];\r\nexp=34.2104815;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[256 21 ];\r\nexp=0.0899619;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[91 71 ];\r\nexp=2.4099422;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[247 51 ];\r\nexp=0.2346928;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[56 21 ];\r\nexp=1.8813698;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[135 91 ];\r\nexp=1.4023810;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 3930 ];\r\nexp=12.6682378;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[97 41 ];\r\nexp=1.2237457;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[280 8000 ];\r\nexp=45.0000000;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[280 41 ];\r\nexp=0.1468211;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[147 21 ];\r\nexp=0.2728412;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[23 11 ];\r\nexp=5.8790664;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[139 1 ];\r\nexp=0.0145308;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[78 620 ];\r\nexp=43.5307164;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[250 41 ];\r\nexp=0.1841728;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[69 41 ];\r\nexp=2.4205902;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 2730 ];\r\nexp=8.6467533;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[141 91 ];\r\nexp=1.2854868;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 3800 ];\r\nexp=12.2211854;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[290 11 ];\r\nexp=0.0367211;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[276 21 ];\r\nexp=0.0773963;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[105 11 ];\r\nexp=0.2801172;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[238 81 ];\r\nexp=0.4014801;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[200 91 ];\r\nexp=0.6387576;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[293 41 ];\r\nexp=0.1340815;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[299 9122 ];\r\nexp=44.6851269;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[21 1 ];\r\nexp=0.6366722;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[36 91 ];\r\nexp=21.7406299;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[270 7438 ];\r\nexp=44.5863296;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 5870 ];\r\nexp=19.8652679;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[125 21 ];\r\nexp=0.3773380;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[132 81 ];\r\nexp=1.3055882;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 4510 ];\r\nexp=14.7060881;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[111 91 ];\r\nexp=2.0753631;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[176 11 ];\r\nexp=0.0996981;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[76 81 ];\r\nexp=3.9496009;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[183 51 ];\r\nexp=0.4275657;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[144 41 ];\r\nexp=0.5551429;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[111 11 ];\r\nexp=0.2506519;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[232 21 ];\r\nexp=0.1095376;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[153 2388 ];\r\nexp=44.3197033;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[264 41 ];\r\nexp=0.1651571;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[203 1 ];\r\nexp=0.0068128;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[206 1 ];\r\nexp=0.0066158;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[190 41 ];\r\nexp=0.3188632;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[67 51 ];\r\nexp=3.1962494;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[59 21 ];\r\nexp=1.6946784;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 8380 ];\r\nexp=32.9257979;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[108 51 ];\r\nexp=1.2279321;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[267 7274 ];\r\nexp=44.7042055;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[298 21 ];\r\nexp=0.0663905;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 9070 ];\r\nexp=40.4879078;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[247 31 ];\r\nexp=0.1426554;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 1580 ];\r\nexp=4.9533543;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 310 ];\r\nexp=0.9672092;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[246 91 ];\r\nexp=0.4221877;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[110 81 ];\r\nexp=1.8807470;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[189 1 ];\r\nexp=0.0078595;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[299 91 ];\r\nexp=0.2857755;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 4820 ];\r\nexp=15.8288860;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[184 41 ];\r\nexp=0.3399986;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[173 81 ];\r\nexp=0.7599105;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[201 61 ];\r\nexp=0.4239087;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 1820 ];\r\nexp=5.7152103;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[130 41 ];\r\nexp=0.6811720;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[65 71 ];\r\nexp=4.7395084;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[192 91 ];\r\nexp=0.6931066;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[136 1887 ];\r\nexp=44.4506934;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[171 51 ];\r\nexp=0.4896861;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[236 91 ];\r\nexp=0.4587274;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[173 31 ];\r\nexp=0.2908008;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[35 41 ];\r\nexp=9.5737143;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 9020 ];\r\nexp=39.5832887;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[296 91 ];\r\nexp=0.2915978;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[33 41 ];\r\nexp=10.8258185;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 4110 ];\r\nexp=13.2927675;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[277 1 ];\r\nexp=0.0036590;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[254 31 ];\r\nexp=0.1349008;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[82 81 ];\r\nexp=3.3899244;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[54 21 ];\r\nexp=2.0235395;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[54 91 ];\r\nexp=8.9040499;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[85 71 ];\r\nexp=2.7632032;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[14 1 ];\r\nexp=1.4329920;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[170 81 ];\r\nexp=0.7869742;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[42 51 ];\r\nexp=8.2296248;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[35 125 ];\r\nexp=45.0000000;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 3390 ];\r\nexp=10.8310888;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[122 81 ];\r\nexp=1.5285870;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[74 31 ];\r\nexp=1.5901570;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 8170 ];\r\nexp=31.4129069;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 1660 ];\r\nexp=5.2068859;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[134 41 ];\r\nexp=0.6411051;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[184 3454 ];\r\nexp=44.4258154;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[143 81 ];\r\nexp=1.1123483;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[67 91 ];\r\nexp=5.7294046;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[208 41 ];\r\nexp=0.2660616;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[169 81 ];\r\nexp=0.7963175;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[213 11 ];\r\nexp=0.0680695;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[152 61 ];\r\nexp=0.7413270;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[259 21 ];\r\nexp=0.0878899;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[174 71 ];\r\nexp=0.6584409;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[242 41 ];\r\nexp=0.1965510;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[265 31 ];\r\nexp=0.1239339;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 6930 ];\r\nexp=24.4952155;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[177 1 ];\r\nexp=0.0089613;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 8630 ];\r\nexp=35.0015489;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[281 8057 ];\r\nexp=44.7766386;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 4450 ];\r\nexp=14.4916789;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[257 51 ];\r\nexp=0.2167838;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 7210 ];\r\nexp=25.8644501;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 8110 ];\r\nexp=31.0086245;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[120 31 ];\r\nexp=0.6044357;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 4010 ];\r\nexp=12.9449893;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[85 737 ];\r\nexp=44.2615751;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[287 1 ];\r\nexp=0.0034084;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 6900 ];\r\nexp=24.3530039;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[107 81 ];\r\nexp=1.9878552;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[73 91 ];\r\nexp=4.8168446;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 5830 ];\r\nexp=19.7034001;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[125 51 ];\r\nexp=0.9165221;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[174 31 ];\r\nexp=0.2874678;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[258 91 ];\r\nexp=0.3838254;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[88 51 ];\r\nexp=1.8502291;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 890 ];\r\nexp=2.7806630;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[131 71 ];\r\nexp=1.1618593;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 5890 ];\r\nexp=19.9464871;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[275 81 ];\r\nexp=0.3007089;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[201 31 ];\r\nexp=0.2154232;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[103 61 ];\r\nexp=1.6151178;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[169 11 ];\r\nexp=0.1081282;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[234 81 ];\r\nexp=0.4153242;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[127 41 ];\r\nexp=0.7137400;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[45 61 ];\r\nexp=8.5850615;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[268 71 ];\r\nexp=0.2775328;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[120 81 ];\r\nexp=1.5800158;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 2520 ];\r\nexp=7.9631306;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[39 91 ];\r\nexp=17.9483177;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[113 31 ];\r\nexp=0.6816548;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[152 91 ];\r\nexp=1.1060655;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 1260 ];\r\nexp=3.9429273;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 6980 ];\r\nexp=24.7340581;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[212 61 ];\r\nexp=0.3810567;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[8 1 ];\r\nexp=4.4040343;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[153 61 ];\r\nexp=0.7316660;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[55 1 ];\r\nexp=0.0928099;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 3080 ];\r\nexp=9.7977560;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[108 81 ];\r\nexp=1.9511562;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[81 41 ];\r\nexp=1.7555143;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[242 71 ];\r\nexp=0.3403741;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[46 81 ];\r\nexp=11.0165379;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[221 1 ];\r\nexp=0.0057482;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[249 71 ];\r\nexp=0.3215048;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 7440 ];\r\nexp=27.0544802;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[45 21 ];\r\nexp=2.9165098;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[289 21 ];\r\nexp=0.0705899;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 7520 ];\r\nexp=27.4846425;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[235 1 ];\r\nexp=0.0050837;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[299 1234 ];\r\nexp=3.8870928;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[250 1 ];\r\nexp=0.0044920;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[176 51 ];\r\nexp=0.4622558;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 8510 ];\r\nexp=33.9588221;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[151 31 ];\r\nexp=0.3817151;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[61 1 ];\r\nexp=0.0754501;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[132 31 ];\r\nexp=0.4995219;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[238 21 ];\r\nexp=0.1040843;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[238 91 ];\r\nexp=0.4510494;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[101 31 ];\r\nexp=0.8533003;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[252 1 ];\r\nexp=0.0044210;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[101 41 ];\r\nexp=1.1286835;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[152 51 ];\r\nexp=0.6197772;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 8830 ];\r\nexp=37.0236469;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[240 31 ];\r\nexp=0.1510984;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[134 51 ];\r\nexp=0.7975086;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 1020 ];\r\nexp=3.1884039;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[257 91 ];\r\nexp=0.3868183;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[128 11 ];\r\nexp=0.1884927;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 6160 ];\r\nexp=21.0627029;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[213 31 ];\r\nexp=0.1918335;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[255 51 ];\r\nexp=0.2201977;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[126 11 ];\r\nexp=0.1945242;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[280 51 ];\r\nexp=0.1826315;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[150 41 ];\r\nexp=0.5116148;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 7480 ];\r\nexp=27.2684278;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 4140 ];\r\nexp=13.3975114;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[133 51 ];\r\nexp=0.8095495;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[168 41 ];\r\nexp=0.4078483;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[281 71 ];\r\nexp=0.2524469;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[147 2205 ];\r\nexp=45.0000000;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[113 1 ];\r\nexp=0.0219868;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[242 61 ];\r\nexp=0.2924323;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[56 91 ];\r\nexp=8.2607465;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[260 21 ];\r\nexp=0.0872152;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[22 31 ];\r\nexp=19.4398009;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[165 71 ];\r\nexp=0.7322451;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 2190 ];\r\nexp=6.8980297;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 7570 ];\r\nexp=27.7582308;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[141 41 ];\r\nexp=0.5790205;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 4840 ];\r\nexp=15.9022391;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[142 11 ];\r\nexp=0.1531570;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 7750 ];\r\nexp=28.7765421;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[232 81 ];\r\nexp=0.4225163;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[53 21 ];\r\nexp=2.1007558;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[123 81 ];\r\nexp=1.5038100;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[210 51 ];\r\nexp=0.3246830;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[273 1 ];\r\nexp=0.0037670;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[50 81 ];\r\nexp=9.2565056;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[298 1 ];\r\nexp=0.0031614;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[166 11 ];\r\nexp=0.1120718;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 6260 ];\r\nexp=21.4861399;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[253 81 ];\r\nexp=0.3552825;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[144 91 ];\r\nexp=1.2324494;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[288 8463 ];\r\nexp=44.6385985;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[268 7328 ];\r\nexp=44.5316039;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[297 61 ];\r\nexp=0.1941507;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[62 41 ];\r\nexp=2.9999445;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[223 5074 ];\r\nexp=44.6458418;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[248 91 ];\r\nexp=0.4154052;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[106 61 ];\r\nexp=1.5249020;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[211 41 ];\r\nexp=0.2585494;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[120 21 ];\r\nexp=0.4094400;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[210 1 ];\r\nexp=0.0063662;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 4660 ];\r\nexp=15.2461386;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[172 71 ];\r\nexp=0.6738453;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[214 91 ];\r\nexp=0.5579047;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[131 11 ];\r\nexp=0.1799582;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[50 255 ];\r\nexp=44.1896883;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[227 51 ];\r\nexp=0.2778715;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 4330 ];\r\nexp=14.0654935;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[115 1 ];\r\nexp=0.0212287;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[80 91 ];\r\nexp=4.0049368;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[228 21 ];\r\nexp=0.1134147;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[104 11 ];\r\nexp=0.2855301;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[260 61 ];\r\nexp=0.2533422;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[290 1 ];\r\nexp=0.0033383;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[105 81 ];\r\nexp=2.0644344;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[57 71 ];\r\nexp=6.1830728;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[43 188 ];\r\nexp=42.5787456;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[214 71 ];\r\nexp=0.4352775;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[284 11 ];\r\nexp=0.0382891;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[267 41 ];\r\nexp=0.1614665;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[270 31 ];\r\nexp=0.1193862;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[131 51 ];\r\nexp=0.8344642;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[70 71 ];\r\nexp=4.0817971;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[21 41 ];\r\nexp=32.8296766;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[282 91 ];\r\nexp=0.3212706;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[24 11 ];\r\nexp=5.3933350;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[226 21 ];\r\nexp=0.1154310;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[227 11 ];\r\nexp=0.0599322;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 4800 ];\r\nexp=15.7556484;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[134 81 ];\r\nexp=1.2668806;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[256 61 ];\r\nexp=0.2613212;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 8860 ];\r\nexp=37.3715407;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[230 81 ];\r\nexp=0.4298969;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[182 91 ];\r\nexp=0.7713825;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[142 2057 ];\r\nexp=44.3369812;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[32 71 ];\r\nexp=21.4019868;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[142 61 ];\r\nexp=0.8494455;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 3170 ];\r\nexp=10.0963242;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[191 61 ];\r\nexp=0.4694629;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[190 71 ];\r\nexp=0.5522004;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[205 71 ];\r\nexp=0.4743394;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[248 71 ];\r\nexp=0.3241029;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[166 31 ];\r\nexp=0.3158443;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[145 51 ];\r\nexp=0.6810732;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 6050 ];\r\nexp=20.6033628;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[254 71 ];\r\nexp=0.3089712;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[185 71 ];\r\nexp=0.5824565;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 3380 ];\r\nexp=10.7975318;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[296 71 ];\r\nexp=0.2275088;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[38 81 ];\r\nexp=16.6740056;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[24 1 ];\r\nexp=0.4874355;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[280 31 ];\r\nexp=0.1110109;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 8690 ];\r\nexp=35.5640799;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 4160 ];\r\nexp=13.4674481;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[252 61 ];\r\nexp=0.2696832;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[98 71 ];\r\nexp=2.0773304;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[209 81 ];\r\nexp=0.5206370;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 2710 ];\r\nexp=8.5814338;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[57 21 ];\r\nexp=1.8158465;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[102 51 ];\r\nexp=1.3767520;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 1770 ];\r\nexp=5.5561708;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 8160 ];\r\nexp=31.3447605;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[74 71 ];\r\nexp=3.6499694;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[51 41 ];\r\nexp=4.4432920;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[297 91 ];\r\nexp=0.2896374;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[48 71 ];\r\nexp=8.7887794;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[140 41 ];\r\nexp=0.5873229;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[284 61 ];\r\nexp=0.2123322;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[229 41 ];\r\nexp=0.2195007;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[294 81 ];\r\nexp=0.2630966;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[138 71 ];\r\nexp=1.0469250;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[84 11 ];\r\nexp=0.4376931;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[220 11 ];\r\nexp=0.0638067;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 650 ];\r\nexp=2.0293307;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[261 31 ];\r\nexp=0.1277617;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[259 11 ];\r\nexp=0.0460375;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[150 21 ];\r\nexp=0.2620364;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 3580 ];\r\nexp=11.4717190;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[295 71 ];\r\nexp=0.2290539;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 8330 ];\r\nexp=32.5500293;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[127 21 ];\r\nexp=0.3655463;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[196 91 ];\r\nexp=0.6651000;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 7230 ];\r\nexp=25.9654030;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[55 51 ];\r\nexp=4.7550987;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[118 61 ];\r\nexp=1.2303199;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[172 61 ];\r\nexp=0.5789235;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 3990 ];\r\nexp=12.8756810;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[49 41 ];\r\nexp=4.8168001;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 8400 ];\r\nexp=33.0792168;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[272 51 ];\r\nexp=0.1935327;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[246 51 ];\r\nexp=0.2366048;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[209 71 ];\r\nexp=0.4563550;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[113 51 ];\r\nexp=1.1216128;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[58 11 ];\r\nexp=0.9181841;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[90 21 ];\r\nexp=0.7279469;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 5580 ];\r\nexp=18.7080845;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[26 1 ];\r\nexp=0.4153242;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 6020 ];\r\nexp=20.4792082;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[153 71 ];\r\nexp=0.8516442;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[231 71 ];\r\nexp=0.3735643;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[296 41 ];\r\nexp=0.1313774;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[218 51 ];\r\nexp=0.3012894;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[156 71 ];\r\nexp=0.8191945;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[244 91 ];\r\nexp=0.4291377;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[97 61 ];\r\nexp=1.8213680;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[33 21 ];\r\nexp=5.4466530;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[48 21 ];\r\nexp=2.5623281;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 5180 ];\r\nexp=17.1679811;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 3630 ];\r\nexp=11.6413032;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[164 81 ];\r\nexp=0.8456275;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[180 3306 ];\r\nexp=44.7534375;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[49 61 ];\r\nexp=7.2085690;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[89 21 ];\r\nexp=0.7444009;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 2110 ];\r\nexp=6.6413404;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[199 4040 ];\r\nexp=44.3892211;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[297 31 ];\r\nexp=0.0986662;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 5920 ];\r\nexp=20.0686784;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 7180 ];\r\nexp=25.7138602;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 5210 ];\r\nexp=17.2814667;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[212 11 ];\r\nexp=0.0687132;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[246 1 ];\r\nexp=0.0046393;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[250 11 ];\r\nexp=0.0494119;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[47 1 ];\r\nexp=0.1270938;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[112 41 ];\r\nexp=0.9177847;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 5110 ];\r\nexp=16.9043649;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 6410 ];\r\nexp=22.1324926;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 7030 ];\r\nexp=24.9752527;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 7970 ];\r\nexp=30.1045540;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[255 1 ];\r\nexp=0.0043176;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[222 5028 ];\r\nexp=44.4345459;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[247 61 ];\r\nexp=0.2807124;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[40 163 ];\r\nexp=43.3665978;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[88 21 ];\r\nexp=0.7614192;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[91 51 ];\r\nexp=1.7300957;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[145 21 ];\r\nexp=0.2804200;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[170 61 ];\r\nexp=0.5926273;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[95 11 ];\r\nexp=0.3421957;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[137 1 ];\r\nexp=0.0149581;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[220 51 ];\r\nexp=0.2958362;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[132 51 ];\r\nexp=0.8218652;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 6850 ];\r\nexp=24.1177523;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[271 61 ];\r\nexp=0.2331926;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[184 31 ];\r\nexp=0.2570695;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 3250 ];\r\nexp=10.3626812;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[11 1 ];\r\nexp=2.3227865;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[148 81 ];\r\nexp=1.0384257;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 5400 ];\r\nexp=18.0076051;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[287 31 ];\r\nexp=0.1056617;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[183 11 ];\r\nexp=0.0922168;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[278 81 ];\r\nexp=0.2942536;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[291 1 ];\r\nexp=0.0033154;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[64 71 ];\r\nexp=4.8902189;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[290 61 ];\r\nexp=0.2036368;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[124 51 ];\r\nexp=0.9313695;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[230 21 ];\r\nexp=0.1114509;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[109 51 ];\r\nexp=1.2054913;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[84 91 ];\r\nexp=3.6304847;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[289 81 ];\r\nexp=0.2722793;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[138 1 ];\r\nexp=0.0147421;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[130 91 ];\r\nexp=1.5124296;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[182 21 ];\r\nexp=0.1779910;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 8780 ];\r\nexp=36.4745305","published":true,"deleted":false,"likes_count":3,"comments_count":3,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":20,"test_suite_updated_at":"2014-02-10T18:16:06.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2013-09-15T23:22:36.000Z","updated_at":"2014-02-10T18:22:50.000Z","published_at":"2013-09-15T23:34:41.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis Challenge is derived from\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://code.google.com/codejam/contest/2933486/dashboard#s=p1\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eGJam 2013 China Captain Hammer\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. The problem is modified to fit within Cody dimensions.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe Challenge is to return the lower angle of a cannon given a target distance and an initial cannonball velocity. Gravity is a constant at 9.8m/sec^2, A valid solution is assured. (Error tolerance 2e-6).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e [v d] Velocity and Distance in meters.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e theta in units of degrees with an accuracy of 2e-6\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCompetition Summary:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Best Time of 8 minutes, 755/1070 completed\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe winner completed all three GJam China Challenges in 26 minutes with second at 43 minutes.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":2083,"title":"Independent direction vectors of a plane","description":"Given the equation of a plan of the form ax+by+cz=d, return 2 independent direction vectors which could e.g. be used to determine a parametric equation.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 21px; transform-origin: 407px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 379px 8px; transform-origin: 379px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven the equation of a plan of the form ax+by+cz=d, return 2 independent direction vectors which could e.g. be used to determine a parametric equation.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [v1,v2] = directionvectors(a,b,c,d)\r\n  y = x;\r\nend","test_suite":"%%\r\na=1;\r\nb=1;\r\nc=1;\r\nd=1234;\r\n[v1,v2] = directionvectors(a,b,c,d);\r\n\r\nassert(abs(sum([a b c].*(v1+[0 0 d/c]))-d)\u003c1e-4);\r\nassert(abs(sum([a b c].*(v2+[0 0 d/c]))-d)\u003c1e-4);\r\nassert(dot(v1,v2)~=0);\r\n\r\n%%\r\na=0;\r\nb=5;\r\nc=7;\r\nd=1234;\r\n[v1,v2] = directionvectors(a,b,c,d);\r\n\r\nassert(abs(sum([a b c].*(v1+[0 0 d/c]))-d)\u003c1e-4);\r\nassert(abs(sum([a b c].*(v2+[0 0 d/c]))-d)\u003c1e-4);\r\nassert(dot(v1,v2)~=0);\r\n\r\n%%\r\na=0;\r\nb=randi(10);\r\nc=-randi(10);\r\nd=randi(100);\r\n[v1,v2] = directionvectors(a,b,c,d);\r\n\r\nassert(abs(sum([a b c].*(v1+[0 0 d/c]))-d)\u003c1e-4);\r\nassert(abs(sum([a b c].*(v2+[0 0 d/c]))-d)\u003c1e-4);\r\nassert(dot(v1,v2)~=0);\r\n\r\n%%\r\na=0;\r\nb=0;\r\nc=randi(100)-50;\r\nd=0;\r\n[v1,v2] = directionvectors(a,b,c,d);\r\n\r\nassert(abs(sum([a b c].*(v1+[0 0 d/c]))-d)\u003c1e-4);\r\nassert(abs(sum([a b c].*(v2+[0 0 d/c]))-d)\u003c1e-4);\r\nassert(dot(v1,v2)~=0);","published":true,"deleted":false,"likes_count":0,"comments_count":9,"created_by":20079,"edited_by":223089,"edited_at":"2023-02-26T20:11:42.000Z","deleted_by":null,"deleted_at":null,"solvers_count":19,"test_suite_updated_at":"2023-02-26T20:11:42.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2013-12-29T12:54:54.000Z","updated_at":"2024-11-11T02:43:11.000Z","published_at":"2013-12-29T13:08:35.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven the equation of a plan of the form ax+by+cz=d, return 2 independent direction vectors which could e.g. be used to determine a parametric equation.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":43025,"title":"Check if a directory is on the current MATLAB search path","description":"Given a directory name as a string, return true if the directory is on the current MATLAB search path, and false otherwise.","description_html":"\u003cp\u003eGiven a directory name as a string, return true if the directory is on the current MATLAB search path, and false otherwise.\u003c/p\u003e","function_template":"function tf = isonpath(str)\r\n    tf = 0;\r\nend","test_suite":"%%\r\nstr = '/opt/mlsedu/matlab/R2016b/toolbox/matlab/mss/mlt_rmt_tmw/scoring-engine';\r\nassert(isequal(isonpath(str),true))\r\n\r\n%%\r\nstr = '/opt/mlsedu/matlab/R2016b/toolbox/matlab/testframework/parallel';\r\nassert(isequal(isonpath(str),true))\r\n\r\n%%\r\nstr = '/opt/mlsedu/matlab/R2016b/toolbox/shared/imageslib';\r\nassert(isequal(isonpath(str),true))\r\n\r\n%%\r\nstr = '/opt/mlsedu/matlab/R2016b/help/toolbox/vision/examples';\r\nassert(isequal(isonpath(str),true))\r\n\r\n%%\r\nstr = '/opt/mlsedu/matlab/R2016b/toolbox/shared/bigdata';\r\nassert(isequal(isonpath(str),true))\r\n\r\n%%\r\nstr = '/opt/mlsedu/matlab/R2016b/toolbox/matlab/demos';\r\nassert(isequal(isonpath(str),true))\r\n\r\n%%\r\nstr = '/opt/mlsedu/matlab/R2016b/toolbox/matlab/funfun';\r\nassert(isequal(isonpath(str),true))\r\n\r\n%%\r\nstr = '/opt/mlsedu/matlab/R2016b/toolbox/matlab/system';\r\nassert(isequal(isonpath(str),true))\r\n\r\n%%\r\nstr = '/opt/mlsedu/matlab/R2016b/toolbox/shared/simulink';\r\nassert(isequal(isonpath(str),true))\r\n\r\n%%\r\nstr = '';\r\nassert(isequal(isonpath(str),false))\r\n\r\n%%\r\nstr = '/opt/';\r\nassert(isequal(isonpath(str),false))\r\n\r\n%%\r\nstr = 'matlab';\r\nassert(isequal(isonpath(str),false))\r\n\r\n%%\r\nstr = '/matlab/R2016b/toolbox';\r\nassert(isequal(isonpath(str),false))\r\n\r\n%%\r\nstr = 'not a directory';\r\nassert(isequal(isonpath(str),false))\r\n\r\n%%\r\nstr = '/opt/mlsedu/matlab/R2016b/toolbox/matlab/timefun/fakedirectory';\r\nassert(isequal(isonpath(str),false))\r\n\r\n%%\r\nstr = 'blah/blah/blah';\r\nassert(isequal(isonpath(str),false))\r\n\r\n%%\r\nstr = 'C:\\Program Files\\MATLAB\\R2016a\\toolbox\\matlab\\datafun';\r\nassert(isequal(isonpath(str),false))\r\n\r\n%%\r\nstr = [];\r\nassert(isequal(isonpath(str),false))\r\n\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":3,"created_by":4793,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":15,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2016-10-04T20:08:03.000Z","updated_at":"2024-11-13T11:24:47.000Z","published_at":"2016-10-04T20:08:03.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a directory name as a string, return true if the directory is on the current MATLAB search path, and false otherwise.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44074,"title":"GJam 2017 Kickstart: Parentheses (Small)","description":"This Challenge is derived from \u003chttp://code.google.com/codejam/contest/6304486/dashboard#s=p2 GJam 2017 Kickstart Parentheses\u003e. This is the first 100 small cases with max L+R\u003c=20.\r\n\r\n\u003chttp://code.google.com/codejam Google Code Jam 2017 Qualifier\u003e is March 7, 2017. Typically four challenges with small and large aspects with 27 hours to complete.\r\n\r\nThe GJam story is given L left and R right parentheses determine the maximum number of parentheses pairings.\r\n\r\n*Input:* [L,R], the quantity of parentheses types\r\n\r\n*Output:* [V], the maximum number of parentheses pairings\r\n\r\n*Examples:* [L,R] [V]; [3,2] [3]\r\n\r\nFor the case ()()(, for example, the three balanced groups are () from indexes 1 to 2, () from indexes 3 to 4, and ()() from indexes 1 to 4.\r\n\r\n*Theory:* Brute force permutations and counting will not succeed in a timely manner for L+R=20. Determining the inherent mathematical pattern is usually the best way to succeed in GJam.   \u003chttp://code.google.com/codejam/contest/6304486/scoreboard#vf=1 GJam Kickstart solutions(C++,Python)\u003e. ","description_html":"\u003cp\u003eThis Challenge is derived from \u003ca href = \"http://code.google.com/codejam/contest/6304486/dashboard#s=p2\"\u003eGJam 2017 Kickstart Parentheses\u003c/a\u003e. This is the first 100 small cases with max L+R\u0026lt;=20.\u003c/p\u003e\u003cp\u003e\u003ca href = \"http://code.google.com/codejam\"\u003eGoogle Code Jam 2017 Qualifier\u003c/a\u003e is March 7, 2017. Typically four challenges with small and large aspects with 27 hours to complete.\u003c/p\u003e\u003cp\u003eThe GJam story is given L left and R right parentheses determine the maximum number of parentheses pairings.\u003c/p\u003e\u003cp\u003e\u003cb\u003eInput:\u003c/b\u003e [L,R], the quantity of parentheses types\u003c/p\u003e\u003cp\u003e\u003cb\u003eOutput:\u003c/b\u003e [V], the maximum number of parentheses pairings\u003c/p\u003e\u003cp\u003e\u003cb\u003eExamples:\u003c/b\u003e [L,R] [V]; [3,2] [3]\u003c/p\u003e\u003cp\u003eFor the case ()()(, for example, the three balanced groups are () from indexes 1 to 2, () from indexes 3 to 4, and ()() from indexes 1 to 4.\u003c/p\u003e\u003cp\u003e\u003cb\u003eTheory:\u003c/b\u003e Brute force permutations and counting will not succeed in a timely manner for L+R=20. Determining the inherent mathematical pattern is usually the best way to succeed in GJam.   \u003ca href = \"http://code.google.com/codejam/contest/6304486/scoreboard#vf=1\"\u003eGJam Kickstart solutions(C++,Python)\u003c/a\u003e.\u003c/p\u003e","function_template":"function val=parenc(L,R)\r\n% L number of Left parentheses, R number of Right parentheses \r\n% Determine maxinum number of parenthese pairings\r\n% http://code.google.com/codejam/contest/6304486/dashboard#s=p2\r\n\r\nval=0;\r\n \r\nend","test_suite":"%%\r\nv=parenc(19,1);\r\nassert(~isempty(v))\r\nassert(v==1)\r\n%%\r\nv=parenc(14,4);\r\nassert(~isempty(v))\r\nassert(v==10)\r\n%%\r\nv=parenc(4,15);\r\nassert(~isempty(v))\r\nassert(v==10)\r\n%%\r\nv=parenc(8,6);\r\nassert(~isempty(v))\r\nassert(v==21)\r\n%%\r\nv=parenc(14,1);\r\nassert(~isempty(v))\r\nassert(v==1)\r\n%%\r\nv=parenc(10,2);\r\nassert(~isempty(v))\r\nassert(v==3)\r\n%%\r\nv=parenc(10,10);\r\nassert(~isempty(v))\r\nassert(v==55)\r\n%%\r\nv=parenc(3,7);\r\nassert(~isempty(v))\r\nassert(v==6)\r\n%%\r\nv=parenc(3,13);\r\nassert(~isempty(v))\r\nassert(v==6)\r\n%%\r\nv=parenc(4,12);\r\nassert(~isempty(v))\r\nassert(v==10)\r\n%%\r\nv=parenc(2,2);\r\nassert(~isempty(v))\r\nassert(v==3)\r\n%%\r\nv=parenc(6,11);\r\nassert(~isempty(v))\r\nassert(v==21)\r\n%%\r\nv=parenc(4,12);\r\nassert(~isempty(v))\r\nassert(v==10)\r\n%%\r\nv=parenc(15,5);\r\nassert(~isempty(v))\r\nassert(v==15)\r\n%%\r\nv=parenc(14,3);\r\nassert(~isempty(v))\r\nassert(v==6)\r\n%%\r\nv=parenc(20,0);\r\nassert(~isempty(v))\r\nassert(v==0)\r\n%%\r\nv=parenc(12,3);\r\nassert(~isempty(v))\r\nassert(v==6)\r\n%%\r\nv=parenc(0,10);\r\nassert(~isempty(v))\r\nassert(v==0)\r\n%%\r\nv=parenc(18,2);\r\nassert(~isempty(v))\r\nassert(v==3)\r\n%%\r\nv=parenc(16,4);\r\nassert(~isempty(v))\r\nassert(v==10)\r\n%%\r\nv=parenc(3,12);\r\nassert(~isempty(v))\r\nassert(v==6)\r\n%%\r\nv=parenc(8,12);\r\nassert(~isempty(v))\r\nassert(v==36)\r\n%%\r\nv=parenc(8,6);\r\nassert(~isempty(v))\r\nassert(v==21)\r\n%%\r\nv=parenc(1,8);\r\nassert(~isempty(v))\r\nassert(v==1)\r\n%%\r\nv=parenc(7,13);\r\nassert(~isempty(v))\r\nassert(v==28)\r\n%%\r\nv=parenc(7,6);\r\nassert(~isempty(v))\r\nassert(v==21)\r\n%%\r\nv=parenc(11,8);\r\nassert(~isempty(v))\r\nassert(v==36)\r\n%%\r\nv=parenc(17,1);\r\nassert(~isempty(v))\r\nassert(v==1)\r\n%%\r\nv=parenc(4,2);\r\nassert(~isempty(v))\r\nassert(v==3)\r\n%%\r\nv=parenc(1,6);\r\nassert(~isempty(v))\r\nassert(v==1)\r\n%%\r\nv=parenc(5,4);\r\nassert(~isempty(v))\r\nassert(v==10)\r\n%%\r\nv=parenc(1,1);\r\nassert(~isempty(v))\r\nassert(v==1)\r\n%%\r\nv=parenc(7,13);\r\nassert(~isempty(v))\r\nassert(v==28)\r\n%%\r\nv=parenc(6,12);\r\nassert(~isempty(v))\r\nassert(v==21)\r\n%%\r\nv=parenc(15,2);\r\nassert(~isempty(v))\r\nassert(v==3)\r\n%%\r\nv=parenc(14,2);\r\nassert(~isempty(v))\r\nassert(v==3)\r\n%%\r\nv=parenc(12,1);\r\nassert(~isempty(v))\r\nassert(v==1)\r\n%%\r\nv=parenc(4,15);\r\nassert(~isempty(v))\r\nassert(v==10)\r\n%%\r\nv=parenc(12,7);\r\nassert(~isempty(v))\r\nassert(v==28)\r\n%%\r\nv=parenc(5,1);\r\nassert(~isempty(v))\r\nassert(v==1)\r\n%%\r\nv=parenc(19,1);\r\nassert(~isempty(v))\r\nassert(v==1)\r\n%%\r\nv=parenc(6,5);\r\nassert(~isempty(v))\r\nassert(v==15)\r\n%%\r\nv=parenc(11,5);\r\nassert(~isempty(v))\r\nassert(v==15)\r\n%%\r\nv=parenc(8,12);\r\nassert(~isempty(v))\r\nassert(v==36)\r\n%%\r\nv=parenc(18,2);\r\nassert(~isempty(v))\r\nassert(v==3)\r\n%%\r\nv=parenc(18,1);\r\nassert(~isempty(v))\r\nassert(v==1)\r\n%%\r\nv=parenc(13,4);\r\nassert(~isempty(v))\r\nassert(v==10)\r\n%%\r\nv=parenc(3,6);\r\nassert(~isempty(v))\r\nassert(v==6)\r\n%%\r\nv=parenc(6,1);\r\nassert(~isempty(v))\r\nassert(v==1)\r\n%%\r\nv=parenc(3,3);\r\nassert(~isempty(v))\r\nassert(v==6)\r\n%%\r\nv=parenc(19,1);\r\nassert(~isempty(v))\r\nassert(v==1)\r\n%%\r\nv=parenc(9,11);\r\nassert(~isempty(v))\r\nassert(v==45)\r\n%%\r\nv=parenc(10,1);\r\nassert(~isempty(v))\r\nassert(v==1)\r\n%%\r\nv=parenc(0,11);\r\nassert(~isempty(v))\r\nassert(v==0)\r\n%%\r\nv=parenc(11,3);\r\nassert(~isempty(v))\r\nassert(v==6)\r\n%%\r\nv=parenc(3,2);\r\nassert(~isempty(v))\r\nassert(v==3)\r\n%%\r\nv=parenc(18,2);\r\nassert(~isempty(v))\r\nassert(v==3)\r\n%%\r\nv=parenc(1,0);\r\nassert(~isempty(v))\r\nassert(v==0)\r\n%%\r\nv=parenc(9,1);\r\nassert(~isempty(v))\r\nassert(v==1)\r\n%%\r\nv=parenc(1,19);\r\nassert(~isempty(v))\r\nassert(v==1)\r\n%%\r\nv=parenc(4,3);\r\nassert(~isempty(v))\r\nassert(v==6)\r\n%%\r\nv=parenc(13,7);\r\nassert(~isempty(v))\r\nassert(v==28)\r\n%%\r\nv=parenc(8,6);\r\nassert(~isempty(v))\r\nassert(v==21)\r\n%%\r\nv=parenc(7,1);\r\nassert(~isempty(v))\r\nassert(v==1)\r\n%%\r\nv=parenc(16,2);\r\nassert(~isempty(v))\r\nassert(v==3)\r\n%%\r\nv=parenc(16,4);\r\nassert(~isempty(v))\r\nassert(v==10)\r\n%%\r\nv=parenc(7,8);\r\nassert(~isempty(v))\r\nassert(v==28)\r\n%%\r\nv=parenc(13,3);\r\nassert(~isempty(v))\r\nassert(v==6)\r\n%%\r\nv=parenc(4,14);\r\nassert(~isempty(v))\r\nassert(v==10)\r\n%%\r\nv=parenc(7,8);\r\nassert(~isempty(v))\r\nassert(v==28)\r\n%%\r\nv=parenc(9,5);\r\nassert(~isempty(v))\r\nassert(v==15)\r\n%%\r\nv=parenc(4,7);\r\nassert(~isempty(v))\r\nassert(v==10)\r\n%%\r\nv=parenc(12,2);\r\nassert(~isempty(v))\r\nassert(v==3)\r\n%%\r\nv=parenc(10,1);\r\nassert(~isempty(v))\r\nassert(v==1)\r\n%%\r\nv=parenc(17,3);\r\nassert(~isempty(v))\r\nassert(v==6)\r\n%%\r\nv=parenc(4,13);\r\nassert(~isempty(v))\r\nassert(v==10)\r\n%%\r\nv=parenc(11,1);\r\nassert(~isempty(v))\r\nassert(v==1)\r\n%%\r\nv=parenc(10,5);\r\nassert(~isempty(v))\r\nassert(v==15)\r\n%%\r\nv=parenc(7,7);\r\nassert(~isempty(v))\r\nassert(v==28)\r\n%%\r\nv=parenc(6,4);\r\nassert(~isempty(v))\r\nassert(v==10)\r\n%%\r\nv=parenc(5,13);\r\nassert(~isempty(v))\r\nassert(v==15)\r\n%%\r\nv=parenc(10,10);\r\nassert(~isempty(v))\r\nassert(v==55)\r\n%%\r\nv=parenc(14,3);\r\nassert(~isempty(v))\r\nassert(v==6)\r\n%%\r\nv=parenc(8,4);\r\nassert(~isempty(v))\r\nassert(v==10)\r\n%%\r\nv=parenc(14,5);\r\nassert(~isempty(v))\r\nassert(v==15)\r\n%%\r\nv=parenc(0,20);\r\nassert(~isempty(v))\r\nassert(v==0)\r\n%%\r\nv=parenc(0,1);\r\nassert(~isempty(v))\r\nassert(v==0)\r\n%%\r\nv=parenc(1,10);\r\nassert(~isempty(v))\r\nassert(v==1)\r\n%%\r\nv=parenc(13,3);\r\nassert(~isempty(v))\r\nassert(v==6)\r\n%%\r\nv=parenc(0,9);\r\nassert(~isempty(v))\r\nassert(v==0)\r\n%%\r\nv=parenc(1,17);\r\nassert(~isempty(v))\r\nassert(v==1)\r\n%%\r\nv=parenc(0,2);\r\nassert(~isempty(v))\r\nassert(v==0)\r\n%%\r\nv=parenc(2,0);\r\nassert(~isempty(v))\r\nassert(v==0)\r\n%%\r\nv=parenc(4,12);\r\nassert(~isempty(v))\r\nassert(v==10)\r\n%%\r\nv=parenc(11,9);\r\nassert(~isempty(v))\r\nassert(v==45)\r\n%%\r\nv=parenc(18,2);\r\nassert(~isempty(v))\r\nassert(v==3)\r\n%%\r\nv=parenc(15,3);\r\nassert(~isempty(v))\r\nassert(v==6)\r\n%%\r\nv=parenc(16,2);\r\nassert(~isempty(v))\r\nassert(v==3)\r\n%%\r\nv=parenc(17,2);\r\nassert(~isempty(v))\r\nassert(v==3)\r\n%%\r\nv=parenc(14,5);\r\nassert(~isempty(v))\r\nassert(v==15)\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":3,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":18,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2017-02-25T21:52:46.000Z","updated_at":"2017-02-25T22:07:38.000Z","published_at":"2017-02-25T22:07:38.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis Challenge is derived from\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://code.google.com/codejam/contest/6304486/dashboard#s=p2\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eGJam 2017 Kickstart Parentheses\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. This is the first 100 small cases with max L+R\u0026lt;=20.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"http://code.google.com/codejam\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eGoogle Code Jam 2017 Qualifier\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e is March 7, 2017. Typically four challenges with small and large aspects with 27 hours to complete.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe GJam story is given L left and R right parentheses determine the maximum number of parentheses pairings.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e [L,R], the quantity of parentheses types\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e [V], the maximum number of parentheses pairings\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExamples:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e [L,R] [V]; [3,2] [3]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor the case ()()(, for example, the three balanced groups are () from indexes 1 to 2, () from indexes 3 to 4, and ()() from indexes 1 to 4.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eTheory:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Brute force permutations and counting will not succeed in a timely manner for L+R=20. Determining the inherent mathematical pattern is usually the best way to succeed in GJam. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://code.google.com/codejam/contest/6304486/scoreboard#vf=1\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eGJam Kickstart solutions(C++,Python)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44075,"title":"GJam 2017 Kickstart: Parentheses (Large)","description":"This Challenge is derived from \u003chttp://code.google.com/codejam/contest/6304486/dashboard#s=p2 GJam 2017 Kickstart Parentheses\u003e. This is the first 100 large cases with  1\u003c=L+R\u003c=10^5.\r\n\r\n\u003chttp://code.google.com/codejam Google Code Jam 2017 Qualifier\u003e is March 7, 2017. Typically four challenges with small and large aspects with 27 hours to complete.\r\n\r\nThe GJam story is given L left and R right parentheses determine the maximum number of parentheses pairings.\r\n\r\n*Input:* [L,R], the quantity of parentheses types\r\n\r\n*Output:* [V], the maximum number of parentheses pairings\r\n\r\n*Examples:* [L,R] [V]; [3,2] [3]\r\n\r\nFor the case ()()(, for example, the three balanced groups are () from indexes 1 to 2, () from indexes 3 to 4, and ()() from indexes 1 to 4.\r\n\r\n*Theory:* Brute force permutations and counting will not succeed in a timely manner for L+R=10^5. Determining the inherent mathematical pattern is usually the best way to succeed in GJam.   \u003chttp://code.google.com/codejam/contest/6304486/scoreboard#vf=1 GJam Kickstart solutions(C++,Python)\u003e. ","description_html":"\u003cp\u003eThis Challenge is derived from \u003ca href = \"http://code.google.com/codejam/contest/6304486/dashboard#s=p2\"\u003eGJam 2017 Kickstart Parentheses\u003c/a\u003e. This is the first 100 large cases with  1\u0026lt;=L+R\u0026lt;=10^5.\u003c/p\u003e\u003cp\u003e\u003ca href = \"http://code.google.com/codejam\"\u003eGoogle Code Jam 2017 Qualifier\u003c/a\u003e is March 7, 2017. Typically four challenges with small and large aspects with 27 hours to complete.\u003c/p\u003e\u003cp\u003eThe GJam story is given L left and R right parentheses determine the maximum number of parentheses pairings.\u003c/p\u003e\u003cp\u003e\u003cb\u003eInput:\u003c/b\u003e [L,R], the quantity of parentheses types\u003c/p\u003e\u003cp\u003e\u003cb\u003eOutput:\u003c/b\u003e [V], the maximum number of parentheses pairings\u003c/p\u003e\u003cp\u003e\u003cb\u003eExamples:\u003c/b\u003e [L,R] [V]; [3,2] [3]\u003c/p\u003e\u003cp\u003eFor the case ()()(, for example, the three balanced groups are () from indexes 1 to 2, () from indexes 3 to 4, and ()() from indexes 1 to 4.\u003c/p\u003e\u003cp\u003e\u003cb\u003eTheory:\u003c/b\u003e Brute force permutations and counting will not succeed in a timely manner for L+R=10^5. Determining the inherent mathematical pattern is usually the best way to succeed in GJam.   \u003ca href = \"http://code.google.com/codejam/contest/6304486/scoreboard#vf=1\"\u003eGJam Kickstart solutions(C++,Python)\u003c/a\u003e.\u003c/p\u003e","function_template":"function val=parenc(L,R)\r\n% L number of Left parentheses, R number of Right parentheses \r\n% Determine maxinum number of parenthese pairings\r\n% http://code.google.com/codejam/contest/6304486/dashboard#s=p2\r\n\r\nval=0;\r\n \r\nend","test_suite":"%%\r\nv=parenc(36499,40104);\r\nassert(~isempty(v))\r\nassert(v==666106750)\r\n%%\r\nv=parenc(75814,21934);\r\nassert(~isempty(v))\r\nassert(v==240561145)\r\n%%\r\nv=parenc(88684,2943);\r\nassert(~isempty(v))\r\nassert(v==4332096)\r\n%%\r\nv=parenc(63688,19182);\r\nassert(~isempty(v))\r\nassert(v==183984153)\r\n%%\r\nv=parenc(71034,19757);\r\nassert(~isempty(v))\r\nassert(v==195179403)\r\n%%\r\nv=parenc(95210,572);\r\nassert(~isempty(v))\r\nassert(v==163878)\r\n%%\r\nv=parenc(50000,50000);\r\nassert(~isempty(v))\r\nassert(v==1250025000)\r\n%%\r\nv=parenc(37583,54023);\r\nassert(~isempty(v))\r\nassert(v==706259736)\r\n%%\r\nv=parenc(13403,50583);\r\nassert(~isempty(v))\r\nassert(v==89826906)\r\n%%\r\nv=parenc(74324,16176);\r\nassert(~isempty(v))\r\nassert(v==130839576)\r\n%%\r\nv=parenc(95662,20);\r\nassert(~isempty(v))\r\nassert(v==210)\r\n%%\r\nv=parenc(84426,8859);\r\nassert(~isempty(v))\r\nassert(v==39245370)\r\n%%\r\nv=parenc(1764,75732);\r\nassert(~isempty(v))\r\nassert(v==1556730)\r\n%%\r\nv=parenc(75135,17355);\r\nassert(~isempty(v))\r\nassert(v==150606690)\r\n%%\r\nv=parenc(16014,48995);\r\nassert(~isempty(v))\r\nassert(v==128232105)\r\n%%\r\nv=parenc(100000,0);\r\nassert(~isempty(v))\r\nassert(v==0)\r\n%%\r\nv=parenc(90812,5679);\r\nassert(~isempty(v))\r\nassert(v==16128360)\r\n%%\r\nv=parenc(55860,34690);\r\nassert(~isempty(v))\r\nassert(v==601715395)\r\n%%\r\nv=parenc(82678,16936);\r\nassert(~isempty(v))\r\nassert(v==143422516)\r\n%%\r\nv=parenc(50696,22228);\r\nassert(~isempty(v))\r\nassert(v==247053106)\r\n%%\r\nv=parenc(60183,19425);\r\nassert(~isempty(v))\r\nassert(v==188675025)\r\n%%\r\nv=parenc(88288,3180);\r\nassert(~isempty(v))\r\nassert(v==5057790)\r\n%%\r\nv=parenc(18628,32214);\r\nassert(~isempty(v))\r\nassert(v==173510506)\r\n%%\r\nv=parenc(99681,195);\r\nassert(~isempty(v))\r\nassert(v==19110)\r\n%%\r\nv=parenc(7,13);\r\nassert(~isempty(v))\r\nassert(v==28)\r\n%%\r\nv=parenc(62367,35577);\r\nassert(~isempty(v))\r\nassert(v==632879253)\r\n%%\r\nv=parenc(54171,29950);\r\nassert(~isempty(v))\r\nassert(v==448516225)\r\n%%\r\nv=parenc(22417,8626);\r\nassert(~isempty(v))\r\nassert(v==37208251)\r\n%%\r\nv=parenc(37824,9490);\r\nassert(~isempty(v))\r\nassert(v==45034795)\r\n%%\r\nv=parenc(95981,624);\r\nassert(~isempty(v))\r\nassert(v==195000)\r\n%%\r\nv=parenc(57025,7699);\r\nassert(~isempty(v))\r\nassert(v==29641150)\r\n%%\r\nv=parenc(1,1);\r\nassert(~isempty(v))\r\nassert(v==1)\r\n%%\r\nv=parenc(16007,35971);\r\nassert(~isempty(v))\r\nassert(v==128120028)\r\n%%\r\nv=parenc(2306,52078);\r\nassert(~isempty(v))\r\nassert(v==2659971)\r\n%%\r\nv=parenc(70555,4927);\r\nassert(~isempty(v))\r\nassert(v==12140128)\r\n%%\r\nv=parenc(19454,63092);\r\nassert(~isempty(v))\r\nassert(v==189238785)\r\n%%\r\nv=parenc(73352,18081);\r\nassert(~isempty(v))\r\nassert(v==163470321)\r\n%%\r\nv=parenc(71344,18591);\r\nassert(~isempty(v))\r\nassert(v==172821936)\r\n%%\r\nv=parenc(76452,13351);\r\nassert(~isempty(v))\r\nassert(v==89131276)\r\n%%\r\nv=parenc(88885,3106);\r\nassert(~isempty(v))\r\nassert(v==4825171)\r\n%%\r\nv=parenc(53619,9977);\r\nassert(~isempty(v))\r\nassert(v==49775253)\r\n%%\r\nv=parenc(39466,15681);\r\nassert(~isempty(v))\r\nassert(v==122954721)\r\n%%\r\nv=parenc(33791,51813);\r\nassert(~isempty(v))\r\nassert(v==570932736)\r\n%%\r\nv=parenc(40408,42624);\r\nassert(~isempty(v))\r\nassert(v==816423436)\r\n%%\r\nv=parenc(998,12);\r\nassert(~isempty(v))\r\nassert(v==78)\r\n%%\r\nv=parenc(58818,23613);\r\nassert(~isempty(v))\r\nassert(v==278798691)\r\n%%\r\nv=parenc(82533,6389);\r\nassert(~isempty(v))\r\nassert(v==20412855)\r\n%%\r\nv=parenc(73823,18704);\r\nassert(~isempty(v))\r\nassert(v==174929160)\r\n%%\r\nv=parenc(24046,69819);\r\nassert(~isempty(v))\r\nassert(v==289117081)\r\n%%\r\nv=parenc(83603,2337);\r\nassert(~isempty(v))\r\nassert(v==2731953)\r\n%%\r\nv=parenc(95719,1658);\r\nassert(~isempty(v))\r\nassert(v==1375311)\r\n%%\r\nv=parenc(9,11);\r\nassert(~isempty(v))\r\nassert(v==45)\r\n%%\r\nv=parenc(29910,7601);\r\nassert(~isempty(v))\r\nassert(v==28891401)\r\n%%\r\nv=parenc(59540,36291);\r\nassert(~isempty(v))\r\nassert(v==658536486)\r\n%%\r\nv=parenc(45871,53970);\r\nassert(~isempty(v))\r\nassert(v==1052097256)\r\n%%\r\nv=parenc(92763,325);\r\nassert(~isempty(v))\r\nassert(v==52975)\r\n%%\r\nv=parenc(9038,44798);\r\nassert(~isempty(v))\r\nassert(v==40847241)\r\n%%\r\nv=parenc(1,0);\r\nassert(~isempty(v))\r\nassert(v==0)\r\n%%\r\nv=parenc(86549,6287);\r\nassert(~isempty(v))\r\nassert(v==19766328)\r\n%%\r\nv=parenc(14401,46864);\r\nassert(~isempty(v))\r\nassert(v==103701601)\r\n%%\r\nv=parenc(93424,6259);\r\nassert(~isempty(v))\r\nassert(v==19590670)\r\n%%\r\nv=parenc(52933,31692);\r\nassert(~isempty(v))\r\nassert(v==502207278)\r\n%%\r\nv=parenc(91388,2050);\r\nassert(~isempty(v))\r\nassert(v==2102275)\r\n%%\r\nv=parenc(83487,14454);\r\nassert(~isempty(v))\r\nassert(v==104466285)\r\n%%\r\nv=parenc(26996,20778);\r\nassert(~isempty(v))\r\nassert(v==215873031)\r\n%%\r\nv=parenc(88436,1856);\r\nassert(~isempty(v))\r\nassert(v==1723296)\r\n%%\r\nv=parenc(52967,22634);\r\nassert(~isempty(v))\r\nassert(v==256160295)\r\n%%\r\nv=parenc(24373,71635);\r\nassert(~isempty(v))\r\nassert(v==297033751)\r\n%%\r\nv=parenc(25964,41310);\r\nassert(~isempty(v))\r\nassert(v==337077630)\r\n%%\r\nv=parenc(89807,7750);\r\nassert(~isempty(v))\r\nassert(v==30035125)\r\n%%\r\nv=parenc(84029,12987);\r\nassert(~isempty(v))\r\nassert(v==84337578)\r\n%%\r\nv=parenc(23884,41559);\r\nassert(~isempty(v))\r\nassert(v==285234670)\r\n%%\r\nv=parenc(96652,1790);\r\nassert(~isempty(v))\r\nassert(v==1602945)\r\n%%\r\nv=parenc(72470,2981);\r\nassert(~isempty(v))\r\nassert(v==4444671)\r\n%%\r\nv=parenc(51157,44196);\r\nassert(~isempty(v))\r\nassert(v==976665306)\r\n%%\r\nv=parenc(5964,125);\r\nassert(~isempty(v))\r\nassert(v==7875)\r\n%%\r\nv=parenc(5011,79606);\r\nassert(~isempty(v))\r\nassert(v==12557566)\r\n%%\r\nv=parenc(54850,32315);\r\nassert(~isempty(v))\r\nassert(v==522145770)\r\n%%\r\nv=parenc(94427,666);\r\nassert(~isempty(v))\r\nassert(v==222111)\r\n%%\r\nv=parenc(61766,28774);\r\nassert(~isempty(v))\r\nassert(v==413985925)\r\n%%\r\nv=parenc(90805,8083);\r\nassert(~isempty(v))\r\nassert(v==32671486)\r\n%%\r\nv=parenc(50250,34260);\r\nassert(~isempty(v))\r\nassert(v==586890930)\r\n%%\r\nv=parenc(59514,16501);\r\nassert(~isempty(v))\r\nassert(v==136149751)\r\n%%\r\nv=parenc(21448,21340);\r\nassert(~isempty(v))\r\nassert(v==227708470)\r\n%%\r\nv=parenc(48294,20183);\r\nassert(~isempty(v))\r\nassert(v==203686836)\r\n%%\r\nv=parenc(0,100000);\r\nassert(~isempty(v))\r\nassert(v==0)\r\n%%\r\nv=parenc(0,1);\r\nassert(~isempty(v))\r\nassert(v==0)\r\n%%\r\nv=parenc(9321,9795);\r\nassert(~isempty(v))\r\nassert(v==43445181)\r\n%%\r\nv=parenc(33373,207);\r\nassert(~isempty(v))\r\nassert(v==21528)\r\n%%\r\nv=parenc(78080,18989);\r\nassert(~isempty(v))\r\nassert(v==180300555)\r\n%%\r\nv=parenc(89341,7009);\r\nassert(~isempty(v))\r\nassert(v==24566545)\r\n%%\r\nv=parenc(0,2);\r\nassert(~isempty(v))\r\nassert(v==0)\r\n%%\r\nv=parenc(2,0);\r\nassert(~isempty(v))\r\nassert(v==0)\r\n%%\r\nv=parenc(90124,7716);\r\nassert(~isempty(v))\r\nassert(v==29772186)\r\n%%\r\nv=parenc(36611,12311);\r\nassert(~isempty(v))\r\nassert(v==75786516)\r\n%%\r\nv=parenc(45498,3564);\r\nassert(~isempty(v))\r\nassert(v==6352830)\r\n%%\r\nv=parenc(28355,23958);\r\nassert(~isempty(v))\r\nassert(v==287004861)\r\n%%\r\nv=parenc(58516,24422);\r\nassert(~isempty(v))\r\nassert(v==298229253)\r\n%%\r\nv=parenc(42157,56858);\r\nassert(~isempty(v))\r\nassert(v==888627403)\r\n%%\r\nv=parenc(32854,55517);\r\nassert(~isempty(v))\r\nassert(v==539709085)\r\n\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":17,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2017-02-25T22:17:05.000Z","updated_at":"2017-02-25T22:18:40.000Z","published_at":"2017-02-25T22:18:40.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis Challenge is derived from\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://code.google.com/codejam/contest/6304486/dashboard#s=p2\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eGJam 2017 Kickstart Parentheses\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. This is the first 100 large cases with 1\u0026lt;=L+R\u0026lt;=10^5.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"http://code.google.com/codejam\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eGoogle Code Jam 2017 Qualifier\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e is March 7, 2017. Typically four challenges with small and large aspects with 27 hours to complete.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe GJam story is given L left and R right parentheses determine the maximum number of parentheses pairings.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e [L,R], the quantity of parentheses types\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e [V], the maximum number of parentheses pairings\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExamples:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e [L,R] [V]; [3,2] [3]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor the case ()()(, for example, the three balanced groups are () from indexes 1 to 2, () from indexes 3 to 4, and ()() from indexes 1 to 4.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eTheory:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Brute force permutations and counting will not succeed in a timely manner for L+R=10^5. Determining the inherent mathematical pattern is usually the best way to succeed in GJam. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://code.google.com/codejam/contest/6304486/scoreboard#vf=1\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eGJam Kickstart solutions(C++,Python)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":739,"title":"Battleship_000 : (TM)  Classic Game - Easy computer bot","description":"The Classic Battleship(TM) game implemented between a computer bot and a player's bot.\r\n\r\n\u003chttp://en.wikipedia.org/wiki/Battleship_%28game%29 Battleship\u003e\r\n\r\nYou and your opponent have 9 ships of various sizes.\r\n\r\nThese Ships/Sizes/Qty are Carrier-5, Battleship-4, Submarine-3(qty 2), Cruiser-3(qty 2), Destroyer-2(qty 3).\r\n\r\nThe board is 10x10. (index 1-100)\r\nUnknown=0, Miss=1, Hit=2\r\n\r\n*The Play:*\r\n\r\nPlayer places his ships on the board. Ships may not overlap but may touch.\r\n\r\nShips array is [9,2] where 1 is the Carrier and 9 is a Destroyer. \r\n\r\n[start_idx, orientation; start_idx, orientation...]. An orientation of 0 is Down and a 1 is Right. \r\n\r\nShips[1 1;...] places the Carrier in cells [1 11 22 33 44]\r\n\r\nPlayer takes a shot on the board - idx 1:100.\r\n\r\nThe computer bot will take a shot if he has any ships remaining.\r\n\r\nThe player will see an updated board for his next shot if he has any ships remaining.\r\n\r\n*Pass: Win*\r\n\r\nBattleship_bot_000 randomly fires. \r\n\r\nThere is a Bernoulli probability question if this strategy could ever win against anything but another random bot.\r\n\r\n","description_html":"\u003cp\u003eThe Classic Battleship™ game implemented between a computer bot and a player's bot.\u003c/p\u003e\u003cp\u003e\u003ca href=\"http://en.wikipedia.org/wiki/Battleship_%28game%29\"\u003eBattleship\u003c/a\u003e\u003c/p\u003e\u003cp\u003eYou and your opponent have 9 ships of various sizes.\u003c/p\u003e\u003cp\u003eThese Ships/Sizes/Qty are Carrier-5, Battleship-4, Submarine-3(qty 2), Cruiser-3(qty 2), Destroyer-2(qty 3).\u003c/p\u003e\u003cp\u003eThe board is 10x10. (index 1-100)\r\nUnknown=0, Miss=1, Hit=2\u003c/p\u003e\u003cp\u003e\u003cb\u003eThe Play:\u003c/b\u003e\u003c/p\u003e\u003cp\u003ePlayer places his ships on the board. Ships may not overlap but may touch.\u003c/p\u003e\u003cp\u003eShips array is [9,2] where 1 is the Carrier and 9 is a Destroyer.\u003c/p\u003e\u003cp\u003e[start_idx, orientation; start_idx, orientation...]. An orientation of 0 is Down and a 1 is Right.\u003c/p\u003e\u003cp\u003eShips[1 1;...] places the Carrier in cells [1 11 22 33 44]\u003c/p\u003e\u003cp\u003ePlayer takes a shot on the board - idx 1:100.\u003c/p\u003e\u003cp\u003eThe computer bot will take a shot if he has any ships remaining.\u003c/p\u003e\u003cp\u003eThe player will see an updated board for his next shot if he has any ships remaining.\u003c/p\u003e\u003cp\u003e\u003cb\u003ePass: Win\u003c/b\u003e\u003c/p\u003e\u003cp\u003eBattleship_bot_000 randomly fires.\u003c/p\u003e\u003cp\u003eThere is a Bernoulli probability question if this strategy could ever win against anything but another random bot.\u003c/p\u003e","function_template":"function [mv,ships] = Battleship(b)\r\n % b is 10x10; idx 1:100\r\n % output mv is idx 1 thru 100\r\n % b: 0-open ocean; 1-miss shot, 2-Hit\r\n % ships: Placement of player ships\r\n % ships are initialized on first turn sum(b(:))==0\r\n % Place 9 ships [idx1 0/1;idx2 0/1;...idx9 0/1]\r\n % Ship lengths : 5/4/3/3/3/3/2/2/2\r\n % Ship orientation : 0-Vert Down; 1-Horiz Right \r\n % ships=[1 1;2 1;...8 1;99 0] \r\n % Places 8 ships on Left edge, one down in bottom rt corner\r\n % ships may not overlap - Loss\r\n \r\n% Need ships each call or will Lose; Ships placed only on first move\r\n  ships=[1 1;2 1;3 1;4 1;5 1;6 1;7 1;8 1;99 0]; \r\n \r\n % randomly pick an open spot (same as Battleship_bot_000)\r\n mv=randi(100);\r\n \r\nend % Battleship","test_suite":"%%\r\n%Test Suite\r\n%Battleship_000\r\n% Carrier/Battleship/Sub/Cruiser/Destroyer\r\n% 5/4/3/3/2  Qty 1/1/2/2/3\r\n% b 0- Unknown 1-Miss 2-Hit\r\nseed=clock;\r\nseed=1000*seed(6);\r\nrng(seed);\r\ngame_over=false;\r\nwins=0; % player wins\r\nbp=zeros(10);\r\nbc=zeros(10);\r\nships_p=ones(10);\r\nships_c=ones(10);\r\nship_vec=[5 4 3 3 3 3 2 2 2]; % Length of ships\r\n\r\ntic\r\n% initialize Computer Ships\r\nfor ship=1:9\r\n placed=false;\r\n while~placed\r\n  idx=randi(100);\r\n  [r c]=ind2sub([10 10],idx);\r\n  dwn_rt=randi(2)-1; % 0-down, 1-right\r\n  try % may go beyond board size\r\n   if dwn_rt==0 % down\r\n    blocked=any(ships_c(r:r+ship_vec(ship)-1,c)==2);\r\n   else % right\r\n    blocked=any(ships_c(r,c:c+ship_vec(ship)-1)==2);\r\n   end\r\n  catch\r\n   blocked=true; % invalid placement\r\n  end\r\n  if ~blocked % No ship conflict\r\n   if dwn_rt==0 % down\r\n    ships_c(r:r+ship_vec(ship)-1,c)=2;\r\n   else % right\r\n    ships_c(r,c:c+ship_vec(ship)-1)=2;\r\n   end\r\n   placed=true;\r\n  end \r\n end % placed\r\nend % ship\r\n \r\n% Initialize Player's ships and first move\r\n  try % for invalid mvP values\r\n   [mvP,ships]=Battleship(bp); % \r\n   bp(mvP(1))=ships_c(mvP(1));\r\n   \r\n    for ship=1:9\r\n      [r c]=ind2sub([10 10],ships(ship,1));\r\n      dwn_rt=ships(ship,2); \r\n      try % may go beyond board size\r\n       if dwn_rt==0 % down\r\n        blocked=any(ships_p(r:r+ship_vec(ship)-1,c)==2);\r\n       else % right\r\n        blocked=any(ships_p(r,c:c+ship_vec(ship)-1)==2);\r\n       end\r\n      catch\r\n       blocked=true; % invalid placement\r\n      end\r\n      if ~blocked % No ship conflict\r\n       if dwn_rt==0 % down\r\n        ships_p(r:r+ship_vec(ship)-1,c)=2;\r\n       else % right\r\n        ships_p(r,c:c+ship_vec(ship)-1)=2;\r\n       end\r\n      end \r\n    end % ship\r\n   \r\n   if sum(ships_p(:))~=127 % Expect 127 board if all placed\r\n    fprintf('Invalid Ship placement - Game over\\n');\r\n    ships\r\n    ships_p\r\n    game_over=true;\r\n   end\r\n   \r\n  catch\r\n   fprintf('Invalid first respone - Game over\\n');\r\n   mvP\r\n   ships\r\n   game_over=true;\r\n  end\r\n\r\n% Main Game Loop\r\n\r\n while ~game_over \r\n  % Computer move\r\n  % Author: Richard Z\r\n  % Battleship_000 bot: Random\r\n  mvC=randi(100);\r\n  % End Battleship_000 bot: Random\r\n  \r\n  bc(mvC)=ships_p(mvC); % Hit=2, Miss=1\r\n\r\n %figure(1);imagesc(bc,[-2 2]);axis equal;pause(0.1)  \r\n  if length(find(bc==2))\u003e=27 % Computer Wins\r\n   break;\r\n  end\r\n  \r\n  % Player's Second move and thereafter\r\n  try % for invalid mvP values\r\n   [mvP,ships]=Battleship(bp); % \r\n   bp(mvP(1))=ships_c(mvP(1)); % Hit=2, Miss=1\r\n  catch\r\n   fprintf('Ignoring Illegal move %i \\n',mvP(1));\r\n  end\r\n  \r\n %figure(2);imagesc(bp,[-2 2]);axis equal\r\n  if length(find(bp==2))\u003e=27 % All ships sunk\r\n   wins=1;\r\n   break;\r\n  end\r\n  \r\n end % While ~game_over\r\n\r\ntoc\r\n \r\n % Player must win to Pass\r\n assert(isequal(wins,1))\r\n%Pass=1;\r\n%assert(isequal(Pass,1));\r\n\r\n bc\r\n bp\r\n wins","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":16,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2012-06-04T03:25:36.000Z","updated_at":"2024-10-24T20:11:18.000Z","published_at":"2012-06-04T03:50:52.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe Classic Battleship™ game implemented between a computer bot and a player's bot.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/Battleship_%28game%29\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eBattleship\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou and your opponent have 9 ships of various sizes.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThese Ships/Sizes/Qty are Carrier-5, Battleship-4, Submarine-3(qty 2), Cruiser-3(qty 2), Destroyer-2(qty 3).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe board is 10x10. (index 1-100) Unknown=0, Miss=1, Hit=2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eThe Play:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePlayer places his ships on the board. Ships may not overlap but may touch.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eShips array is [9,2] where 1 is the Carrier and 9 is a Destroyer.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e[start_idx, orientation; start_idx, orientation...]. An orientation of 0 is Down and a 1 is Right.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eShips[1 1;...] places the Carrier in cells [1 11 22 33 44]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePlayer takes a shot on the board - idx 1:100.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe computer bot will take a shot if he has any ships remaining.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe player will see an updated board for his next shot if he has any ships remaining.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ePass: Win\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBattleship_bot_000 randomly fires.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThere is a Bernoulli probability question if this strategy could ever win against anything but another random bot.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":843,"title":"Hyperspectral Processing: Determine Material Components given a Hyperspectral vector","description":"Given a hyperspectral data set and Reflectance Spectral Signature Library determine a pixel's component percentages. \r\n\r\n\u003chttp://aviris.jpl.nasa.gov/aviris/index.html NASA AVIRIS\u003e\r\n\r\nA Ground Square is imaged by hundreds of pixels, each at a different wavelength.\r\nThe signal on pixel 1(500nm to 505nm) is a sum of the components (Concrete/Tree/Grass...) by percentage of area covered times the material reflectance.\r\nPixel 2 (510-515nm) is different by the Reflectance deltas between Concrete and a Tree.\r\n\r\nLet S(i,j) be the response of Material i for band j\r\n\r\ng( j )= %(Concrete)*S(1,j)+%(Tree)*S(2,j)+...%(Grass)*S(end,j);\r\n\r\nA 300-Band 9-Material Spectral file is loaded. Comparison between foliage and rocks is quite significant. The materials are Bush, Calcite, Concrete, Conifer, Grass (not that type), Fir tree, Gypsum, Maple, Sage\r\n\r\n*g=S*f*  where f is the percentage of the imaged pixel covered by the\r\nmaterial.\r\n\r\n*Input:* \r\ng spectral sum [301,1]; \r\nS spectral material response [301,9]  Nine materials\r\n\r\n*Output:*\r\nSolve for f  ....( eg f=[0 .5 0 .25 .25 0 0 0 0]' )\r\n\r\n( f should sum to 1, max(f) is 1 and min(f) is 0 )\r\n\r\nThe test Suite will round to 2 decimal places.\r\nCases of \"other materials\" which will induce negative values are not\r\ntested.\r\n\r\nThis is introductory and ignores atmospheric absorption.\r\n\r\nThere is a matrix operation hint in the test suite for a method to solve for f.\r\n\r\n\r\n\u003chttp://aviris.jpl.nasa.gov/data/free_data.html AVARIS Free Data\u003e\r\nThese data files are large with 224 bands x 750 channels x 2000 samples\r\n\r\nTo expand these files may require a tar converter\r\n\u003chttp://aviris.jpl.nasa.gov/alt_locator/111013_AV_Download.readme NASA readme\u003e\r\n...and... \r\n\u003chttp://aviris.jpl.nasa.gov/alt_gulf/ NASA Tools bottom Left\u003e\r\nThere are some possible issues with the NASA tar tool. Two non-standard files can be found at \u003chttp://dll-files.org/7968/index.html libiconv-2.dll\u003e and \u003chttp://dll-files.org/7975/libintl-2.dll.html libintl-2.dll\u003e\r\n\r\nSee the Test Suite for details on opening the AVIRIS Moffett Field file.","description_html":"\u003cp\u003eGiven a hyperspectral data set and Reflectance Spectral Signature Library determine a pixel's component percentages.\u003c/p\u003e\u003cp\u003e\u003ca href=\"http://aviris.jpl.nasa.gov/aviris/index.html\"\u003eNASA AVIRIS\u003c/a\u003e\u003c/p\u003e\u003cp\u003eA Ground Square is imaged by hundreds of pixels, each at a different wavelength.\r\nThe signal on pixel 1(500nm to 505nm) is a sum of the components (Concrete/Tree/Grass...) by percentage of area covered times the material reflectance.\r\nPixel 2 (510-515nm) is different by the Reflectance deltas between Concrete and a Tree.\u003c/p\u003e\u003cp\u003eLet S(i,j) be the response of Material i for band j\u003c/p\u003e\u003cp\u003eg( j )= %(Concrete)*S(1,j)+%(Tree)*S(2,j)+...%(Grass)*S(end,j);\u003c/p\u003e\u003cp\u003eA 300-Band 9-Material Spectral file is loaded. Comparison between foliage and rocks is quite significant. The materials are Bush, Calcite, Concrete, Conifer, Grass (not that type), Fir tree, Gypsum, Maple, Sage\u003c/p\u003e\u003cp\u003e\u003cb\u003eg=S*f\u003c/b\u003e  where f is the percentage of the imaged pixel covered by the\r\nmaterial.\u003c/p\u003e\u003cp\u003e\u003cb\u003eInput:\u003c/b\u003e \r\ng spectral sum [301,1]; \r\nS spectral material response [301,9]  Nine materials\u003c/p\u003e\u003cp\u003e\u003cb\u003eOutput:\u003c/b\u003e\r\nSolve for f  ....( eg f=[0 .5 0 .25 .25 0 0 0 0]' )\u003c/p\u003e\u003cp\u003e( f should sum to 1, max(f) is 1 and min(f) is 0 )\u003c/p\u003e\u003cp\u003eThe test Suite will round to 2 decimal places.\r\nCases of \"other materials\" which will induce negative values are not\r\ntested.\u003c/p\u003e\u003cp\u003eThis is introductory and ignores atmospheric absorption.\u003c/p\u003e\u003cp\u003eThere is a matrix operation hint in the test suite for a method to solve for f.\u003c/p\u003e\u003cp\u003e\u003ca href=\"http://aviris.jpl.nasa.gov/data/free_data.html\"\u003eAVARIS Free Data\u003c/a\u003e\r\nThese data files are large with 224 bands x 750 channels x 2000 samples\u003c/p\u003e\u003cp\u003eTo expand these files may require a tar converter \u003ca href=\"http://aviris.jpl.nasa.gov/alt_locator/111013_AV_Download.readme\"\u003eNASA readme\u003c/a\u003e\r\n...and...  \u003ca href=\"http://aviris.jpl.nasa.gov/alt_gulf/\"\u003eNASA Tools bottom Left\u003c/a\u003e\r\nThere are some possible issues with the NASA tar tool. Two non-standard files can be found at \u003ca href=\"http://dll-files.org/7968/index.html\"\u003elibiconv-2.dll\u003c/a\u003e and \u003ca href=\"http://dll-files.org/7975/libintl-2.dll.html\"\u003elibintl-2.dll\u003c/a\u003e\u003c/p\u003e\u003cp\u003eSee the Test Suite for details on opening the AVIRIS Moffett Field file.\u003c/p\u003e","function_template":"function f = hyperspectral(g,S)\r\n% g is [301,1]\r\n% S is [301,9]\r\n  f = zeros(size(S,2),1);\r\nend","test_suite":"%%\r\n% The AVIRIS fileread info is at the bottom\r\n% Solution Hint:\r\n% The Matrix hint is inv(S'S)(S'S)=I\r\n% With g=Sf multiply both sides by h'\r\n% S'g=S'Sf, now multiply both sides by inv(S'S)\r\n% inv(S'S)(S'g)=inv(S'S)(S'S)f which is I*f\r\n% Now simplify the right side and there is a solution\r\n% Solution Bigger/Better Hint: Search on mldivide\r\n%%\r\nglobal S\r\n%http://tinyurl.com/matlab-hyper-spectra\r\n%http://rmatlabtest.appspot.com/Spectra.mat\r\nurlwrite('http://rmatlabtest.appspot.com/Spectra.mat','Spectra.mat') ;\r\nload('Spectra.mat'); % S is the variable in Spectra.mat\r\nf_exp=[.5 .5 0 0 0 0 0 0 0 ]';\r\ng=S*f_exp;\r\n\r\nf = hyperspectral(g,S);\r\nassert(isequal(round(100*f)/100,f_exp),sprintf('%f\\n',f))\r\n%%\r\nglobal S\r\nf_exp=[0 .5 0.25 0 0 0 0.25 0 0 ]';\r\ng=S*f_exp;\r\nf = hyperspectral(g,S);\r\nassert(isequal(round(100*f)/100,f_exp),sprintf('%f\\n',f))\r\n%%\r\nglobal S\r\nf_exp=[0 .25 0.6 0 0 0 0 0.15 0 ]';\r\ng=S*f_exp;\r\nf = hyperspectral(g,S);\r\nassert(isequal(round(100*f)/100,f_exp),sprintf('%f\\n',f))\r\n%%\r\n%\r\n%Reading of the full Moffett Field file: (8GB RAM recommended)\r\n% The file is 600MB\r\n%cd 'C:\\Users\\???' % Your file location\r\n%fn='f080611t01p00r07rdn_c_sc01_ort_img'\r\n%fid = fopen (fn,'r');\r\n%A = int16(fread(fid, 'int16', 'ieee-be'));\r\n%A2 = reshape (A, 224,753,1924); % Specifics found in text files\r\n%A3 = permute (A2,[3 2 1]); % X Y Band\r\n%figure;imagesc(squeeze(A3(:,:,1))); % To view top layer\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":2,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":"2013-02-02T19:05:40.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-07-19T02:49:02.000Z","updated_at":"2013-02-02T19:05:40.000Z","published_at":"2012-07-19T03:34:29.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a hyperspectral data set and Reflectance Spectral Signature Library determine a pixel's component percentages.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"http://aviris.jpl.nasa.gov/aviris/index.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eNASA AVIRIS\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA Ground Square is imaged by hundreds of pixels, each at a different wavelength. The signal on pixel 1(500nm to 505nm) is a sum of the components (Concrete/Tree/Grass...) by percentage of area covered times the material reflectance. Pixel 2 (510-515nm) is different by the Reflectance deltas between Concrete and a Tree.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLet S(i,j) be the response of Material i for band j\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eg( j )= %(Concrete)*S(1,j)+%(Tree)*S(2,j)+...%(Grass)*S(end,j);\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA 300-Band 9-Material Spectral file is loaded. Comparison between foliage and rocks is quite significant. The materials are Bush, Calcite, Concrete, Conifer, Grass (not that type), Fir tree, Gypsum, Maple, Sage\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eg=S*f\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e where f is the percentage of the imaged pixel covered by the material.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e g spectral sum [301,1]; S spectral material response [301,9] Nine materials\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Solve for f ....( eg f=[0 .5 0 .25 .25 0 0 0 0]' )\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e( f should sum to 1, max(f) is 1 and min(f) is 0 )\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe test Suite will round to 2 decimal places. Cases of \\\"other materials\\\" which will induce negative values are not tested.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis is introductory and ignores atmospheric absorption.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThere is a matrix operation hint in the test suite for a method to solve for f.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"http://aviris.jpl.nasa.gov/data/free_data.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eAVARIS Free Data\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e These data files are large with 224 bands x 750 channels x 2000 samples\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTo expand these files may require a tar converter\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://aviris.jpl.nasa.gov/alt_locator/111013_AV_Download.readme\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eNASA readme\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e ...and... \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://aviris.jpl.nasa.gov/alt_gulf/\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eNASA Tools bottom Left\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e There are some possible issues with the NASA tar tool. Two non-standard files can be found at\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://dll-files.org/7968/index.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003elibiconv-2.dll\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://dll-files.org/7975/libintl-2.dll.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003elibintl-2.dll\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSee the Test Suite for details on opening the AVIRIS Moffett Field file.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":973,"title":"Partial pivoting for Gauss Elimination","description":"Write a function to implement partial pivoting for Gauss elimination, given the pivot element.","description_html":"\u003cp\u003eWrite a function to implement partial pivoting for Gauss elimination, given the pivot element.\u003c/p\u003e","function_template":"function Ab = PartialPivot(A,b,pivot)\r\n% A = m-by-n coefficient matrix\r\n% b = m-by-1 right-hand-side vector\r\n% pivot = pivot row and column\r\n% Ab = m-by-(n+1) Augmented matrix after pivot step\r\n  Ab = \r\nend","test_suite":"%%\r\nA = [0 2; 1 3];\r\nb = [4; 2];\r\nAb = [1 3 2; 0 2 4];\r\nassert(isequal(PartialPivot(A,b,1),Ab))\r\n%%\r\nA = [0 2 3; 4 6 7; 2, -3, 6];\r\nb = [8; -3; 5];\r\nAb = [A([2 1 3],:), b([2 1 3])];\r\nassert(isequal(PartialPivot(A,b,1),Ab))\r\n%%\r\nA = [4 6 7; 0 2 3; 0, -6, 5/2];\r\nb = [-3; 8; 13/2];\r\nAb = [A([1 3 2],:), b([1 3 2])];\r\nassert(isequal(PartialPivot(A,b,2),Ab))\r\n%%\r\nA = [0 2 5; 2 1 1; 3 1 0];\r\nb = [1; 1; 2];\r\nAb = [A([3 2 1],:), b([3 2 1])];\r\nassert(isequal(PartialPivot(A,b,1),Ab))\r\n%%\r\nA = eye(4);\r\nb = ones(4,1);\r\nassert(isequal(PartialPivot(A,b,3),[A,b]))","published":true,"deleted":false,"likes_count":2,"comments_count":4,"created_by":279,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":11,"test_suite_updated_at":"2012-10-10T03:30:19.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-10-08T00:42:34.000Z","updated_at":"2024-10-27T09:13:34.000Z","published_at":"2012-10-08T01:51:50.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to implement partial pivoting for Gauss elimination, given the pivot element.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":52839,"title":"Easy Sequences 33: Web Trapped Ant","description":"An ant is trapped on a spider web inside a can with open top. The can has a radius  and height . A spider sitting on the outside face of the can, sensed the trapped ant and started crawling towards it. The relative positions of the ant and spider are shown in the figure below.\r\n                         \r\n is the initial distance of the spider from the from the bottom of the can,  is the distance of the ant from the top of the can, and  and , are the y-offsets of the spider and ant, respectively, from the center of the circular top.\r\nIf the spider moves at a constant crawling speed, calculate the total length of the path to reach the ant at the quickest possible time. Please round-off your answer to the nearest four decimal places.\r\nCLARIFICATIONS: \r\nIt is understood there can be 2 possible positions, given a single y-offset. In this exercise please consider only the position as drawn above. That means at the top view, the ant and the spidert shall only be within the first and third quadrant, respectively.\r\nThe dotted lines is not the spider's path. They are used only to project the heights to the side.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440000534057617px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 609px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eAn \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003eant is\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e trapped on a spider web \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003einside\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e a can with open top. The can has a radius \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);\"\u003eR\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e and height \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);\"\u003eH\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e. A \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003espider sitting\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e on the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003eoutside\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e face of the can, sensed the trapped ant and started crawling towards it. The relative positions of the ant and spider are shown in the figure below.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 315px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e                         \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"551\" height=\"309\" style=\"vertical-align: baseline;width: 551px;height: 309px\" 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src=\"data:image/png;base64,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\" width=\"18\" height=\"18\" style=\"width: 18px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e is the distance of the ant from the top of the can, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"16.5\" height=\"18\" style=\"width: 16.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"18\" height=\"18\" style=\"width: 18px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e, are the y-offsets of the spider and ant, respectively, from the center of the circular top.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eIf the spider moves at a constant crawling speed, calculate the total length of the path to reach the ant at the quickest possible time. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003ePlease round-off your answer to the nearest four decimal places.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eCLARIFICATIONS: \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 80px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 60px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; text-align: left; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; \"\u003e\u003cspan style=\"\"\u003eIt is understood there can be 2 possible positions, given a single y-offset. In this exercise please consider only the position as drawn above. That means at the top view, the ant and the spidert shall only be within the first and third quadrant, respectively.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; text-align: left; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; \"\u003e\u003cspan style=\"\"\u003eThe dotted lines is not the spider's path. They are used only to project the heights to the side.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function s = spiderPath(H,R,hs,ha,xs,xa)\r\n    y = x;\r\nend","test_suite":"%%\r\nH = 10; R = 5; hs = 1; ha = 1; xs = 1; xa = 1;\r\ns_correct = 18.6210;\r\nassert(isequal(spiderPath(H,R,hs,ha,xs,xa),s_correct))\r\n%%\r\nH = 5; R = 2; hs = 0.3; ha = 0.4; xs = 0.5; xa = 0.6;\r\ns_correct = 8.0120;\r\nassert(isequal(spiderPath(H,R,hs,ha,xs,xa),s_correct))\r\n%%\r\nH = 15.5; R = 5.5; hs = 3; ha = 2.5; xs = 1.5; xa = 1;\r\ns_correct = 22.4960;\r\nassert(isequal(spiderPath(H,R,hs,ha,xs,xa),s_correct))\r\n%%\r\nH = 123; R = 123; hs = 12; ha = 25; xs = 30; xa = 40;\r\ns_correct = 399.8218;\r\nassert(isequal(spiderPath(H,R,hs,ha,xs,xa),s_correct))\r\n%%\r\nH = linspace(5,150,50); R = linspace(5,120,50); \r\nhs = linspace(0.5,10,50); ha = linspace(0.5,20,100); \r\nxs = linspace(0.4,12,50); xa = linspace(0.4,10,50);\r\ns = sum(arrayfun(@(i) spiderPath(H(i),R(i),hs(i),ha(i),xs(i),xa(i)),1:50));\r\ns_correct = 10509.4142;\r\nassert(isequal(s,s_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":8,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":"2021-10-02T18:43:11.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2021-09-30T07:18:49.000Z","updated_at":"2024-11-20T12:40:50.000Z","published_at":"2021-09-30T08:12:11.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAn \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eant is\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e trapped on a spider web \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einside\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e a can with open top. The can has a radius \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and height \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eH\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. A \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003espider sitting\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e on the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eoutside\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e face of the can, sensed the trapped ant and started crawling towards it. The relative positions of the ant and spider are shown in the figure below.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                         \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"309\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"551\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ehs\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the initial distance of the spider from the from the bottom of the can, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eha\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the distance of the ant from the top of the can, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003exs\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003exa\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, are the y-offsets of the spider and ant, respectively, from the center of the circular top.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eIf the spider moves at a constant crawling speed, calculate the total length of the path to reach the ant at the quickest possible time. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ePlease round-off your answer to the nearest four decimal places.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCLARIFICATIONS: \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIt is understood there can be 2 possible positions, given a single y-offset. In this exercise please consider only the position as drawn above. That means at the top view, the ant and the spidert shall only be within the first and third quadrant, respectively.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe dotted lines is not the spider's path. They are used only to project the heights to the 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drawpolygon or patch","description":"Recently, I tried to plot a polygon in matlab, and I found there is a lot of embedded function that can be used. However, some functions will plot points at vertexes, it is really disgusting. Try to use different embedded functions given in the title and find their difference!\r\nvertexes coordinates is given as follow:\r\nx = [0 1 1 0];\r\ny = [0 0 1 1];\r\nTips: patch is the answer!","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 183px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 91.5px; transform-origin: 407px 91.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eRecently, I tried to plot a polygon in matlab, and I found there is a lot of embedded function that can be used. However, some functions will plot points at vertexes, it is really disgusting. Try to use different embedded functions given in the title and find their difference!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003evertexes coordinates is given as follow:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ex = [0 1 1 0];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ey = [0 0 1 1];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTips: patch is the answer!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function Output = Plot_polygon(x,y)\r\nbw = poly2mask(x,y,256,256);\r\nimshow(bw)\r\n\r\nmy_vertices = [x;y];\r\nh = drawpolygon('Position',my_vertices,'LineWidth',1,'Color','cyan');\r\n\r\npatch(x,y,'cyan')\r\n\r\nOutput = 'poly2mask';\r\nend","test_suite":"%%\r\nx = [0 1 1 0];\r\ny = [0 0 1 1];\r\nassert(isequal(Plot_polygon(x,y),'patch'));\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":1133393,"edited_by":427930,"edited_at":"2024-07-08T18:22:03.000Z","deleted_by":null,"deleted_at":null,"solvers_count":14,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-10-03T05:53:41.000Z","updated_at":"2024-11-20T12:34:09.000Z","published_at":"2021-10-03T05:53:41.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRecently, I tried to plot a polygon in matlab, and I found there is a lot of embedded function that can be used. However, some functions will plot points at vertexes, it is really disgusting. Try to use different embedded functions given in the title and find their difference!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003evertexes coordinates is given as follow:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex = [0 1 1 0];\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey = [0 0 1 1];\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTips: patch is the answer!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":490,"title":"Fastest shortest-path-finder in the west","description":"Given connectivity information about a graph, your job is to find the \u003chttp://en.wikipedia.org/wiki/Shortest_path_problem *shortest-path distance*\u003e between every pair of vertices in this graph. \r\n\r\nNote: Valid solutions will be scored based on their *speed*, not their *size* (hence the _fastest in the west_...).\r\n\r\n*Format:* D = mindist(from,to)\r\n\r\n*Inputs:* two vectors, _from_ and _to_, listing the vertex labels for each edge in the graph (note: vertex labels are positive integers, connectivity is unidirectional, meaning that a connection between vertex _a_ and _b_ does not imply a connection between vertex _b_ and _a_; in other words this is a directed graph)\r\n\r\n*Output:* _D_ is a square matrix where _D(a,b)_ is the number of edges in the shortest-path starting from vertex _a_ and ending in vertex _b_ (or _inf_ if there is no path connecting them). Note: Your algorithm is not required to output the actual optimal paths between each pair of vertices, just their distance. \r\n\r\n*Example:* \r\n\r\n    D=mindist([1,2,3],[2,3,4])\r\n    D =\r\n\r\n     0     1     2     3\r\n   Inf     0     1     2\r\n   Inf   Inf     0     1\r\n   Inf   Inf   Inf     0\r\n\r\n     \r\n*Important note \u0026 disclaimer:* Your algorithm will be scored based on its *speed*, not based on its cody *size*. The reported 'size' measure for any valid entry will instead reflect the time (in milliseconds) your algorithm takes to solve various test suite problems (see the test suite for details). There has been some discussion (e.g. \u003chttp://blogs.mathworks.com/desktop/2012/02/06/scoring-in-cody/#comments\u003e) regarding the cody scoring method. This problem is just a little experiment on _tweaking_ cody to use a different scoring method other than the default node-length measure. Of course scoring based on running time has its own issues (e.g. lack of appropriate repeatability), please feel free to comment on ways you would improve how this problem is scored. ","description_html":"\u003cp\u003eGiven connectivity information about a graph, your job is to find the \u003ca href=\"http://en.wikipedia.org/wiki/Shortest_path_problem\"\u003e\u003cb\u003eshortest-path distance\u003c/b\u003e\u003c/a\u003e between every pair of vertices in this graph.\u003c/p\u003e\u003cp\u003eNote: Valid solutions will be scored based on their \u003cb\u003espeed\u003c/b\u003e, not their \u003cb\u003esize\u003c/b\u003e (hence the \u003ci\u003efastest in the west\u003c/i\u003e...).\u003c/p\u003e\u003cp\u003e\u003cb\u003eFormat:\u003c/b\u003e D = mindist(from,to)\u003c/p\u003e\u003cp\u003e\u003cb\u003eInputs:\u003c/b\u003e two vectors, \u003ci\u003efrom\u003c/i\u003e and \u003ci\u003eto\u003c/i\u003e, listing the vertex labels for each edge in the graph (note: vertex labels are positive integers, connectivity is unidirectional, meaning that a connection between vertex \u003ci\u003ea\u003c/i\u003e and \u003ci\u003eb\u003c/i\u003e does not imply a connection between vertex \u003ci\u003eb\u003c/i\u003e and \u003ci\u003ea\u003c/i\u003e; in other words this is a directed graph)\u003c/p\u003e\u003cp\u003e\u003cb\u003eOutput:\u003c/b\u003e \u003ci\u003eD\u003c/i\u003e is a square matrix where \u003ci\u003eD(a,b)\u003c/i\u003e is the number of edges in the shortest-path starting from vertex \u003ci\u003ea\u003c/i\u003e and ending in vertex \u003ci\u003eb\u003c/i\u003e (or \u003ci\u003einf\u003c/i\u003e if there is no path connecting them). Note: Your algorithm is not required to output the actual optimal paths between each pair of vertices, just their distance.\u003c/p\u003e\u003cp\u003e\u003cb\u003eExample:\u003c/b\u003e\u003c/p\u003e\u003cpre\u003e    D=mindist([1,2,3],[2,3,4])\r\n    D =\u003c/pre\u003e\u003cpre\u003e     0     1     2     3\r\n   Inf     0     1     2\r\n   Inf   Inf     0     1\r\n   Inf   Inf   Inf     0\u003c/pre\u003e\u003cp\u003e\u003cb\u003eImportant note \u0026 disclaimer:\u003c/b\u003e Your algorithm will be scored based on its \u003cb\u003espeed\u003c/b\u003e, not based on its cody \u003cb\u003esize\u003c/b\u003e. The reported 'size' measure for any valid entry will instead reflect the time (in milliseconds) your algorithm takes to solve various test suite problems (see the test suite for details). There has been some discussion (e.g. \u003ca href=\"http://blogs.mathworks.com/desktop/2012/02/06/scoring-in-cody/#comments\"\u003ehttp://blogs.mathworks.com/desktop/2012/02/06/scoring-in-cody/#comments\u003c/a\u003e) regarding the cody scoring method. This problem is just a little experiment on \u003ci\u003etweaking\u003c/i\u003e cody to use a different scoring method other than the default node-length measure. Of course scoring based on running time has its own issues (e.g. lack of appropriate repeatability), please feel free to comment on ways you would improve how this problem is scored.\u003c/p\u003e","function_template":"function D = mindist(from,to)\r\n  D=zeros(max([from,to]));\r\nend","test_suite":"%%\r\n% test small connectivity matrix (3x3)\r\nassert(isequal(mindist([1,3,2,3],[2,2,1,2]),[0 1 Inf;1 0 Inf;2 1 0]))\r\nt0=clock;\r\nD=mindist([1,3,2,3],[2,2,1,2]);\r\nt1=etime(clock,t0)*1e3;\r\ndisp('Time (ms)'); \r\ndisp(t1)\r\n\r\n%%\r\n% test small connectivity matrix (10 vertices, 15 edges)\r\nassert(isequal(mindist([10 5 5 7 7 3 3 4 6 6 1 8 7 1 10],[7 4 10 6 8 4 1 7 9 4 6 9 6 10 9]),[0 Inf Inf 2 Inf 1 2 3 2 1;Inf 0 Inf Inf Inf Inf Inf Inf Inf Inf;1 Inf 0 1 Inf 2 2 3 3 2;Inf Inf Inf 0 Inf 2 1 2 3 Inf;Inf Inf Inf 1 0 3 2 3 2 1;Inf Inf Inf 1 Inf 0 2 3 1 Inf;Inf Inf Inf 2 Inf 1 0 1 2 Inf;Inf Inf Inf Inf Inf Inf Inf 0 1 Inf;Inf Inf Inf Inf Inf Inf Inf Inf 0 Inf;Inf Inf Inf 3 Inf 2 1 2 1 0]))\r\nt0=clock;\r\nD=mindist([10 5 5 7 7 3 3 4 6 6 1 8 7 1 10],[7 4 10 6 8 4 1 7 9 4 6 9 6 10 9]);\r\nt1=etime(clock,t0)*1e3;\r\ndisp('Time (ms)');\r\ndisp(t1)\r\n\r\n%%\r\n% test small connectivity matrix (10 vertices, 30 edges)\r\nassert(isequal(mindist([4 10 2 9 8 2 7 10 3 7 5 9 2 6 9 3 2 9 8 7 9 9 10 8 2 7 3 2 1 8],[2 6 9 4 3 1 4 8 10 5 4 6 5 5 7 4 7 1 4 4 3 8 5 7 5 4 7 3 4 1]),[0 2 3 1 3 4 3 4 3 4;1 0 1 2 1 2 1 2 1 2;3 2 0 1 2 2 1 2 3 1;2 1 2 0 2 3 2 3 2 3;3 2 3 1 0 4 3 4 3 4;4 3 4 2 1 0 4 5 4 5;3 2 3 1 1 4 0 4 3 4;1 2 1 1 2 3 1 0 3 2;1 2 1 1 2 1 1 1 0 2;2 3 2 2 1 1 2 1 4 0]))\r\nt0=clock;\r\nD=mindist([4 10 2 9 8 2 7 10 3 7 5 9 2 6 9 3 2 9 8 7 9 9 10 8 2 7 3 2 1 8],[2 6 9 4 3 1 4 8 10 5 4 6 5 5 7 4 7 1 4 4 3 8 5 7 5 4 7 3 4 1]);\r\nt1=etime(clock,t0)*1e3;\r\ndisp('Time (ms)');\r\ndisp(t1)\r\n\r\n%%\r\n% test medium connectivity matrix (100 vertices, 200 edges)\r\ni=[17 21 97 93 63 87 68 14 40 12 30 60 45 63 55 43 71 74 32 66 48 27 10 80 1 50 36 40 100 35 84 75 93 94 79 49 6 6 60 24 80 43 60 41 64 87 1 17 44 63 6 89 15 70 74 48 69 68 63 24 77 82 48 69 33 50 100 90 37 29 10 62 61 87 69 6 45 27 77 8 100 94 77 26 8 72 59 4 4 36 59 47 9 60 95 88 15 27 32 50 51 42 40 76 22 32 68 39 46 82 32 27 15 39 75 63 33 63 63 91 64 43 13 10 2 56 10 62 45 24 44 58 80 2 44 98 80 92 31 97 76 82 48 68 5 100 91 65 65 90 77 96 95 44 84 4 29 85 25 99 26 75 47 2 47 64 63 4 83 73 63 26 56 99 9 98 47 7 82 53 86 84 66 40 83 76 69 86 74 60 18 99 69 3 10 35 85];\r\nj=[6 27 87 92 2 77 23 12 86 60 81 18 14 69 98 84 91 76 12 81 22 81 4 26 25 27 56 39 52 20 56 92 21 37 61 100 24 67 34 76 77 90 46 25 76 69 44 94 65 9 80 28 56 39 65 68 37 51 12 1 64 21 98 50 46 99 86 21 46 99 99 81 16 60 80 20 88 74 68 15 72 55 28 67 11 31 24 39 85 35 64 42 65 87 45 95 78 59 49 13 61 30 28 31 28 35 13 74 13 7 94 60 2 40 74 93 38 18 91 84 25 29 72 36 98 12 41 28 31 54 73 71 49 29 43 82 10 46 8 91 30 80 54 26 83 46 84 51 17 20 78 7 50 30 58 58 27 30 36 15 42 54 32 13 80 89 4 50 56 88 16 98 49 24 91 72 55 77 65 83 79 12 82 70 93 19 95 35 62 98 51 70 48 68 56 28 6];\r\n\r\nassert(isequal(interp2(mindist(i,j),[2 55 45 33 34 87 53 43 99 50],[90 66 53 41 94 68 94 38 23 76],'nearest'),[8,5,8,Inf,7,7,Inf,Inf,Inf,9]))\r\nt0=clock;\r\nD=mindist(i,j);\r\nt1=etime(clock,t0)*1e3;\r\ndisp('Time (ms)');\r\ndisp(t1)\r\n\r\n%%\r\n% Time-score evaluation\r\n% test medium connectivity matrix (100 vertices, 200 edges)\r\nrand('state',2); \r\nn=100;m=200; \r\ni=ceil(n*rand(1,m));\r\nj=ceil(n*rand(1,m));\r\nk=i==j;i(k)=[];j(k)=[];\r\nI=ceil(n*rand(1,10));J=ceil(n*rand(1,10));\r\n\r\n% first run for initialization\r\nassert(isequal(interp2(mindist(i,j),I,J,'nearest'),[6 6 Inf 0 5 Inf 4 8 6 3]))\r\n\r\n% second run for time evaluation\r\nt0=clock;\r\nD=mindist(i,j);\r\nt1(1)=etime(clock,t0)*1e3;\r\n\r\n% test large connectivity matrix (1000 vertices, 2000 edges)\r\nrand('state',0); \r\nn=1000;m=2000; \r\ni=ceil(n*rand(1,m));\r\nj=ceil(n*rand(1,m));\r\nk=i==j;i(k)=[];j(k)=[];\r\nI=ceil(n*rand(1,10));J=ceil(n*rand(1,10));\r\n\r\n% first run for initialization\r\nassert(isequal(interp2(mindist(i,j),I,J,'nearest'),[8 8 9 8 11 7 Inf 5 8 Inf]))\r\n\r\n% second run for time evaluation\r\nt0=clock;\r\nD=mindist(i,j);\r\nt1(2)=etime(clock,t0)*1e3;\r\n\r\n% test large connectivity matrix (1000 vertices, 10000 edges)\r\nrand('state',1); \r\nn=1000;m=10000; \r\ni=ceil(n*rand(1,m));\r\nj=ceil(n*rand(1,m));\r\nk=i==j;i(k)=[];j(k)=[];\r\nI=ceil(n*rand(1,10));J=ceil(n*rand(1,10));\r\n\r\n% second run for time evaluation\r\nt0=clock;\r\nD=mindist(i,j);\r\nt1(3)=etime(clock,t0)*1e3;\r\nassert(isequal(interp2(D,I,J,'nearest'),[3 4 3 4 4 3 3 2 3 3]))\r\n\r\n% convert time to score\r\ndisp('Time (ms)');\r\ndisp(t1);\r\n\r\nurlwrite('https://sites.google.com/a/alfnie.com/alfnie/software/SetSolutionScore.p?attredirects=0\u0026amp;d=1','SetSolutionScore.p');\r\nrehash path; \r\nSetSolutionScore(round(sum(t1)));\r\n%feval(@evalin,'caller',sprintf('score=%d',round(sum(t1))));\r\n%%fh=fopen('mindist.m','wt');\r\n%%fprintf(fh,'%s\\n',repmat('1;',[1,ceil(sum(t1)/2)]));\r\n%%fclose(fh);","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":43,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":15,"test_suite_updated_at":"2015-06-23T04:22:41.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-03-13T04:35:04.000Z","updated_at":"2024-11-12T08:57:02.000Z","published_at":"2012-03-15T18:12:51.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven connectivity information about a graph, your job is to find the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/Shortest_path_problem\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eshortest-path distance\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e between every pair of vertices in this graph.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNote: Valid solutions will be scored based on their\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003espeed\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, not their\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003esize\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (hence the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003efastest in the west\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e...).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eFormat:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e D = mindist(from,to)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInputs:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e two vectors,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003efrom\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eto\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, listing the vertex labels for each edge in the graph (note: vertex labels are positive integers, connectivity is unidirectional, meaning that a connection between vertex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e does not imply a connection between vertex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e; in other words this is a directed graph)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eD\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is a square matrix where\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eD(a,b)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the number of edges in the shortest-path starting from vertex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and ending in vertex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (or\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einf\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if there is no path connecting them). Note: Your algorithm is not required to output the actual optimal paths between each pair of vertices, just their distance.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[    D=mindist([1,2,3],[2,3,4])\\n    D =\\n\\n     0     1     2     3\\n   Inf     0     1     2\\n   Inf   Inf     0     1\\n   Inf   Inf   Inf     0]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eImportant note \u0026amp; disclaimer:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Your algorithm will be scored based on its\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003espeed\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, not based on its cody\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003esize\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. The reported 'size' measure for any valid entry will instead reflect the time (in milliseconds) your algorithm takes to solve various test suite problems (see the test suite for details). There has been some discussion (e.g.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://blogs.mathworks.com/desktop/2012/02/06/scoring-in-cody/#comments\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ehttp://blogs.mathworks.com/desktop/2012/02/06/scoring-in-cody/#comments\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e) regarding the cody scoring method. This problem is just a little experiment on\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003etweaking\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e cody to use a different scoring method other than the default node-length measure. Of course scoring based on running time has its own issues (e.g. lack of appropriate repeatability), please feel free to comment on ways you would improve how this problem is scored.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":58144,"title":"Given the mass and stiffness of an undamped SDOF system, find the natural frequency and the natural period of vibration","description":"Problem Statement\r\nGiven the mass  and stiffness  of an undamped SDOF system, find the system's natural frequency in both Hz and radians per second as well as the natural period of vibration. \r\nBackground\r\nAn undamped, linear single degree-of-freedom (SDOF) system can be visualized as a spring with stiffness , fixed at one end and having a mass  attached to the other:\r\n\r\nOnce set into motion, the system will oscillate at its natural frequency, or fundamental frequency: \r\n\r\nwhere the natural frequency  is in radians per second. \r\nThe time required for the undamped system to complete one cycle of free vibration is the natural period of vibration of the system, , which has units of seconds:\r\n\r\nA system executes  cycles in 1 second. This is the natural cyclic frequency of vibration:\r\n\r\nwhich has units of Hertz (Hz) or cycles per second. The term natural frequency of vibration applies to both  and . They have the relationship:\r\n\r\nExample\r\nm = 10;\r\nk = 2;\r\n[wn,fn,Tn] = udSDOF(m,k)\r\nwn = 5\r\nfn = 0.7958\r\nTn = 1.2566\r\n\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 878.625px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 439.312px; transform-origin: 407px 439.312px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20px; border-block-end-color: rgb(60, 60, 60); border-block-start-color: rgb(60, 60, 60); border-bottom-color: rgb(60, 60, 60); border-inline-end-color: rgb(60, 60, 60); border-inline-start-color: rgb(60, 60, 60); border-left-color: rgb(60, 60, 60); border-right-color: rgb(60, 60, 60); border-top-color: rgb(60, 60, 60); caret-color: rgb(60, 60, 60); color: rgb(60, 60, 60); column-rule-color: rgb(60, 60, 60); font-family: Helvetica, Arial, sans-serif; font-size: 20px; font-weight: 700; line-height: 20px; margin-block-end: 5px; margin-block-start: 3px; margin-bottom: 5px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 3px; outline-color: rgb(60, 60, 60); perspective-origin: 384px 10px; text-align: left; text-decoration: none; text-decoration-color: rgb(60, 60, 60); text-emphasis-color: rgb(60, 60, 60); transform-origin: 384px 10px; white-space: pre-wrap; margin-left: 4px; margin-top: 3px; margin-bottom: 5px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eProblem Statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGiven the mass \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003em\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and stiffness \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ek\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e of an undamped SDOF system, find the system's natural frequency in both Hz and radians per second as well as the natural period of vibration. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20px; border-block-end-color: rgb(60, 60, 60); border-block-start-color: rgb(60, 60, 60); border-bottom-color: rgb(60, 60, 60); border-inline-end-color: rgb(60, 60, 60); border-inline-start-color: rgb(60, 60, 60); border-left-color: rgb(60, 60, 60); border-right-color: rgb(60, 60, 60); border-top-color: rgb(60, 60, 60); caret-color: rgb(60, 60, 60); color: rgb(60, 60, 60); column-rule-color: rgb(60, 60, 60); font-family: Helvetica, Arial, sans-serif; font-size: 20px; font-weight: 700; line-height: 20px; margin-block-end: 5px; margin-block-start: 20px; margin-bottom: 5px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 20px; outline-color: rgb(60, 60, 60); perspective-origin: 384px 10px; text-align: left; text-decoration: none; text-decoration-color: rgb(60, 60, 60); text-emphasis-color: rgb(60, 60, 60); transform-origin: 384px 10px; white-space: pre-wrap; margin-left: 4px; margin-top: 20px; margin-bottom: 5px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eBackground\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eAn undamped, linear single degree-of-freedom (SDOF) system can be visualized as a spring with stiffness \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ek\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, fixed at one end and having a mass \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003em\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e attached to the other:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 99px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 49.5px; text-align: left; transform-origin: 384px 49.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"90\" height=\"93\" style=\"vertical-align: baseline;width: 90px;height: 93px\" src=\"data:image/jpeg;base64,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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eOnce set into motion, the system will oscillate at its \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003enatural frequency\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, or fundamental frequency: \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 41px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 20.5px; text-align: left; transform-origin: 384px 20.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-16px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"62.5\" height=\"41\" style=\"width: 62.5px; height: 41px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.75px; text-align: left; transform-origin: 384px 10.75px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhere the natural frequency \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"18.5\" height=\"20\" style=\"width: 18.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e is in radians per second. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.25px; text-align: left; transform-origin: 384px 21.25px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThe time required for the undamped system to complete one cycle of free vibration is the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003enatural period\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e of vibration of the system, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"16.5\" height=\"20\" style=\"width: 16.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, which has units of seconds:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 37px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 18.5px; text-align: left; transform-origin: 384px 18.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"51.5\" height=\"37\" style=\"width: 51.5px; height: 37px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.75px; text-align: left; transform-origin: 384px 10.75px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eA system executes \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"31.5\" height=\"20\" style=\"width: 31.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e cycles in 1 second. This is the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003enatural cyclic frequency\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e of vibration:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 37px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 18.5px; text-align: left; transform-origin: 384px 18.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFgAAABKCAYAAAA/i5OkAAAAAXNSR0IArs4c6QAABVRJREFUeF7tm1nIVVUUx3+SRdgEpVFUFEX10ENmA0Y9aEiDUERFc1oplWgQURGKikZGEyk2zyOVFZUvoZUF0kxWooiGUpDUQ9gcNEDx51ubezyce+/Z99597uWetUGQj33W2fv3rb3OXv+1vlH4SEpgVFLrbhwHnNgJHLADTkwgsXn3YAecmEBi8+7BDjgxgdbmDwFuBHYDZneyEvfgYmoCewNwKXAA8DAwywF3QmDnZ/YAbgb2B0YDlwB7OuDuwQYLgqrxL3AY8CpwvAPuHeCsJYWJ14ATHbADTkMgsVX3YAecmEBi8+7BDjgxgcTmK/dgZX0nAGcB+wEb7J74U+KN9st8pYD3Bu4wwMrNjwaeAF4ArgX+6BeFhO+tDLCEjjuBy03wWAHcDdwEvG/p5A8JN9ov05UBnmreug64AtgBHAxMB94DPuwXgcTvrQSwvPcBYCZwi3lu4n0NjPlKAE+wOLsXMA1YMzDbT7+QSgDPAZYDnwIXAt+m39fAvCE54DHA4/YRk6p0FfDbwGw//UJOB54EDgL0Yb+6k9tSvqKxD/A0cG6L9Q8zbH1zzrZ/Z1g1Qyh+t/C4Fngb+Krs77dVyegci79S9HVjeLas0Yh5DwHXRcwvmrrVbjcfdWknyeOtAN9qycUWuwN/lmAFtQWso/IIcOWQJxMJfGZnk808WJXUF4FJwKN2jP9LvpohfEEzwKpDPQ8cZX0B9w3h3ivZUjPAuvO+DGyvYYLRU/DNAC8CFgCfAxcA3/T0rQ1jVX7k1EhS1UmcbN+uwgbsKhOMWgJW5vIKcDKwGFiYyHtrYbYoRJxiScXhwEWWJgYYIdPRETgO+B64HrjMerd2NQH+rVrQK7HJIsBSzZ4BNhq4orQwJCHzgH2Br62fSx6v2H1biXfXYkoR4FCteMMSjV9yJPTM/cCZwMfAB4Bi6V0mDKnN881a0CuxyVZiTzOBPZuEqC6nGp3sSCQaZ9e6bSXeXYspecAqZr4E7G7hQWWi/DjNYrRKRzMAaRTHmjAk3Vh9tH/Vgl6JTeYBn2+eKMg66n8X2FD/rMLBEkD3Zc0JiYkEepWYBn2EMNjpOh8EtNe28oEAK5mQHKkPlWKprmcSeT4peHu4I+umIQH6XQsPWrA0ZH0gDwTeAfKxu9PN9Pq5sSYDTASeAh4DJHnq1IXTqatqVgbdBZA+LIdSb4hOqbre2w4B3mTh4EjgdkA3A6XJReNQu7YJngB/Z6K0hKF/gNXWGa6MaVDDhBxI3wuBvTfnhdKm5WQaq0ym/TEDQnueG6M/C/BmYD0g71xqin2z34y6eiS8q5Qy38KDqiBarEosy2zRv7b91fZvgiCeWtAwk5Votbp77M8Jsis9D7imAHzT3dTxj2B0h//CPDQLJpzOk6xEpDCp8lh2qJyk8CgbpUYdAbc7nYrRXwIX2+kuBbLZJAfcIBNuR/qJvilqtvmzK7p2A+jWxjA8n1UQtZ+eiVzuwSPuERKs8YBuDbpu9kSwcsAjgLMtCj3tYnLAI4BDBUf/1x1ZPc9FWWx0OHTAkO9mKp2llaHtgBtC1TG59LgMv7ZzHHBDqBKsovS4LcRWExxw488hxKkoPXbAXRAIypqUMo18DbIL0yOP1t2Dpaw9BxzRpgbZMei6A87KkytNF/+5Bc3oqnqdAaswIME9hIcygAP70lX1OgKeYtVvdY6q9yOM0MWuSsbrgLrZi0ZUVb2OgDuOp/ZgVFXdAcfjjqqqO+B4wFFVdQccBzi6qu6A4wBHV9UdcBzg6Kq6A44DHD3bAUcji3vAAcfxip7tgKORxT3ggON4Rc92wNHI4h74H/oFMlpQtGcCAAAAAElFTkSuQmCC\" width=\"44\" height=\"37\" style=\"width: 44px; height: 37px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.25px; text-align: left; transform-origin: 384px 21.25px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhich has units of Hertz (Hz) or cycles per second. The term natural frequency of vibration applies to both \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"18.5\" height=\"20\" style=\"width: 18.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"12\" height=\"20\" style=\"width: 12px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. They have the relationship:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 38px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 19px; text-align: left; transform-origin: 384px 19px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"47.5\" height=\"38\" style=\"width: 47.5px; height: 38px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20px; border-block-end-color: rgb(60, 60, 60); border-block-start-color: rgb(60, 60, 60); border-bottom-color: rgb(60, 60, 60); border-inline-end-color: rgb(60, 60, 60); border-inline-start-color: rgb(60, 60, 60); border-left-color: rgb(60, 60, 60); border-right-color: rgb(60, 60, 60); border-top-color: rgb(60, 60, 60); caret-color: rgb(60, 60, 60); color: rgb(60, 60, 60); column-rule-color: rgb(60, 60, 60); font-family: Helvetica, Arial, sans-serif; font-size: 20px; font-weight: 700; line-height: 20px; margin-block-end: 5px; margin-block-start: 20px; margin-bottom: 5px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 20px; outline-color: rgb(60, 60, 60); perspective-origin: 384px 10px; text-align: left; text-decoration: none; text-decoration-color: rgb(60, 60, 60); text-emphasis-color: rgb(60, 60, 60); transform-origin: 384px 10px; white-space: pre-wrap; margin-left: 4px; margin-top: 20px; margin-bottom: 5px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eExample\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 122.625px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 61.3125px; transform-origin: 404px 61.3125px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2188px; transform-origin: 404px 10.2188px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003em = 10;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2188px; transform-origin: 404px 10.2188px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003ek = 2;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2188px; transform-origin: 404px 10.2188px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e[wn,fn,Tn] = udSDOF(m,k)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2188px; transform-origin: 404px 10.2188px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003ewn = 5\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2188px; transform-origin: 404px 10.2188px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003efn = 0.7958\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2188px; transform-origin: 404px 10.2188px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eTn = 1.2566\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [wn,fn,Tn] = udSDOF(m,k)\r\n  % put yo answer here ^(o.O)^\r\nend","test_suite":"%%\r\nm = 2;\r\nk = 50;\r\ny_correct = [5 0.7958 1.2566];\r\n[wn,fn,Tn] = udSDOF(m,k);\r\nassert(sum(round([wn,fn,Tn]./y_correct,2))==3)\r\n\r\n%%\r\nm = 0.2;\r\nk = 2000;\r\ny_correct = [100 15.9 0.0628];\r\n[wn,fn,Tn] = udSDOF(m,k);\r\nassert(sum(round([wn,fn,Tn]./y_correct,2))==3)\r\n\r\n%%\r\nm = 0.2533; \r\nk = 10; \r\ny_correct = [6.2832 1 1];\r\n[wn,fn,Tn] = udSDOF(m,k);\r\nassert(sum(round([wn,fn,Tn]./y_correct,2))==3)\r\n\r\n%%\r\nfiletext = fileread('udSDOF.m');\r\nnot_allowed = contains(filetext, 'regex');\r\nassert(~not_allowed)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":91130,"edited_by":91130,"edited_at":"2023-04-28T00:16:14.000Z","deleted_by":null,"deleted_at":null,"solvers_count":31,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-04-27T23:21:12.000Z","updated_at":"2024-11-12T05:54:32.000Z","published_at":"2023-04-28T00:16:14.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"heading\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eProblem Statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven the mass \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003em\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and stiffness \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of an undamped SDOF system, find the system's natural frequency in both Hz and radians per second as well as the natural period of vibration. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"heading\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBackground\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAn undamped, linear single degree-of-freedom (SDOF) system can be visualized as a spring with stiffness \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, fixed at one end and having a mass \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003em\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e attached to the other:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"93\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"90\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOnce set into motion, the system will oscillate at its \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003enatural frequency\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, or fundamental frequency: \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e$\\\\omega_n =\\\\sqrt{\\\\frac{k}{m}}$\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere the natural frequency \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e$\\\\omega_n$\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is in radians per second. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe time required for the undamped system to complete one cycle of free vibration is the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003enatural period\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e of vibration of the system, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eT_n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, which has units of seconds:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e$T_n =\\\\frac{2\\\\pi }{\\\\omega_n }$\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA system executes \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e1/T_n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e cycles in 1 second. This is the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003enatural cyclic frequency\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e of vibration:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e$f_n =\\\\frac{1}{T_n }$\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhich has units of Hertz (Hz) or cycles per second. The term natural frequency of vibration applies to both \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e$\\\\omega_n$\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef_n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. They have the relationship:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e$f_n =\\\\frac{\\\\omega_n }{2\\\\pi }$\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"heading\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[m = 10;\\nk = 2;\\n[wn,fn,Tn] = udSDOF(m,k)\\nwn = 5\\nfn = 0.7958\\nTn = 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the Voltage Through a Step-Up Transformer","description":"Given a step-up transformer has a primary coil with A number loops, a secondary coil with B number loops, and a primary voltage of 12 volts. What is the secondary voltage in each transformer?","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407.5px 21px; transform-origin: 407.5px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 21px; text-align: left; transform-origin: 384.5px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGiven a step-up transformer has a primary coil with A number loops, a secondary coil with B number loops, and a primary voltage of 12 volts. What is the secondary voltage in each transformer?\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function V_s = SecVolt(A,B)\r\n  V_s = ;\r\nend","test_suite":"%%\r\nA = 30;\r\nB = 75;\r\nassert(isequal(SecVolt(A,B),30))\r\n%%\r\nA = 20;\r\nB = 40;\r\nassert(isequal(SecVolt(A,B),24))\r\n%%\r\nA = 40;\r\nB = 90;\r\nassert(isequal(SecVolt(A,B),27))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":3227359,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":41,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-05-17T17:08:40.000Z","updated_at":"2024-11-19T12:00:46.000Z","published_at":"2023-05-17T17:08:40.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a step-up transformer has a primary coil with A number loops, a secondary coil with B number loops, and a primary voltage of 12 volts. What is the secondary voltage in each transformer?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":55920,"title":"Juros Simples","description":"Faça uma função que calcule o montagem de um investimento com juros simples que receba como argumentos o capital inicial C, a taxa de juros i em %, e o tempo de aplicação t.\r\nO valor deve ser arrendondado em 2 casas.\r\nJurosSimples(2490, 2.5, 8) = 2988;","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 102.438px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 51.2188px; transform-origin: 407px 51.2188px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFaça uma função que calcule o montagem de um investimento com juros simples que receba como argumentos o capital inicial \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eC\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, a taxa de juros \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ei \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eem %\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e e o tempo de aplicação \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003et\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eO valor deve ser arrendondado em 2 casas.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20.4375px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 10.2188px; transform-origin: 404px 10.2188px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; 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\"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eJurosSimples(2490, 2.5, 8) = 2988;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function m = JurosSimples(c, i, t)\r\n  %faça a sua função aqui\r\nend","test_suite":"%%\r\nc = 2490;\r\ni = 2.5;\r\nt = 8;\r\ny_correct = 2988;\r\nassert(isequal(JurosSimples(c, i, t),y_correct))\r\n\r\n%%\r\nc = 400;\r\ni = 4;\r\nt = 5;\r\ny_correct = 480;\r\nassert(isequal(JurosSimples(c, i, t),y_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2564100,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":42,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-17T19:18:46.000Z","updated_at":"2024-11-17T23:57:56.000Z","published_at":"2022-09-17T19:18:46.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFaça uma função que calcule o montagem de um investimento com juros simples que receba como argumentos o capital inicial \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eC\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, a taxa de juros \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ei \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eem %\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e e o tempo de aplicação \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eO valor deve ser arrendondado em 2 casas.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[JurosSimples(2490, 2.5, 8) = 2988;]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":58653,"title":"Alternate Arrangement","description":"Determine the ways of arranging 'm' men and 'w' women alternatively in a row of 's' seats.\r\nAssumptions :\r\ns\u003cm and s\u003cw","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 81px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 40.5px; transform-origin: 407px 40.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eDetermine the ways of arranging 'm' men and 'w' women alternatively in a row of 's' seats.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eAssumptions :\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003es\u0026lt;m and s\u0026lt;w\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = arrangement(m,w,s)\r\n  y = x;\r\nend","test_suite":"%%\r\nm = 2\r\nw = 3\r\ns = 3\r\nx = 1;\r\ny_correct = 9;\r\nassert(isequal(arrangement(m,w,s),y_correct))\r\n","published":true,"deleted":false,"likes_count":13,"comments_count":3,"created_by":3495088,"edited_by":3495088,"edited_at":"2023-07-18T15:12:10.000Z","deleted_by":null,"deleted_at":null,"solvers_count":17,"test_suite_updated_at":"2023-07-18T15:12:10.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2023-07-18T15:00:55.000Z","updated_at":"2024-11-12T13:44:57.000Z","published_at":"2023-07-18T15:12:10.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDetermine the ways of arranging 'm' men and 'w' women alternatively in a row of 's' seats.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAssumptions :\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003es\u0026lt;m and s\u0026lt;w\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":56035,"title":"sinus de pulsation a","description":"Ecrire une fonction sinat qui prend en entrée un vecteur t  (de valeurs croissantes)  et renvoie un vecteur y de de même dimension que t qui contient les valeurs de sin(at) où la pulsation a est choisie de façon à ce qu'il y ait excatement une période de sin(at) sur l'intervalle [min(t), max(t)] ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 63px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 31.5px; transform-origin: 407px 31.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 380px 8px; transform-origin: 380px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eEcrire une fonction sinat qui prend en entrée un vecteur t  (de valeurs croissantes)  et renvoie un vecteur y de de même dimension que t qui contient les valeurs de sin(at) où la pulsation a est choisie de façon à ce qu'il y ait excatement une période de sin(at) sur l'intervalle [min(t), max(t)] \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [y] = sinat(t)\r\n  %à vous de jouer\r\nend","test_suite":"%%\r\na=rand\r\nt=linspace(-pi/a,pi/a)\r\ny_correct = sin(a*t);\r\nassert(max(abs(sinat(t)-y_correct))\u003c=1e-10)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":63915,"edited_by":223089,"edited_at":"2022-10-22T13:06:29.000Z","deleted_by":null,"deleted_at":null,"solvers_count":28,"test_suite_updated_at":"2022-10-22T13:06:29.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-23T12:46:39.000Z","updated_at":"2024-11-18T00:12:54.000Z","published_at":"2022-09-23T12:46:39.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eEcrire une fonction sinat qui prend en entrée un vecteur t  (de valeurs croissantes)  et renvoie un vecteur y de de même dimension que t qui contient les valeurs de sin(at) où la pulsation a est choisie de façon à ce qu'il y ait excatement une période de sin(at) sur l'intervalle [min(t), max(t)] \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":58797,"title":"Array Width (no usage of size)","description":"Find the array width. \r\nSize may not be used.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 51px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 25.5px; transform-origin: 407px 25.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 66.5px 8px; transform-origin: 66.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFind the array width. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 69.5px 8px; transform-origin: 69.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSize may not be used.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function w = find_width(m)\r\n%Size is not allowed\r\n  w=0;\r\nend","test_suite":"%%\r\nw=randi(10);\r\nh=randi(10);\r\nm=ones(h,w);\r\nassert(isequal(find_width(m),w))\r\n%%\r\nfiletext = fileread('find_width.m');\r\nassert(~contains(filetext,'size'));\r\n\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":3097,"edited_by":3097,"edited_at":"2023-08-04T14:35:36.000Z","deleted_by":null,"deleted_at":null,"solvers_count":41,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-08-04T14:29:25.000Z","updated_at":"2024-11-18T00:47:52.000Z","published_at":"2023-08-04T14:35:36.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the array width. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSize may not be used.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":58877,"title":"Neural Net Image Convolution: Return only Valid portion of conv2","description":"This challenge is to return only the Valid portion of a 2-D convolution. Valid is deemed to be where all elements of the kernel are applied against the image. The (1,1) point with a ones(3) kernel would be invalid while point (2,2) would return a Valid convolution value. The images will be even-square,m, and the kernels will be odd-square,K.The m=ones(6) and K=ones(3) would return a 4x4 matrix of 9s.\r\nmValidConv2=create_ValidConv2(m,K)\r\nIn neural net processing of the Mnist database of digits(0-9) one Convolutional Neural Network method uses 9x9 kernels on the 28x28 images to return the Valid 20x20 central core for the next processing step. The third image includes a black border of four around Valid to maintain scale.\r\n  \r\nThe entire Matlab code from Convolutional Neural Networks in Matlab by Nuruzzaman Faruqui , a Matlab Neural Net Tutorial for Mnist processing, is included in the function template. Loading the Mnist Train/Test Images/Labels from posted MAT files or THE MNIST DATABASE of handwritten digits are provided. The Neural Net tutorial explains Neural Net processing for Digit Recognition. The neural net training method uses 784 input nodes,  20 convolutions(9x9), ReLU, Pooling, batch sampling, single hidden layer of 100 nodes, updating parameters via backwards propagation, and updating convolution kernels. The digit prediction accuracy is \u003e94% after 50s of training. The final feature kernels are very amorphous and unexpected.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 545.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 272.75px; transform-origin: 407px 272.75px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 369.5px 8px; transform-origin: 369.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis challenge is to return only the Valid portion of a 2-D convolution. Valid is deemed to be where all elements of the kernel are applied against the image. The (1,1) point with a ones(3) kernel would be invalid while point (2,2) would return a Valid convolution value. The images will be even-square,m, and the kernels will be odd-square,K.The m=ones(6) and K=ones(3) would return a 4x4 matrix of 9s.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 121.5px 8px; transform-origin: 121.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003emValidConv2=create_ValidConv2(m,K)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 379px 8px; transform-origin: 379px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn neural net processing of the Mnist database of digits(0-9) one Convolutional Neural Network method uses 9x9 kernels on the 28x28 images to return the Valid 20x20 central core for the next processing step. The third image includes a black border of four around Valid to maintain scale.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 194.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 97.25px; text-align: left; transform-origin: 384px 97.25px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline;width: 252px;height: 189px\" 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pWdaWlo+/fTTffv27dy5c+nSpZ2dnW1tbfPmzavgJgGYuOhB+uSTTz755JMnn3/zzTfb29uf/X5iSpoJljrLLmncXOosu6QZYmWdZZe0OHV9fmfZJf1TL/Xgd+/eHf/i1KtPHkV/yw6AKUKQAAhBkAAIQZAACEGQAAhBkAAIQZAACEGQAAhBkAAIQZAACEGQAAgh+iw7xiNpVFrq0Lb+/v7yHTxJqFl25Rutlnrkurq68S9OuppZlvX19Y1/ceprmDRWMfVlSR2rSATukAAIQZAACEGQAAhBkAAIQZAACEGQAAhBkAAIQZAACEGQAAhBkAAIQZAACMEsu2pQvrlqqQdPmk6WJQ4cS51OVtaXpXxSTzNpgtzt27eTDj537tzxLy7rsMGcXk2SuEMCIARBAiAEQQIgBEECIARBAiAEQQIgBEECIARBAiAEQQIgBEECIARBAiAEQQIgBMNVpxxDKoMr64jSO3fuJB385s2b41+cuvOkMbJJp5l68NSBtpSJOyQAQhAkAEIQJABCECQAQhAkAEIQJABCECQAQhAkAEIQJABCECQAQhAkAEIwyw5iSZ0I19vbW6bFWZb97W9/S1oPE+EOCYAQ8nGH1NPT09vb29DQ8Prrr489Mzg4eP369dKCQqEwe/bsCu0OgEmQgyDt2bPn3LlzK1eu7OrqqqurO3r0aG1t7alTp/bv319bWzu25uDBg2vWrKnsPgGYkNHYrly58uqrrw4NDY09XLdu3Zdffjk6OvrRRx998cUXP/5nC4VCpV9dgCgKhULZv2VPTPTPkOrr648cOTJnzpyxh4sXL75161aWZVevXl2yZMng4ODw8HBFNwjA5Jg2Ojpa6T2MV29v77p16/785z83NTX94he/+PnPfz40NFQsFjdu3Lh3794n1zc1NZW+7u7ufoY7BYji++8VdXV1VXAn/12lb9HGq7+//1e/+tUf//jH0dHRmzdv/uEPf7h58+bY82vWrPnTn/705B/xlh1AibfsJsc333yzYcOGzZs3b9++PcuyxsbGQ4cONTY2Zlk2f/785ubmjo6OSu8RgAnJQZAuXbq0devW3bt3b9myZeyZ3t7ekydPlhY8fPiwpiYHJwLAj6n0Ldp/8a9//eu11147e/bsw//16NGja9euvfLKK93d3aOjo/39/atXr75w4cKTf9ZbdgAl8d+yi/57SMeOHfvuu++2bdtWeqalpeXTTz9tbW3dtGnTihUrLl++vGPHDr+EBJB3efopu1RNTU1+uA5gTKFQCP5Tdj56ASAEQQIgBEECIARBAiAEQQIgBEECIARBAiAEQQIgBEECIARBAiAEQQIgBEECIARBAiAEQQIgBEECIARBAiAEQQIgBEECIARBAiAEQQIgBEECIARBAiAEQQIgBEECIARBAiAEQQIgBEECIARBAiAEQQIgBEECIARBAiAEQQIgBEHKjUKhUOktPCNT5EynyGlmU+ZMp8hplpUgARCCIAEQwrTR0dFK76FcmpqaKr0FgEC6uroqvYUfU81BAiBHvGUHQAiCBEAIggRACIIEQAiCBEAIggRACIIEQAiCBEAIz1V6A/x3g4OD169fLz0sFAqzZ8+u4H7K5OLFi2vWrCk97Ovru3bt2ssvv1x9Eze+f6ZVeXF7enp6e3sbGhpef/310pNVeUGfPNOqvKDPjCDlwKlTp/bv319bWzv28ODBg9//xl0dDh8+fPz48YsXL449PH36dFtb2+rVqzs6Ot5///0PP/ywstubRD840+q7uHv27Dl37tzKlSu7urrq6uqOHj1aW1tblRf0qWdafRf0mRolvI8++uiLL76o9C7KZWho6OOPP37ttdfeeuutsWcePXr02muvdXd3j46O3rlz55e//OU///nPiu5xcjx5pqNVd3GvXLny6quvDg0NjT1ct27dl19+WZUX9KlnOlp1F/QZ8xlSDly9enXJkiWDg4PDw8OV3svkO3DgQENDw2effVZ65sKFC/X19cuWLcuyrKGhYe3ate3t7ZXb4KR58kyzqru49fX1R44cmTNnztjDxYsX37p1qyov6FPPNKu6C/qMecsuupGRkRs3buzZs2doaKhYLG7cuHHv3r2V3tRk2rVrV01Nzfnz50vPFIvF5cuXlx7OmjUr+IjicXryTKvv4i5atGjRokVjX/f29p49e3bbtm1dXV3Vd0GfeqbVd0GfMXdI0fX39zc3Nx85cuTrr7/+6quvLly4cPz48UpvajLV1PzwL+HIyMi0adNKD6dPnz5aFTPpnzzTKr64AwMDH3zwwfbt21955ZVqvaBjvn+mVXxBnw1Biq6xsfHQoUONjY1Zls2fP7+5ubmjo6PSmyqvGTNmPH78uPRwZGRk+vTpFdxP+VTrxf3mm282bNiwefPm7du3Z1V9QX9wptV6QZ8ZQYqut7f35MmTpYcPHz588h/aVeaFF17o7OwsPSwWiytXrqzgfsqnKi/upUuXtm7dunv37i1btow9U60X9MkzrcoL+ix5saJ78ODBrl27enp6siwbGBg4e/bs+vXrK72p8nrjjTeyLBv7rKWnp6e9vX3VqlWV3lRZVN/F7evr27Fjx+eff/7OO+8MDw8PDw+PjIxU5QV96plW3wV9xvxQQ3RNTU2tra2bNm1asWLF5cuXd+zYUfW/1lBTU7Nv376dO3cuXbq0s7Ozra1t3rx5ld5UWVTfxT127Nh33323bdu20jMtLS2ffvpp9V3Q/+tMq+yCPmP+F+b58Pjx4/v378+cOXNKvQPw73//eyqc8tS5uC4oP06QAAhBwAEIQZAACEGQAAhBkAAIQZAACEGQAAhBkAAIQZAACEGQAAhBkAAIQZAACEGQAAhBkAAIQZAACEGQAAhBkAAIQZAACEGQAAhBkAAIQZAACEGQAAhBkAAIQZAACEGQAAhBkAAI4X8AiB24LVwZWacAAAAASUVORK5CYII=\" data-image-state=\"image-loaded\" width=\"252\" height=\"189\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 147px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 73.5px; text-align: left; transform-origin: 384px 73.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 91px 8px; transform-origin: 91px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe entire Matlab code from \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.youtube.com/watch?v=ZOXOwYUVCqw\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eConvolutional Neural Networks in Matlab by Nuruzzaman Faruqui\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 70px 8px; transform-origin: 70px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e , a Matlab Neural Net Tutorial for Mnist processing, is included in the function template. Loading the Mnist Train/Test Images/Labels from posted MAT files or \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"/#null\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eTHE MNIST DATABASE of handwritten digits\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 181.5px 8px; transform-origin: 181.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are provided. The Neural Net tutorial explains Neural Net processing for Digit Recognition. The neural net training method uses 784 input nodes,  20 convolutions(9x9), ReLU, Pooling, batch sampling, single hidden layer of 100 nodes, updating parameters via backwards propagation, and updating convolution kernels. The digit prediction accuracy is \u0026gt;94% after 50s of training. The final feature kernels are very amorphous and unexpected.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function mValidConv2=create_ValidConv2(m,K)\r\n  mValidConv2=conv2(m,K,'same');\r\nend\r\n\r\n% Code from Convolutional Neural Network in Matlab by Nuruzzaman Faruqui\r\n% Youtube:  https://www.youtube.com/watch?v=ZOXOwYUVCqw\r\n% I have made comments noted by raz and a couple speed enhancements\r\n% I also provide alternate direct source for MNIST files as .mat files\r\n%{\r\nfunction MNIST_Process\r\n%Based upon https://www.youtube.com/watch?v=ZOXOwYUVCqw\r\n%784 input nodes;20 conv 9x9 filters,ReLU;2x2 submatrix Pooling layer,single hidden layer 100 nodes\r\n\r\n%Matlab Convolutional Neural Network in Matlab\r\n%Processing MNIST digits using conv, contents, \r\n%MNIST files  http://yann.lecun.com/exdb/mnist/\r\n%Create filters\r\n%File Exchange NN https://www.mathworks.com/matlabcentral/fileexchange/59223-convolution-neural-network-simple-code-simple-to-use?s_tid=ta_fx_results\r\n%\r\n%use Test_images.mat if avail, use MNIST ubyte files if avail, load Test_images.mat\r\ndir_struct=dir;\r\nfilenames={dir_struct.name};\r\nfn='Test_images.mat';\r\nptr=find(ismember(filenames,fn));\r\nif ~isempty(ptr) % Test images/labels mat files exist\r\n tic;\r\n load('Test_images'); % images [28,28,10000] uint8\r\n load('Test_labels'); % labels [10000,1] uint8 values 0:9\r\n fprintf('Images:%i  Time:%.2f\\n',size(images,3),toc);\r\n Images=double(images)/255; %raz values must be 0:1 or bad things happen\r\n Labels=double(labels);\r\n Labels(Labels==0)=10; % 0 remapped to 10\r\n\r\nelse % Check for Mnist file\r\n %MNIST files source  http://yann.lecun.com/exdb/mnist/\r\n fn='t10k-images.idx3-ubyte'; %NMIST gzip expanded file for Test Images 10K\r\n filenames={dir_struct.name};\r\n ptr=find(ismember(filenames,fn));\r\n if ~isempty(ptr)\r\n  tic\r\n  Images=loadMNISTImages(fn);\r\n  fprintf('MNIST Images Process Time: %.2f\\n',toc); %raz\r\n  Images=reshape(Images,28,28,[]); % Un-vectorize the images\r\n  %Images already scaled by 1/255 in loadMNISTImages\r\n \r\n  Labels=loadMNISTLabels('t10k-labels.idx1-ubyte');\r\n  Labels(Labels==0)=10; % 0 to 10\r\nelse % download Test_images.mat, Test_labels.mat and load\r\n fnameTestI='Test_images.mat'; %load('Test_images.mat') creates images(28,28,10000) 1.6MB\r\n fnameTrainI='Train_images.mat'; %load('Train_images.mat') creates images(28,28,60000)  9.9MB\r\n fnameTestL='Test_labels.mat'; %load('Test_images.mat') creates labels(10000,1) 5KB\r\n fnameTrainL='Train_labels.mat'; %load('Train_images.mat') creates labels(60000,1) 30KB\r\n \r\n %Google Drive Dowloads need to come from shared files\r\n% Tweak link: file/d/ to uc?export=download\u0026id=   while removing /view?usp=sharing\r\n% https://drive.google.com/file/d/1v3GsGgP3p905wzdvUqypL_-djYmxiyzK/view?usp=sharing\r\n% https://drive.google.com/uc?export=download\u0026id=1v3GsGgP3p905wzdvUqypL_-djYmxiyzK\r\n \r\n\r\n  urlTeI='https://drive.google.com/uc?export=download\u0026id=10ReGWlfSvr9p6uq6FQlqw6vw3UXgWo57';\r\n  urlTeL='https://drive.google.com/uc?export=download\u0026id=105zTcVgItZ2JjFiUkJulU33R7lXNl29-';\r\n  urlTrI='https://drive.google.com/uc?export=download\u0026id=1HJZssH6_9OcQ8mXwS_DtvsS_Kk86BDFY';\r\n  urlTrL='https://drive.google.com/uc?export=download\u0026id=1KNTn2eNXbQkQJNe6xhO1LMmvkDRP-XLq';\r\n \r\n  tic\r\n  urlwrite(urlTeI,fnameTestI); %Writing GoogleDrive MNIST_Test_images.pdf  Test_images.mat \r\n  fprintf('Download 1.6MB Time: %.1f  sec\\n\\n',toc); %1.6MB download Time, about 1.1 sec\r\n \r\n  tic\r\n  urlwrite(urlTeL,fnameTestL); %Writing GoogleDrive MNIST_Test_labels.pdf  Test_labels.mat\r\n  fprintf('Download 5KB Time: %.1f  sec\\n\\n',toc); %5KB download Time, about 0.5 sec\r\n \r\n  tic\r\n  urlwrite(urlTrI,fnameTrainI); %Writing GoogleDrive MNIST_Train_images.pdf  Train_images.mat\r\n  fprintf('Download 9.9MB Time: %.1f  sec\\n\\n',toc); %9.9MB download Time, about 4.1 sec\r\n \r\n  tic\r\n  urlwrite(urlTrL,fnameTrainL); %Writing GoogleDrive MNIST_Train_labels.pdf  Train_labels.mat\r\n  fprintf('Download 30KB Time: %.1f  sec\\n\\n',toc); %30KB download Time, about 0.6 sec\r\n\r\n  tic\r\n  load('Test_images'); % images [28,28,10000] uint8\r\n  load('Test_labels'); % labels [10000,1] uint8 values 0:9\r\n  fprintf('Images:%i  Time:%.2f\\n',size(images,3),toc); %.05s\r\n  Images=double(images)/255; %raz values must be 0:1 or bad things happen\r\n  Labels=double(labels);\r\n  Labels(Labels==0)=10; % 0 to 10\r\n end % if MNIST ubyte files\r\n\r\nend % if Test_images.mat\r\n\r\n\r\nrng(1); %raz not liked by curretn matlab\r\n\r\nW1=.01*randn([9 9 20]); %Conv Kernels   base .01\r\nW5=(2*rand(100,2000)-1)*sqrt(6)/sqrt(360+2000); %Hidden layer coeff of 100 pooled\r\nWo=(2*rand(10, 100)-1)*sqrt(6)/sqrt( 10+ 100); %Output coeff to find 0:9 best match\r\n\r\nX=Images(:,:,1:8000);\r\nD=Labels(1:8000);\r\nztic=tic;\r\nfor epoch=1:3  %Repeat cycles of all Training data\r\n fprintf('epoch:%i  Time:%.2f\\n',epoch,toc(ztic));\r\n [W1, W5, Wo]=MnistConv(W1,W5,Wo,X,D);\r\nend %epoch\r\n\r\n%save('MnistConv.mat'); % Used for Post analysis, see video\r\n\r\nX=Images(:,:,8001:10000);\r\nD=Labels(8001:10000);\r\nacc=0;\r\nN=length(D);\r\n\r\nfor k=1:N\r\n x=X(:,:,k);\r\n y1=Conv(x,W1); %Neural Net Processing  W1 kernels on image-x\r\n y2=ReLU(y1);   %Rectification process\r\n y3=Pool(y2);   %Take 20x20 conv images into 100 values\r\n y4=reshape(y3,[],1);\r\n v5=W5*y4;      %Hidden layer weights\r\n y5=ReLU(v5);   %Rectification process\r\n v=Wo*y5;       %Wo Output weight processing\r\n y=Softmax(v);  %create vector length 10 of expected probability, uses exp(x) smoothing\r\n                %Needed in training but not sure why in evaluation\r\n \r\n [~,i]=max(y);\r\n if i==D(k)\r\n  acc=acc+1;\r\n end\r\nend %k\r\n\r\n acc=acc/N;\r\n fprintf('Accuracy is %.2f%%  Time:%.2f\\n',100*acc,toc(ztic));  %raz output/time\r\n\r\nend% MNIST_Process\r\n\r\nfunction [W1, W5,Wo]=MnistConv(W1, W5,Wo,X,D)\r\n alpha=.01;\r\n beta=0.95;\r\n z=reshape(1:100,10,10); % raz\r\n kmap=kron(z,ones(2)); % raz\r\n \r\n momentum1=zeros(size(W1));\r\n momentum5=zeros(size(W5));\r\n momentumo=zeros(size(Wo));\r\n \r\n N=length(D);\r\n \r\n bsize=100;\r\n blist=1:bsize:(N-bsize+1);\r\n \r\n for batch=1:length(blist) % Batch/Updates, each Batch creates updates to Params\r\n  dW1=zeros(size(W1));\r\n  dW5=zeros(size(W5));\r\n  dWo=zeros(size(Wo));\r\n  \r\n  begin=blist(batch);\r\n  for k=begin:begin+bsize-1  %Subset Group of Training samples for param adjust\r\n   x=X(:,:,k);\r\n   y1=Conv(x,W1); %8K/5.8s  3.5s\r\n   y2=ReLU(y1);\r\n   y3=Pool(y2);\r\n   y4=reshape(y3,[],1);\r\n   v5=W5*y4;\r\n   y5=ReLU(v5);\r\n   v=Wo*y5;\r\n   y=Softmax(v); %10 Probability Bins for [1-9 0] \r\n   \r\n   d=zeros(10,1);\r\n   d(sub2ind(size(d),D(k),1))=1;\r\n   \r\n    e=d-y; % raz should this be (e-y)^2*sign(e-y)?\r\n    delta=e;\r\n    e5=Wo'*delta;\r\n    delta5=(y5\u003e0).*e5;\r\n    e4=W5'*delta5;\r\n    e3=reshape(e4,size(y3));\r\n    e2=zeros(size(y2));\r\n    W3=ones(size(y2))/(2*2);\r\n    \r\n    for c=1:20\r\n     %e2(:,:,c)=kron(e3(:,:,c),ones([2 2])).*W3(:,:,c); %160K/4.5s\r\n     e3c=e3(:,:,c); %160K/.27 raz\r\n     e2(:,:,c)=e3c(kmap).*W3(:,:,c);  %160K/.8s  raz\r\n    end %c\r\n    \r\n    delta2=(y2\u003e0).*e2;\r\n    delta1_x=zeros(size(W1)); \r\n    \r\n    for c=1:20\r\n     delta1_x(:,:,c)=conv2(x(:,:),rot90(delta2(:,:,c),2),'valid'); %160K/5.3s\r\n    end %c\r\n    \r\n    dW1=dW1+delta1_x; %error per kernel plane\r\n    dW5=dW5+delta5*y4'; %8K/4.2s  100x2000\r\n    dWo=dWo+delta*y5';\r\n  end %k\r\n  dW1=dW1/bsize;\r\n  dW5=dW5/bsize;\r\n  dWo=dWo/bsize;\r\n  \r\n  momentum1=alpha*dW1+beta*momentum1;\r\n  W1       = W1+momentum1;\r\n  \r\n  momentum5=alpha*dW5+beta*momentum5;\r\n  W5       = W5+momentum5;\r\n  \r\n  momentumo=alpha*dWo+beta*momentumo;\r\n  Wo       = Wo+momentumo;\r\n  \r\n end % batch\r\n \r\nend %MnistConv\r\n\r\nfunction rng(x)\r\n randn('seed',x);\r\n rand('seed',x);\r\nend % rng\r\n\r\nfunction y=Pool(x)\r\n [xrow,xcol,numFilters]=size(x);\r\n y=zeros(xrow/2,xcol/2,numFilters);\r\n for k=1:numFilters\r\n  filter=ones(2)/(2*2);\r\n  image=conv2(x(:,:,k),filter,'valid');\r\n  y(:,:,k)=image(1:2:end,1:2:end);\r\n end\r\n\r\nend %Pool\r\n\r\nfunction y=Conv(x,W)\r\n [wrow,wcol,numFilters]=size(W);\r\n [xrow,xcol,~         ]=size(x);\r\n \r\n yrow=xrow-wrow+1;\r\n ycol=xcol-wcol+1;\r\n \r\n y=zeros(yrow,ycol,numFilters);\r\n \r\n for k=1:numFilters\r\n  filter=W(:,:,k);\r\n  filter=rot90(squeeze(filter),2); %200K/2.5s  raz remove test/92.15%\r\n  y(:,:,k)=conv2(x,filter,'valid'); %200K/3.7s  3.5s\r\n end\r\nend %Conv\r\n\r\nfunction y=Softmax(x)\r\n ex=exp(x);\r\n y=ex/sum(ex);\r\nend %Softmax\r\n\r\nfunction y=ReLU(x)\r\n y=max(0,x);\r\nend %ReLU\r\n\r\n\r\n\r\nfunction images=loadMNISTImages(filename)\r\n%\r\nfp=fopen(filename,'rb');\r\nassert(fp~=-1,['Could not open', filename,'']);\r\nmagic=fread(fp,1,'int32',0,'ieee-be');\r\nassert(magic==2051,['Bad magic number in', filename, '']); %2051 Images\r\nnumImages=fread(fp,1,'int32',0,'ieee-be');\r\nnumRows=fread(fp,1,'int32',0,'ieee-be');\r\nnumCols=fread(fp,1,'int32',0,'ieee-be');\r\nimages=fread(fp,inf,'unsigned char=\u003eunsigned char');\r\nfclose(fp);\r\nfprintf('Images:%i  rows:%i  cols:%i\\n',numImages,numRows,numCols); %raz\r\n\r\nimages=reshape(images,numCols,numRows,numImages);\r\nimages=permute(images,[2 1 3]); \r\n\r\nimages=reshape(images,size(images,1)*size(images,2),size(images,3)); %raz Will be reverted\r\nimages=double(images)/255;\r\n \r\nend %loadMNISTImages\r\n\r\nfunction labels=loadMNISTLabels(filename)\r\n%\r\nfp=fopen(filename,'rb');\r\nassert(fp~=-1,['Could not open', filename,'']);\r\nmagic=fread(fp,1,'int32',0,'ieee-be');\r\nassert(magic==2049,['Bad magic number in ', filename,'']);\r\nnumLabels=fread(fp,1,'int32',0,'ieee-be');\r\nlabels=fread(fp,inf,'unsigned char');\r\nassert(size(labels,1)==numLabels,'Mismatch in label count');\r\nfclose(fp);\r\nfprintf('Labels:%i\\n',numLabels); %raz\r\n\r\n\r\nend %loadMNISTLabels\r\n%}","test_suite":"%%\r\n%Google Drive Dowloads need to come from shared files\r\n% Tweak link: file/d/ to uc?export=download\u0026id=   while removing /view?usp=sharing\r\n% https://drive.google.com/file/d/1v3GsGgP3p905wzdvUqypL_-djYmxiyzK/view?usp=sharing\r\n% https://drive.google.com/uc?export=download\u0026id=1v3GsGgP3p905wzdvUqypL_-djYmxiyzK\r\n fnameTestI='Test_images.mat'; %load('Test_images.mat') creates images(28,28,10000) 1.6MB\r\n fnameTrainI='Train_images.mat'; %load('Train_images.mat') creates images(28,28,60000)  9.9MB\r\n fnameTestL='Test_labels.mat'; %load('Test_images.mat') creates labels(10000,1) 5KB\r\n fnameTrainL='Train_labels.mat'; %load('Train_images.mat') creates labels(60000,1) 30KB\r\n \r\n urlTeI='https://drive.google.com/uc?export=download\u0026id=10ReGWlfSvr9p6uq6FQlqw6vw3UXgWo57';\r\n urlTeL='https://drive.google.com/uc?export=download\u0026id=105zTcVgItZ2JjFiUkJulU33R7lXNl29-';\r\n urlTrI='https://drive.google.com/uc?export=download\u0026id=1HJZssH6_9OcQ8mXwS_DtvsS_Kk86BDFY';\r\n urlTrL='https://drive.google.com/uc?export=download\u0026id=1KNTn2eNXbQkQJNe6xhO1LMmvkDRP-XLq';\r\n \r\n % fn.mat  https://drive.google.com/file/d/10GsOZTIjzMIuO7xAYIqLT1zIq9Cyubl-/view?usp=drive_link\r\n % Google Gives warning thus aborts urlwrite\r\n %\r\n %fname='Mnist_Test_images.pdf'\r\n %Fake name of .pdf on GoogleDrive,  write as a mat\r\n \r\n %url='https://drive.google.com/file/d/1mgxzsmVQNXgqHEdd61QR2r0STm3N9lgG/view?usp=drive_link';\r\n %ptr=strfind(url,'/view'); % Tweaking the url\r\n %url(ptr:end)=[];\r\n %url=strrep(url,'file/d/','uc?export=download\u0026id=');\r\n \r\n tic\r\n urlwrite(urlTeI,fnameTestI); %Writing GoogleDrive MNIST_Test_images.pdf  Test_images.mat\r\n fprintf('Download 1.6MB Time: %.1f  sec\\n',toc); %1.6MB download Time, about 1.5 sec\r\n \r\n tic\r\n urlwrite(urlTeL,fnameTestL); %Writing GoogleDrive MNIST_Test_labels.pdf  Test_labels.mat\r\n fprintf('Download 5KB Time: %.1f  sec\\n',toc); %5KB download Time, about .5 sec\r\n \r\n global labels images \r\n \r\n load('Test_images'); % images [28,28,10000] uint8\r\n load('Test_labels'); % labels [10000,1] uint8 values 0:9\r\n \r\n %Showing a Label and an image from Mnist\r\n ptr=randi(10000);\r\n fprintf('Label:%i\\n',labels(ptr));\r\n figure(1);imagesc(images(:,:,ptr)); colormap gray;\r\n \r\n \r\nvalid=1;\r\nassert(valid)\r\n%%\r\n%Showing a Label and an image from Mnist\r\n global labels images\r\n valid=1;\r\n ptr=randi(10000);\r\n fprintf('Label:%i\\n',labels(ptr));\r\n m=double(images(:,:,ptr))/255;\r\n figure(2);imagesc(m); colormap gray;\r\n \r\n K=repmat([0 0 .5 1 1 1 .5 0 0],9,1); % Vert Bar\r\n mValidConv2=create_ValidConv2(m,K);\r\n figure(3);imagesc(mValidConv2); colormap gray;\r\n mc=conv2(m,K,'same');\r\n if ~isequal(mc(5:end-4,5:end-4),mValidConv2)\r\n  valid=0;\r\n end\r\n \r\nassert(valid)\r\n\r\n%%\r\n%Showing a Label and an image from Mnist\r\n global labels images\r\n valid=1;\r\n ptr=randi(10000);\r\n fprintf('Label:%i\\n',labels(ptr));\r\n m=double(images(:,:,ptr))/255;\r\n figure(2);imagesc(m); colormap gray;\r\n \r\n K=repmat([0 0 .5 1 1 1 .5 0 0]',1,9); %Horiz Bar\r\n mValidConv2=create_ValidConv2(m,K);\r\n figure(3);imagesc(mValidConv2); colormap gray;\r\n mc=conv2(m,K,'same');\r\n if ~isequal(mc(5:end-4,5:end-4),mValidConv2)\r\n  valid=0;\r\n end\r\n \r\nassert(valid)\r\n\r\n%%\r\n%Showing a Label and an image from Mnist\r\n global labels images\r\n valid=1;\r\n m=rand(24);\r\n K=repmat([0 .5 1 1 1 .5 0]',1,7); %Horiz Bar\r\n mValidConv2=create_ValidConv2(m,K)\r\n mc=conv2(m,K,'same');\r\n if ~isequal(mc(4:end-3,4:end-3),mValidConv2)\r\n  valid=0;\r\n end\r\n \r\nassert(valid)\r\n\r\n%%\r\n%Showing a Label and an image from Mnist\r\n global labels images\r\n valid=1;\r\n m=rand(8);\r\n K=ones(3)/9;\r\n mValidConv2=create_ValidConv2(m,K)\r\n mc=conv2(m,K,'same');\r\n if ~isequal(mc(2:end-1,2:end-1),mValidConv2)\r\n  valid=0;\r\n end\r\n \r\nassert(valid)\r\n\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":3097,"edited_by":3097,"edited_at":"2023-08-17T19:33:19.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-08-17T14:03:38.000Z","updated_at":"2024-11-12T13:42:48.000Z","published_at":"2023-08-17T19:33:20.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis challenge is to return only the Valid portion of a 2-D convolution. Valid is deemed to be where all elements of the kernel are applied against the image. The (1,1) point with a ones(3) kernel would be invalid while point (2,2) would return a Valid convolution value. The images will be even-square,m, and the kernels will be odd-square,K.The m=ones(6) and K=ones(3) would return a 4x4 matrix of 9s.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003emValidConv2=create_ValidConv2(m,K)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn neural net processing of the Mnist database of digits(0-9) one Convolutional Neural Network method uses 9x9 kernels on the 28x28 images to return the Valid 20x20 central core for the next processing step. The third image includes a black border of four around Valid to maintain scale.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"189\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"252\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"189\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"252\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"189\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"252\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId3\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe entire Matlab code from \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.youtube.com/watch?v=ZOXOwYUVCqw\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eConvolutional Neural Networks in Matlab by Nuruzzaman Faruqui\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e , a Matlab Neural Net Tutorial for Mnist processing, is included in the function template. Loading the Mnist Train/Test Images/Labels from posted MAT files or \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eTHE MNIST DATABASE of handwritten digits\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e are provided. The Neural Net tutorial explains Neural Net processing for Digit Recognition. The neural net training method uses 784 input nodes,  20 convolutions(9x9), ReLU, Pooling, batch sampling, single hidden layer of 100 nodes, updating parameters via backwards propagation, and updating convolution kernels. The digit prediction accuracy is \u0026gt;94% after 50s of training. The final feature kernels are very amorphous and 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Nets: Activation functions","description":"Return values of selected Activation function type for value,vector, and matrices.\r\ny=Activation(x,id); where id is 1:4 for ReLU, sigmoid, hyperbolic_tan, Softmax\r\nReLU: Rectified Linear Unit, clips negatives  max(0,x)   Trains faster than sigmoid\r\nSigmoid: Exponential normalization [0:1]      \r\nHyperTan: Normalization[-1:1]   tanh(x)\r\nSoftmax: Normalizes output sum to 1, individual values [0:1]      Used on Output node\r\n\r\nWorking though a series of Neural Net challenges from Perceptron, Hidden Layers, Back Propogation, ..., to the Convolutional Neural Net/Training for Handwritten Digits from Mnist. \r\nMight take a day or two  to completely cover Neural Nets in a Matlab centric fashion. \r\nEssentially Out=Softmax(ReLU(X*W)*WP)","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: 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0px; perspective-origin: 252.5px 8px; transform-origin: 252.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eReturn values of selected Activation function type for value,vector, and matrices.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 240.5px 8px; transform-origin: 240.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ey=Activation(x,id); where id is 1:4 for ReLU, sigmoid, hyperbolic_tan, Softmax\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 253.5px 8px; transform-origin: 253.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eReLU: Rectified Linear Unit, clips negatives  max(0,x)   Trains faster than sigmoid\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 137px 8px; transform-origin: 137px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSigmoid: Exponential normalization [0:1]      \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 72.5px; height: 19.5px;\" width=\"72.5\" height=\"19.5\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 120.5px 8px; transform-origin: 120.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHyperTan: Normalization[-1:1]   tanh(x)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 192px 8px; transform-origin: 192px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSoftmax: Normalizes output sum to 1, individual values [0:1]   \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 43px; height: 19.5px;\" width=\"43\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 73.5px 8px; transform-origin: 73.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e   Used on Output node\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 352.5px 8px; transform-origin: 352.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWorking though a series of Neural Net challenges from Perceptron, Hidden Layers, Back Propogation, ..., to the Convolutional Neural Net/Training for Handwritten Digits from Mnist. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 265px 8px; transform-origin: 265px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eMight take a day or two  to completely cover Neural Nets in a Matlab centric fashion. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 130px 8px; transform-origin: 130px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eEssentially Out=Softmax(ReLU(X*W)*WP)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = Activation(x,id)\r\n%id/function 1/ReLU 2/Sigmoid 3/Hyperbolictan 4/Softmax\r\n%x may be a point, vector or matrix\r\n  y = x;\r\nend","test_suite":"%%\r\nvalid=1;\r\nx = 2;\r\ny = Activation(x,1);\r\nif y~=max(0,x),valid=0;end\r\ny = Activation(x,2);\r\nif y~=1./(1+exp(-x)),valid=0;end\r\ny = Activation(x,3);\r\nif y~=tanh(x),valid=0;end\r\ny = Activation(x,4);\r\nif y~=1,valid=0;end\r\nassert(valid)\r\n%%\r\nvalid=1;\r\nx = [-1 0 1 2];\r\ny = Activation(x,1);\r\nif y~=max(0,x),valid=0;end\r\ny = Activation(x,2);\r\nif y~=1./(1+exp(-x)),valid=0;end\r\ny = Activation(x,3);\r\nif y~=tanh(x),valid=0;end\r\ny = Activation(x,4);\r\nif y~=exp(x)./sum(exp(x)),valid=0;end\r\nassert(valid)\r\n%%\r\nvalid=1;\r\nx = [-1 0 1 2;.5 .25 -2 5];\r\ny = Activation(x,1);\r\nif y~=max(0,x),valid=0;end\r\ny = Activation(x,2);\r\nif y~=1./(1+exp(-x)),valid=0;end\r\ny = Activation(x,3);\r\nif y~=tanh(x),valid=0;end\r\ny = Activation(x,4);\r\nif y~=exp(x)./sum(sum(exp(x))),valid=0;end\r\nassert(valid)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":3097,"edited_by":3097,"edited_at":"2023-08-19T14:59:54.000Z","deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-08-19T14:02:05.000Z","updated_at":"2024-11-11T13:31:29.000Z","published_at":"2023-08-19T14:59:56.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eReturn values of selected Activation function type for value,vector, and matrices.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ey=Activation(x,id); where id is 1:4 for ReLU, sigmoid, hyperbolic_tan, Softmax\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eReLU: Rectified Linear Unit, clips negatives  max(0,x)   Trains faster than sigmoid\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSigmoid: Exponential normalization [0:1]      \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e1/(1+e^{-x})\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHyperTan: Normalization[-1:1]   tanh(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSoftmax: Normalizes output sum to 1, individual values [0:1]   \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ee^x/\\\\Sigma e^x\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e   Used on Output node\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWorking though a series of Neural Net challenges from Perceptron, Hidden Layers, Back Propogation, ..., to the Convolutional Neural Net/Training for Handwritten Digits from Mnist. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMight take a day or two  to completely cover Neural Nets in a Matlab centric fashion. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eEssentially Out=Softmax(ReLU(X*W)*WP)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":58887,"title":"Neural Net: Best Index of Prediction array","description":"The final ouput of a neural net application is a Prediction matrix/vector,P, that gives the probability of the input being of a set of N classes represented by the columns.\r\nFor the XOR function the input matrix is [0 0;0 1;1 0;1 1] with an expected output vector of [0;1;1;0]. Ouput of Zero would be represented by a higher likelihood in column 1 than column 2 of the Prediction matrix.\r\nGiven a P matrix [m,n] where there are m cases and n possible outcomes return peak value for each case and the index of the most likely outcome.\r\n[case_peak,case_idx]=Prediction(P)\r\nif P was [0.1 0.5 0.9;0.2 0.8 0.4] (2 cases with 3 possible outcomes 1:3) return case_peak=[0.9;0.8] and case_idx=[3;2]\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 234px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 117px; transform-origin: 407px 117px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 379px 8px; transform-origin: 379px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe final ouput of a neural net application is a Prediction matrix/vector,P, that gives the probability of the input being of a set of N classes represented by the columns.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 379.5px 8px; transform-origin: 379.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor the XOR function the input matrix is [0 0;0 1;1 0;1 1] with an expected output vector of [0;1;1;0]. Ouput of Zero would be represented by a higher likelihood in column 1 than column 2 of the Prediction matrix.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 378.5px 8px; transform-origin: 378.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven a P matrix [m,n] where there are m cases and n possible outcomes return peak value for each case and the index of the most likely outcome.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 113px 8px; transform-origin: 113px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e[case_peak,case_idx]=Prediction(P)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 373px 8px; transform-origin: 373px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eif P was [0.1 0.5 0.9;0.2 0.8 0.4] (2 cases with 3 possible outcomes 1:3) return case_peak=[0.9;0.8] and case_idx=[3;2]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [case_peak,case_idx]=Prediction(P)\r\n%P provides probability that an input is probably type n\r\n%P may represent [Prob_dog Prob_cat Prob_cow Prob_sheep] when trained on four anaimals\r\n%P may be a [1,n] prediction vector for a single case or\r\n%P may be an [m,n] prediction matrix of m cases\r\n case_peak=max(P);\r\n case_idx=find(P==max(P));\r\nend","test_suite":"%%\r\nvalid=1;\r\n%Binary functions AND/OR/XOR\r\n%input [0 0;0 1;1 0;1 1] cases\r\nPor=[.75 .25;.1 .9;.2 .8;.05 .95]; % [Prob-0 Prob-1] Notional values\r\n[case_peak,case_idx]=Prediction(Por);\r\nif ~isequal(case_peak,max(Por,[],2))\r\n valid=0;\r\nend\r\nfor i=1:size(Por,1)\r\n    if case_idx(i)~=find(Por(i,:)==max(Por(i,:)))\r\n     valid=0;\r\n    end\r\nend\r\n\r\n%input [0 0;0 1;1 0;1 1] cases\r\nPand=[1 0;.8 0;.9 .1;.1 .9]; %[Prob-0 Prob-1] Notional values\r\n[case_peak,case_idx]=Prediction(Pand);\r\nif ~isequal(case_peak,max(Pand,[],2))\r\n valid=0;\r\nend\r\nfor i=1:size(Pand,1)\r\n    if case_idx(i)~=find(Pand(i,:)==max(Pand(i,:)))\r\n     valid=0;\r\n    end\r\nend\r\n\r\nPxor=[.9 .2;.1 .8;.3 .8;.8 .1]; % [Prob-0 Prob-1] Notional values\r\n[case_peak,case_idx]=Prediction(Pxor);\r\nif ~isequal(case_peak,max(Pxor,[],2))\r\n valid=0;\r\nend\r\nfor i=1:size(Pxor,1)\r\n    if case_idx(i)~=find(Pxor(i,:)==max(Pxor(i,:)))\r\n     valid=0;\r\n    end\r\nend\r\n\r\n\r\n\r\nassert(valid)\r\n%%\r\nvalid=1;\r\n%input [dog;cat;cow;sheep] cases\r\n%[Prob-dog Prob-cat Prob-cow Prob-sheep] Notional values\r\nP=[.8 .3 .2 .1;.3 .9 .2 .1;.1 .1 .7 .2;.25 .3 .1 .6]; \r\n[case_peak,case_idx]=Prediction(P);\r\nif ~isequal(case_peak,max(P,[],2))\r\n valid=0;\r\nend\r\nfor i=1:size(P,1)\r\n    if case_idx(i)~=find(P(i,:)==max(P(i,:)))\r\n     valid=0;\r\n    end\r\nend\r\n\r\nassert(valid)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":3097,"edited_by":3097,"edited_at":"2023-08-19T23:47:40.000Z","deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-08-19T22:24:20.000Z","updated_at":"2024-11-18T00:32:01.000Z","published_at":"2023-08-19T23:47:40.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe final ouput of a neural net application is a Prediction matrix/vector,P, that gives the probability of the input being of a set of N classes represented by the columns.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor the XOR function the input matrix is [0 0;0 1;1 0;1 1] with an expected output vector of [0;1;1;0]. Ouput of Zero would be represented by a higher likelihood in column 1 than column 2 of the Prediction matrix.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a P matrix [m,n] where there are m cases and n possible outcomes return peak value for each case and the index of the most likely outcome.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e[case_peak,case_idx]=Prediction(P)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eif P was [0.1 0.5 0.9;0.2 0.8 0.4] (2 cases with 3 possible outcomes 1:3) return case_peak=[0.9;0.8] and case_idx=[3;2]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":58892,"title":"Neural Net: Calculate Perceptron","description":"This challenge is to calculate the Neural Net Perceptron value,P, given X, WH, and WP using ReLU on the hidden layer. This example is for two inputs, two hidden nodes, and a single output. No offset terms are applied.\r\n \r\nThe function template includes the code to create this figure using Matlab Latex","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 626.85px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 313.425px; transform-origin: 407px 313.425px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 375.5px 8px; transform-origin: 375.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis challenge is to calculate the Neural Net Perceptron value,P, given X, WH, and WP using ReLU on the hidden layer. This example is for two inputs, two hidden nodes, and a single output. No offset terms are applied.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 545.85px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 272.925px; text-align: left; transform-origin: 384px 272.925px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline\" 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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 250px 8px; transform-origin: 250px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe function template includes the code to create this figure using Matlab Latex\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function P=Calc_Perceptron(X,WH,WP)\r\n%The P value in this case is a single value\r\n%No ReLU,Softmax, or Sigmoid applied to the output P\r\n  P=0;\r\nend\r\n\r\n%The figure was generated using Matlab and Latex\r\n%{\r\nfunction perceptron\r\n% put figure code into cody\r\nfigure(1);clf;\r\nplot([0;140;140;0;0],[-5;-5;100;100;-5],'k','linewidth',2);hold on\r\nxticks([]);yticks([]); %Tciks/Labels off\r\n\r\naxis equal;\r\naxis tight\r\n\r\n\r\nr = 10;\r\nphi = 0:0.01:2*pi;\r\ncxA = r*cos(phi);\r\ncyA = r*sin(phi);\r\n\r\nrxA=[0 2*r 2*r   0 0]';\r\nryA=[0   0 2*r 2*r 0]';\r\n\r\npatch(cxA+10,cyA+80,'y');text(10-2,80,'X_{1}','Fontsize',20);\r\npatch(cxA+10,cyA+20,'y');text(10-2,20,'X_{2}','Fontsize',20);\r\n\r\npatch(cxA+80,cyA+80,'y');text(80-6,94,'H_{1}','Fontsize',20);text(80-8,80,'\\Sigma','Fontsize',30);\r\npatch(cxA+80,cyA+20,'y');text(80-6,34,'H_{2}','Fontsize',20);text(80-8,20,'\\Sigma','Fontsize',30);\r\n\r\npatch(cxA+130,cyA+50,'y');text(130-2,50,'P','Fontsize',20);\r\n\r\npatch(rxA+80,ryA+70,'y');text(85,80,'ReLU','Fontsize',20);text(102,88,'Y_{1}','Fontsize',20);\r\npatch(rxA+80,ryA+10,'y');text(85,20,'ReLU','Fontsize',20);text(102,32,'Y_{2}','Fontsize',20);\r\n\r\nquiver(20,20,55,0,'k','LineWidth',3.5); % line arrowhead x,y,dx,dy,  VectorLine draw\r\nquiver(20,80,55,0,'k','LineWidth',3.5); % line arrowhead x,y,dx,dy,  VectorLine draw\r\nquiver(20,20,58.5,58.5,'k','LineWidth',3.5); % line arrowhead x,y,dx,dy,  VectorLine draw\r\nquiver(20,80,58.5,-58.5,'k','LineWidth',3.5); % line arrowhead x,y,dx,dy,  VectorLine draw\r\n\r\nquiver(100,20,25,25,'k','LineWidth',3.5,'MaxHeadSize',.5); % line arrowhead x,y,dx,dy,  VectorLine draw\r\nquiver(100,80,25,-25,'k','LineWidth',3.5,'MaxHeadSize',.5); % line arrowhead x,y,dx,dy,  VectorLine draw\r\n\r\ntext(40,85,'WH_{11}','Fontsize',20);\r\ntext(20,65,'WH_{12}','Fontsize',20);\r\ntext(40,25,'WH_{22}','Fontsize',20);\r\ntext(20,38,'WH_{21}','Fontsize',20);\r\n\r\ntext(115,68,'WP_{11}','Fontsize',20);\r\ntext(115,28,'WP_{21}','Fontsize',20);\r\n\r\nstr='$$ X=\\left[\\matrix{ X_{1} \u0026 X_{2}} \\right]  $$'; %valid\r\ntext(1,50,str,'Interpreter','latex','Fontsize',20);\r\n\r\nstr='$$ WH=\\left[\\matrix{ WH_{11} \u0026 WH_{12}\\cr WH_{21} \u0026 WH_{22} } \\right]  $$'; %valid\r\ntext(1,5,str,'Interpreter','latex','Fontsize',20);\r\n\r\nstr='$$ H=\\left[\\matrix{ H_{1} \u0026 H_{2}} \\right]  $$'; %valid\r\ntext(75,65,str,'Interpreter','latex','Fontsize',20);\r\n\r\nstr='$$ ReLU(H)=Y  $$'; %valid\r\ntext(75,58,str,'Interpreter','latex','Fontsize',20);\r\n\r\nstr='$$ Y=\\left[\\matrix{ Y_{1} \u0026 Y_{2}} \\right]  $$'; %valid\r\ntext(75,51,str,'Interpreter','latex','Fontsize',20);\r\n\r\nstr='$$ X*WH=H  $$'; %valid\r\ntext(60,5,str,'Interpreter','latex','Fontsize',20);\r\n\r\nstr='$$ Y*WP=P  $$'; %valid\r\ntext(60,0,str,'Interpreter','latex','Fontsize',20);\r\n\r\nstr='$$ WP=\\left[\\matrix{ WP_{11}\\cr WP_{21} } \\right]  $$'; %valid\r\ntext(100,5,str,'Interpreter','latex','Fontsize',20);\r\n\r\n\r\n\r\nend % Perceptron \r\n%}\r\n","test_suite":"%%\r\nX=[1 2]; WH=[1 2;3 4];WP=[.5; -1];\r\nP=Calc_Perceptron(X,WH,WP);\r\nPexp=-6.5;\r\nvalid=isequal(P,Pexp);\r\nassert(valid)\r\n%%\r\nX=[3 1.5]; WH=[1 -3;3 4];WP=[1; 2];\r\nP=Calc_Perceptron(X,WH,WP);\r\nPexp=7.5;\r\nvalid=isequal(P,Pexp);\r\nassert(valid)\r\n%%\r\nX=[-.5 .5]; WH=[4 2;1 4];WP=[.1; .4];\r\nP=Calc_Perceptron(X,WH,WP);\r\nPexp=0.4;\r\nvalid=isequal(P,Pexp);\r\nassert(valid)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":3097,"edited_by":3097,"edited_at":"2023-08-20T22:48:06.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-08-20T22:16:25.000Z","updated_at":"2023-08-20T22:48:07.000Z","published_at":"2023-08-20T22:48:07.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis challenge is to calculate the Neural Net Perceptron value,P, given X, WH, and WP using ReLU on the hidden layer. This example is for two inputs, two hidden nodes, and a single output. No offset terms are applied.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"864\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"1228\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe function template includes the code to create this figure using Matlab 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"rela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Net: Calculate Bias Single Perceptron (AND/NAND/OR/NOR/XOR)","description":"This challenge is to calculate the Neural Net Bias Perceptron vector,P, given X, WH, and WP using ReLU on the hidden layer. Test Cases will be all two input conditions for functions  XOR, AND, NAND, OR, and NOR.\r\nSince X wll be a 4x3 matrix the output P will be a 4x1 vector with values 0 or 1.\r\n \r\nThe function template includes the code to create this figure using Matlab Latex","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 664.65px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 332.325px; transform-origin: 407px 332.325px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 374px 8px; transform-origin: 374px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis challenge is to calculate the Neural Net Bias Perceptron vector,P, given X, WH, and WP using ReLU on the hidden layer. Test Cases will be all two input conditions for functions  XOR, AND, NAND, OR, and NOR.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 243.5px 8px; transform-origin: 243.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSince X wll be a 4x3 matrix the output P will be a 4x1 vector with values 0 or 1.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 553.65px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 276.825px; text-align: left; transform-origin: 384px 276.825px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline\" 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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 250px 8px; transform-origin: 250px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe function template includes the code to create this figure using Matlab Latex\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function P=Calc_Single_Bias_Perceptron(X,WH,WP)\r\n%The P value in this case is a single value for each case\r\n%X will be four rows and three columns\r\n%No ReLU,Softmax, or Sigmoid applied to the output P\r\n  P=[0 0 0 0]';\r\nend\r\n\r\n%The figure was generated using Matlab and Latex\r\n%{\r\nfunction perceptron_bias\r\nfigure(1);clf;\r\nplot([0;140;140;0;0],[-5;-5;100;100;-5],'k','linewidth',2);hold on\r\nxticks([]);yticks([]); %Ticks/Labels off\r\n\r\naxis equal;\r\naxis tight\r\n\r\nr = 10;\r\nphi = 0:0.01:2*pi;\r\ncxA = r*cos(phi);\r\ncyA = r*sin(phi);\r\n\r\nrxA=[0 2*r 2*r   0 0]';\r\nryA=[0   0 2*r 2*r 0]';\r\n\r\ntext(1,95,'Single Bias Perceptron','Fontsize',20);\r\n\r\npatch(cxA+10,cyA+80,'y');text(10-2,80,'X_{1}','Fontsize',20);\r\npatch(cxA+10,cyA+20,'y');text(10-2,20,'X_{2}','Fontsize',20);\r\n\r\npatch(cxA+80,cyA+80,'y');text(80-6,94,'H_{1}','Fontsize',20);text(80-8,80,'\\Sigma','Fontsize',30);\r\npatch(cxA+80,cyA+20,'y');text(80-6,34,'H_{2}','Fontsize',20);text(80-8,20,'\\Sigma','Fontsize',30);\r\n\r\npatch(cxA+130,cyA+50,'y');text(130-2,50,'P','Fontsize',20);\r\n\r\npatch(rxA+80,ryA+70,'y');text(85,80,'ReLU','Fontsize',20);text(100,92,'Y_{1}','Fontsize',20);\r\npatch(rxA+80,ryA+10,'y');text(85,20,'ReLU','Fontsize',20);text(100,32,'Y_{2}','Fontsize',20);\r\n\r\nquiver(20,20,55,0,'k','LineWidth',3.5); % line arrowhead x,y,dx,dy,  VectorLine draw\r\nquiver(20,80,55,0,'k','LineWidth',3.5); % line arrowhead x,y,dx,dy,  VectorLine draw\r\nquiver(20,20,58.5,58.5,'k','LineWidth',3.5); % line arrowhead x,y,dx,dy,  VectorLine draw\r\nquiver(20,80,58.5,-58.5,'k','LineWidth',3.5); % line arrowhead x,y,dx,dy,  VectorLine draw\r\n\r\nquiver(100,20,25,25,'k','LineWidth',3.5,'MaxHeadSize',.5); % line arrowhead x,y,dx,dy,  VectorLine draw\r\nquiver(100,80,25,-25,'k','LineWidth',3.5,'MaxHeadSize',.5); % line arrowhead x,y,dx,dy,  VectorLine draw\r\n%quiver(100,80,25,-25,'k','LineWidth',3.5,'Color','r'); % line arrowhead x,y,dx,dy,  VectorLine draw\r\nquiver(53,93,20,-10,'k','LineWidth',3.5,'MaxHeadSize',.6); text(53-8,92,'bH_{31}','Fontsize',20);\r\nquiver(60,5,13,10,'k','LineWidth',3.5,'MaxHeadSize',.7); text(60-6,4,'bH_{32}','Fontsize',20);\r\nquiver(130,26,0,15,'k','LineWidth',3.5,'MaxHeadSize',.8); text(130-6,25,'bP_{31}','Fontsize',20);\r\n\r\n\r\ntext(30,85,'WH_{11}','Fontsize',20);\r\ntext(20,65,'WH_{12}','Fontsize',20);\r\ntext(40,25,'WH_{22}','Fontsize',20);\r\ntext(20,38,'WH_{21}','Fontsize',20);\r\n\r\ntext(110,73,'WP_{11}','Fontsize',20);\r\ntext(107,23,'WP_{21}','Fontsize',20);\r\n\r\nstr='$$ X=\\left[\\matrix{ X_{1} \u0026 X_{2} \u0026 1} \\right]  $$'; %valid\r\ntext(1,50,str,'Interpreter','latex','Fontsize',20);\r\n\r\nstr='$$ WH=\\left[\\matrix{ WH_{11} \u0026 WH_{12} \u0026 0 \\cr WH_{21} \u0026 WH_{22} \u0026 0 \\cr bH_{31} \u0026 bH_{32} \u0026 1 } \\right]  $$'; %valid\r\ntext(1,3,str,'Interpreter','latex','Fontsize',20);\r\n\r\nstr='$$ H=\\left[\\matrix{ H_{1} \u0026 H_{2} \u0026 1} \\right]  $$'; %valid\r\ntext(75,65,str,'Interpreter','latex','Fontsize',20);\r\n\r\nstr='$$ ReLU(H)=Y  $$'; %valid\r\ntext(75,58,str,'Interpreter','latex','Fontsize',20);\r\n\r\nstr='$$ Y=\\left[\\matrix{ Y_{1} \u0026 Y_{2} \u0026 1} \\right]  $$'; %valid\r\ntext(75,51,str,'Interpreter','latex','Fontsize',20);\r\n\r\nstr='$$ X*WH=H  $$'; %valid\r\ntext(80,5,str,'Interpreter','latex','Fontsize',20);\r\n\r\nstr='$$ Y*WP=P  $$'; %valid\r\ntext(80,0,str,'Interpreter','latex','Fontsize',20);\r\n\r\nstr='$$ WP=\\left[\\matrix{ WP_{11}\\cr WP_{21} \\cr bP_{31} } \\right]  $$'; %valid\r\ntext(110,5,str,'Interpreter','latex','Fontsize',20);\r\n\r\nend %perceptron_bias\r\n\r\n%}","test_suite":"%%\r\n%XOR\r\nX=[0 0 1;0 1 1;1 0 1;1 1 1]; %All four cases  P will have results from all four input sets\r\nWH=[1 1 0;1 1 0;0 -1 1];\r\nWP=[1;-2;0];\r\n\r\nP=Calc_Single_Bias_Perceptron(X,WH,WP)\r\nvalid=isequal(P,[0 1 1 0]')\r\nassert(valid)\r\n%%\r\n%AND\r\nX=[0 0 1;0 1 1;1 0 1;1 1 1]; %All four cases  P will have results from all four input sets\r\nWH=[1 1 0;1 1 0;-1 -1 1];\r\nWP=[.5;.5;0];\r\n\r\nP=Calc_Single_Bias_Perceptron(X,WH,WP)\r\nvalid=isequal(P,[0 0 0 1]')\r\nassert(valid)\r\n%%\r\n%NAND\r\nX=[0 0 1;0 1 1;1 0 1;1 1 1]; %All four cases  P will have results from all four input sets\r\nWH=[1 1 0;1 1 0;-1 -1 1];\r\nWP=[-.5;-.5;1];\r\n\r\nP=Calc_Single_Bias_Perceptron(X,WH,WP)\r\nvalid=isequal(P,[1 1 1 0]')\r\nassert(valid)\r\n%%\r\n%OR\r\nX=[0 0 1;0 1 1;1 0 1;1 1 1]; %All four cases  P will have results from all four input sets\r\nWH=[1 -.5 0;-.5 1 0;0 0 1];\r\nWP=[1;1;0];\r\n\r\nP=Calc_Single_Bias_Perceptron(X,WH,WP)\r\nvalid=isequal(P,[0 1 1 1]')\r\nassert(valid)\r\n%%\r\n%NOR\r\nX=[0 0 1;0 1 1;1 0 1;1 1 1]; %All four cases  P will have results from all four input sets\r\nWH=[-1 -1 0;-1 -1 0;0.5 .5 1];\r\nWP=[1;1;0];\r\n\r\nP=Calc_Single_Bias_Perceptron(X,WH,WP)\r\nvalid=isequal(P,[1 0 0 0]')\r\nassert(valid)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":3097,"edited_by":3097,"edited_at":"2023-08-21T05:50:47.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-08-21T04:23:55.000Z","updated_at":"2023-08-21T05:50:47.000Z","published_at":"2023-08-21T05:50:47.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis challenge is to calculate the Neural Net Bias Perceptron vector,P, given X, WH, and WP using ReLU on the hidden layer. Test Cases will be all two input conditions for functions  XOR, AND, NAND, OR, and NOR.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSince X wll be a 4x3 matrix the output P will be a 4x1 vector with values 0 or 1.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"930\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"1303\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe function template includes the code to create this figure using Matlab 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.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Net: Back Propagation of Quad Output with Bias, ReLU","description":"This challenge is to return the WH_delta and WP_delta, given X, WH, WP, EPY using ReLU on the hidden layer and Softmax on the output layer. Test Cases will accumulate dWP and dWH to solve neural nets for Counter, Subtractor,Mux. Test Cases will have four output cases. ReLU performs well on multiple output cases.\r\n[dWP,dWH]=Neural_Back_Propagation_ReLU(X,WH,WP,EPY)\r\n \r\n \r\nThe matlab Latex code for making the Back Propagation chart included in template.\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 1230px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 615px; transform-origin: 407px 615px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 364px 8px; transform-origin: 364px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis challenge is to return the WH_delta and WP_delta, given X, WH, WP, EPY using ReLU on the hidden layer and Softmax on the output layer. Test Cases will accumulate dWP and dWH to solve neural nets for Counter, Subtractor,Mux. Test Cases will have four output cases. ReLU performs well on multiple output cases.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 192.5px 8px; transform-origin: 192.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e[dWP,dWH]=Neural_Back_Propagation_ReLU(X,WH,WP,EPY)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 529.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 264.75px; text-align: left; transform-origin: 384px 264.75px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline;width: 875px;height: 524px\" 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\" data-image-state=\"image-loaded\" width=\"875\" height=\"524\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 262px 8px; transform-origin: 262px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe matlab Latex code for making the Back Propagation chart included in template.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [dWP,dWH]=Neural_Back_Propagation_ReLU(X,WH,WP,EPY)\r\n%Comments/structure credit Christian Schröder\r\n% X will be single case [x1 x2 1]\r\n\r\n%Removing the comments below should make a working function\r\n\r\n  % Learning rate\r\n  %LR=1;\r\n  \r\n  % Forward pass\r\n  %H=X*WH; \r\n  % %HY=1./(1+exp(-H)); %[HY1 HY2 1]  Sigmoid\r\n  % %HY(:,end)=1; %Sigmoid\r\n  %HY=max(0,H); \r\n  \r\n  % Output layer, softmax activation function\r\n  %P=HY*WP;  %\r\n  %PY=exp(P)./sum(exp(P),2); %Softmax [PY1 PY2]\r\n  \r\n  % Backward pass\r\n  % Error\r\n  %ErrPY=EPY-PY; \r\n  \r\n  % Approx. changes for output layer\r\n  %dPY=PY.*(1-PY).*ErrPY;\r\n  %dWP=LR*HY'.*dPY;\r\n  \r\n  % Approx. changes for hidden layer\r\n  %dHY=HY.*(1-HY).*sum(WP.*dPY,2)';\r\n  %dWH=LR*X'.*dHY;\r\n  \r\nend % Neural_Back_Propagation_ReLU\r\n\r\n%Code to make the Back Prop chart\r\n%{\r\nfunction Back_Propagation_ReLU_Soft\r\n%Quad output classifier\r\n%Softmax y=exp(x)./sum(exp(x),2)\r\n\r\n% Back Propagation ReLU\r\n% https://www.youtube.com/watch?v=tUoUdOdTkRw\r\n% #1 Solved Example Back Propagation Algorithm Multi-Layer Perceptron Network by Dr. Mahesh Huddar\r\n% \r\n%                                                 Input     Expected Output\r\n%                                                 Cases         0 1 Logic Values/Classes\r\n% WH [0.2 -0.9 0  WP [ 9.5 -1.9 6.0 0.5  X [0 0 1  EPY [0 1 0 0  Case 1\r\n%     0.8 -0.1 0      -0.5  8.0 7.2 0.2     0 1 1       0 0 1 0  C2\r\n%     0.3  1.4 1]      3.5  6.4 3.6 9.6]    1 0 1       0 0 1 0  C3\r\n%                                           1 1 1]      1 0 0 0] C4\r\n% WH [WH11 WH12 0   WP [WP11 WP12 WP13 WP14\r\n%     WH21 WH22 0       WP21 WP22 WP23 WP24\r\n%     bH31 bH32 1]      bP31 bP32 bP33 bP34]\r\n% All four cases. Rows represent case(C)\r\n% HY =ReLU(X*WH)      PY = Softmax(HY*WP)                     ErrPY = EPY-PY \r\n% [0.3 1.4 1       [0.0000    0.8243    0.1750    0.0008    [-0.0000    0.1757   -0.1750   -0.0008\r\n%  1.1 1.3 1        0.0019    0.0078    0.9903    0.0001     -0.0019   -0.0078    0.0097   -0.0001\r\n%  0.5 0.5 1        0.0469    0.2000    0.4234    0.3297     -0.0469   -0.2000   -0.4234    0.6703\r\n%  1.3 0.4 1]       0.7942    0.0002    0.2018    0.0039]     0.2058   -0.0002   -0.2018   -0.0039]\r\n% \r\n% \r\n% d_j=o_j(1-o_j)(Truth_j-o_j) if j is an output layer\r\n% dPY=PY.*(1-PY).*ErrPY  thus dPY =[dPY_1 dPY_2]; C=case (rows 1 thru 4)\r\n% dPY=PY(1-PY)*ErrPY  [PY_C1*(1-PY_C1)*ErrPY_C1 PY_C2*(1-PY_C2)*ErrPY_C2]\r\n% dPY=PY.*(1-PY).*ErrPY   %Matlab per case [dPY1 dPY2]\r\n% -0.0000    0.0255   -0.0253   -0.0000  % All four cases \r\n% -0.0358   -0.5963    0.9413   -0.0001  1e-4 \r\n% -0.0021   -0.0320   -0.1034    0.1481\r\n%  0.0336   -0.0000   -0.0325   -0.0000\r\n%\r\n% gtw_ij=n*o_i*d_j, gtWP where o_i is Output(HY) and d_j is a delta(dPY)  \r\n% dWP=n*HY'.*dPY  %Matlab for a single case, n is learning rate set to 1 \r\n% n*[HY1;HY2;1].*[dPY1 dPY2]=n*[dPY1*HY1 dPY2*HY1  =gtWP \r\n%                               dPY1*HY2 dPY2*HY2  \r\n%                               dPY1*1   dPY2*1  ] \r\n% The WP values affecting P1/PY1 adjusted by dPY1. gtw=dWP\r\n% Cycle over all four cases\r\n% dWP=dWP+n*HY'.*dPY;  %Matlab combining single cases\r\n% [0 .0076 -.0076 0  [0 0 0 0   [-.0010 -.0160 -.0517 .0741  [.0437 0 -.0423 0\r\n%  0 .0356 -.0354 0   0 0 0 0    -.0010 -.0160 -.0517 .0741   .0135 0 -.0130 0\r\n%  0 .0255 -.0253 0]+ 0 0 0 0]+  -.0021 -.0320 -.1034 .1481]+ .0336 0 -.0325 0]\r\n% \r\n% d_j=o_j(1-o_j)Sigma_k(WP_jk*d_k) if j is a hidden layer, d_k is from next layer\r\n%   next layer WP and d terms combined and scaled by Hidden layer Output function\r\n%   Generate a dHY to apply against WH terms\r\n% dHY=HY.*(1-HY).*sum(WP.*dPY,2)'\r\n% dHY=HY(1-HY)*SumdW  \r\n% [HY_C1*(1-HY_C1)*SumdW_C1 HY_C2*(1-HY_C2)*SumdW_C2 HY_C3*(1-HY_C3)*SumdW_C3] where\r\n% SumdW_C1 = WP_11*dPY1+WP_12*dPY2   \r\n% SumdW_C2 = WP_21*dPY1+WP_22*dPY2   \r\n% SumdW_C3 = WP_31*dPY1+WP_32*dPY2 since HY_C3=1 this term is unused\r\n% dHY=HY.*(1-HY).*sum(WP.*dPY,2)'  % Matlab per case\r\n% dHY = [-.0420  -.0122 0  (9.5*0-1.9*.0255+6*-.0253+.5*0)=-.200 SumdW_11\r\n%                           (-.5*0+8*.0255+7.2*-.0253+.2*0)=.0218 SumdW_12\r\n%        -.0000 -0.0000 0\r\n%        -.1263 -0.2424 0\r\n%        -.0486  0.0602 0]\r\n%  -0.0420   -0.0122         0\r\n%  -0.7085   -0.7898         0  *1e-4\r\n%  -0.1263   -0.2424         0\r\n%  -0.0486   -0.0602         0\r\n% \r\n% \r\n% n*xc'.*dHy  % xc is a single row of x\r\n% dWH=n*XC'.*dHY   %Matlab single case\r\n% n*[XC1;XC2;1].*[dHY1 dHY2 dHY3]=\r\n% n*[dHY1*XC1 dHY2*XC1 dHY3*XC1  =gtWH \r\n%    dHY1*XC2 dHY2*XC2 dHY3*XC2\r\n%    dHY1*1   dHY2*1   dHY3*1 ]  since dHY3=0 end col is 0\r\n% dWH=dWH+n*XC'.*dHY; % matlab for accumulating cases\r\n% The WH values affecting H1/HY1 adjusted by dHY1. gtw=dWH\r\n% The WH values affecting H2/HY2 adjusted by dHY2\r\n% dWH=\r\n%  [ 0         0   0       [-.1263 -.2424 0  [-.0486   -.0602 0\r\n%    0         0   0           0       0  0   -.0486   -.0602 0\r\n%   -.042   -0.0122 0]+[0]+ -.1263 -.2424 0]+ -.0486   -.0602 0]\r\n\r\nf=figure(1);clf;\r\nf.Position=[1935 122 1459 873]; % Dual Monitor setting\r\n\r\nplot([0;160;160;0;0],[-5;-5;100;100;-5],'k','linewidth',2);hold on\r\nxticks([]);yticks([]); %Ticks/Labels off\r\n\r\naxis equal;\r\naxis tight\r\n\r\n% Back Propagation ReLU\r\n% https://www.youtube.com/watch?v=tUoUdOdTkRw\r\n% #1 Solved Example Back Propagation Algorithm Multi-Layer Perceptron Network by Dr. Mahesh Huddar\r\n\r\ntext(1,98,'Back Propagation ReLU','Fontsize',16);\r\ntext(37,98,'based upon #1 Solved Example Back Propagation Algorithm Multi-Layer Perceptron Network by Dr. Mahesh Huddar','Fontsize',12);\r\ntext(34,95,'https://www.youtube.com/watch?v=tUoUdOdTkRw ','Fontsize',12);\r\n\r\n% WH [0.2 -0.9 0  WP [ 9.5 -1.9 6.0 0.5  X [0 0 1  EPY [0 1 0 0  Case 1\r\n%     0.8 -0.1 0      -0.5  8.0 7.2 0.2     0 1 1       0 0 1 0  C2\r\n%     0.3  1.4 1]      3.5  6.4 3.6 9.6]    1 0 1       0 0 1 0  C3\r\n%                                           1 1 1]      1 0 0 0] C4\r\ntext(5,95,'WH','Fontsize',12);\r\nstr='$$ \\left[\\matrix{ .2 \u0026 -.9 \u0026 0 \\cr .8 \u0026 -.1 \u0026 0 \\cr .3 \u0026 1.4 \u0026 1 } \\right]  $$'; \r\ntext(1,89,str,'Interpreter','latex','Fontsize',11);\r\n\r\ntext(21,95,'WP','Fontsize',12);\r\nstr='$$ \\left[\\matrix{ 9.5 \u0026 -1.9 \u0026 6.0 \u0026 0.5 \\cr -.5 \u0026 8.0 \u0026 7.2 \u00260.2 \\cr 3.5 \u0026 6.4 \u0026 3.6 \u0026 9.6 } \\right]  $$'; \r\ntext(18,89,str,'Interpreter','latex','Fontsize',11);\r\n\r\nstr='$$ X=\\left[\\matrix{ 0 \u0026 0 \u0026 1 \\cr 0 \u0026 1 \u00261 \\cr 1 \u0026 0 \u0026 1 \\cr 1 \u0026 1 \u0026 1 } \\right]  $$'; \r\ntext(42,88,str,'Interpreter','latex','Fontsize',11);\r\n\r\nstr='$$ EPY=\\left[\\matrix{ 0\u00261\u00260\u00260 \\cr 0\u00260\u00261\u00260 \\cr 0\u00260\u00260\u00261 \\cr 1\u00260\u00260\u00260 } \\right]  $$'; \r\ntext(58,88,str,'Interpreter','latex','Fontsize',11);\r\n\r\n% WH [WH11 WH12 0   WP [WP11 WP12 WP13 WP14\r\n%     WH21 WH22 0       WP21 WP22 WP23 WP24\r\n%     bH31 bH32 1]      bP31 bP32 bP33 bP34]\r\n% str='$$ WH=\\left[\\matrix{ WH_{11} \u0026 WH_{12} \u0026 0 \\cr WH_{21} \u0026 WH_{22} \u0026 0 \\cr bH_{31} \u0026 bH_{32} \u0026 1 } \\right]  $$'; \r\n% text(1,80,str,'Interpreter','latex','Fontsize',12);\r\ntext(93,95,'WH','Fontsize',12);\r\nstr='$$ \\left[\\matrix{ WH_{11} \u0026 WH_{12} \u0026 0 \\cr WH_{21} \u0026 WH_{22} \u0026 0 \\cr bH_{31} \u0026 bH_{32} \u0026 1 } \\right]  $$'; \r\ntext(83,89,str,'Interpreter','latex','Fontsize',12);\r\n\r\nstr='$$ WP=\\left[\\matrix{ WP_{11} \u0026 WP_{12} \u0026 WP_{13} \u0026 WP_{14} \\cr WP_{21} \u0026 WP_{22} \u0026 WP_{23} \u0026 WP_{24} \\cr bP_{31} \u0026 bP_{32} \u0026 bP_{33} \u0026 bP_{34} } \\right]  $$'; \r\ntext(107,89,str,'Interpreter','latex','Fontsize',12);\r\n\r\n% All four cases. Rows represent case(C)\r\n% HY =ReLU(X*WH)      PY = Softmax(HY*WP)                     ErrPY = EPY-PY \r\n% [0.3 1.4 1       [0.0000    0.8243    0.1750    0.0008    [-0.0000    0.1757   -0.1750   -0.0008\r\n%  1.1 1.3 1        0.0019    0.0078    0.9903    0.0001     -0.0019   -0.0078    0.0097   -0.0001\r\n%  0.5 0.5 1        0.0469    0.2000    0.4234    0.3297     -0.0469   -0.2000   -0.4234    0.6703\r\n%  1.3 0.4 1]       0.7942    0.0002    0.2018    0.0039]     0.2058   -0.0002   -0.2018   -0.0039]\r\ntext(1,83,'All four cases. Rows represent case(C)','Fontsize',12);\r\ntext(0.5,80,'HY =ReLU(X*WH)        PY = Softmax(HY*WP)                ErrPY = EPY-PY','Fontsize',10);\r\nstr='$$ \\left[\\matrix{ 0.3 \u0026 1.4 \u0026 1 \\cr 1.1 \u0026 1.3 \u0026 1 \\cr 0.5 \u0026 0.5 \u0026 1 \\cr 1.3 \u0026 0.4 \u0026 1 } \\right]  $$'; \r\ntext(0,73,str,'Interpreter','latex','Fontsize',10);\r\nstr='$$ \\left[\\matrix{ .0000 \u0026 .8243 \u0026 .1750 \u0026 .0008 \\cr .0019 \u0026 .0078 \u0026 .9903 \u0026 .0001 \\cr .0469 \u0026 .2000 \u0026 .4234 \u0026 .3297 \\cr .7942 \u0026 .0002 \u0026 .2018 \u0026 .0039 } \\right]  $$'; \r\ntext(14,73,str,'Interpreter','latex','Fontsize',11);\r\nstr='$$ \\left[\\matrix{ -.0000 \u0026 .1757 \u0026 -.1750 \u0026 -.0008  \\cr -.0019  \u0026 -.0078 \u0026 .0097 \u0026 -.0001 \\cr -.0469 \u0026 -.2000 \u0026 -.4234 \u0026 0.6703 \\cr .2058 \u0026 -.0002 \u0026 -.2018 \u0026 -.0039 } \\right]  $$'; \r\ntext(43,73,str,'Interpreter','latex','Fontsize',11);\r\n\r\n% d_j=o_j(1-o_j)(Truth_j-o_j) if j is an output layer\r\n% dPY=PY.*(1-PY).*ErrPY  thus dPY =[dPY_1 dPY_2]; C=case (rows 1 thru 4)\r\n% dPY=PY(1-PY)*ErrPY  [PY_C1*(1-PY_C1)*ErrPY_C1 ...  PY_C4*(1-PY_C4)*ErrPY_C4]\r\n% dPY=PY.*(1-PY).*ErrPY   %Matlab per case [dPY1 dPY2]\r\n\r\n% -0.0000    0.0255   -0.0253   -0.0000  % All four cases \r\n% -0.0358   -0.5963    0.9413   -0.0001  1e-4 \r\n% -0.0021   -0.0320   -0.1034    0.1481\r\n%  0.0336   -0.0000   -0.0325   -0.0000\r\n\r\ntext(1,65,'\\delta_{j}=o_{j}(1-o_{j})(Truth_{j}-o_{j}) if j is an Output layer','Fontsize',14);\r\ntext(1,60,'\\deltaPY=PY*(1-PY)*ErrPY  thus \\deltaPY =[\\deltaPY_{1}   \\deltaPY_{2}   \\deltaPY_{3}   \\deltaPY_{4}]','Fontsize',14);\r\ntext(1,56,'\\deltaPY=[ PY_{C1}*(1-PY_{C1})*ErrPY_{C1} ... PY_{C4}*(1-PY_{C4})*ErrPY_{C4} ]','Fontsize',14);\r\ntext(1,52,'dPY=PY.*(1-PY).*ErrPY','Fontsize',14,'Color','b');\r\ntext(32,52,'%Matlab per case [dPY1 dPY2 dPY3 dPY4]','Fontsize',12,'Color','b');\r\ntext(43,49,'% All four cases','Fontsize',12);\r\ntext(43,45.7,' [-.0358 -.5963 .9413 -.0001]*1E-4','Fontsize',12);\r\nstr='$$ \\left[\\matrix{ -.0000 \u0026 0.0255 \u0026 -.0253 \u0026 -.0000 \\cr -.0000 \u0026 -.0000 \u0026 0.0000 \u0026 -.0000 \\cr -.0021 \u0026 -.0320 \u0026 -.1034 \u0026 0.1481 \\cr 0.0336 \u0026 -.0000 \u0026 -.0325 \u0026 -.0000 } \\right]  $$'; \r\ntext(3,44,str,'Interpreter','latex','Fontsize',12);\r\n\r\n% gtw_ij=n*o_i*d_j, gtWP where o_i is Output(HY) and d_j is a delta(dPY)  \r\n% dWP=n*HY'.*dPY  %Matlab for a single case, n is learning rate set to 1 \r\n% n*[HY1;HY2;1].*[dPY1 dPY2]=n*[dPY1*HY1 dPY2*HY1  =gtWP \r\n%                               dPY1*HY2 dPY2*HY2  \r\n%                               dPY1*1   dPY2*1  ] \r\n% The WP values affecting P1/PY1 adjusted by dPY1. gtw=dWP\r\n% Cycle over all four cases\r\n% dWP=dWP+n*HY'.*dPY;  %Matlab combining single cases\r\n\r\n% [0 .0076 -.0076 0  [0 0 0 0   [-.0010 -.0160 -.0517 .0741  [.0437 0 -.0423 0\r\n%  0 .0356 -.0354 0   0 0 0 0    -.0010 -.0160 -.0517 .0741   .0135 0 -.0130 0\r\n%  0 .0255 -.0253 0]+ 0 0 0 0]+  -.0021 -.0320 -.1034 .1481]+ .0336 0 -.0325 0]\r\n%case1\r\n%    -.0000    .0076   -.0076   -.0000\r\n%    -.0000    .0356   -.0354   -.0000\r\n%    -.0000    .0255   -.0253   -.0000\r\n%\r\n%case2    1.0e-03 *\r\n%    -0.0039   -0.0656    0.1035   -0.0000\r\n%    -0.0046   -0.0775    0.1224   -0.0000\r\n%    -0.0036   -0.0596    0.0941   -0.0000\r\n%case3\r\n%    -.0010 -.0160 -.0517 .0741\r\n%    -.0010 -.0160 -.0517 .0741\r\n%    -.0021 -.0320 -.1034 .1481\r\n%case4\r\n%     .0437 -.0 -.0423 -.0\r\n%     .0135 -.0 -.0130 -.0\r\n%     .0336 -.0 -.0325 -.0\r\n\r\ntext(1,36,'\\DeltaW_{ij}=n*o_{i}*\\delta_{j}, \\DeltaWP where o_{i} is Output(HY) and \\delta_{j} is a delta(dPY) ','Fontsize',14);\r\ntext(1,32,'dWP=n*HY''.*dPY  %Matlab for a single case, n=1 learning rate','Fontsize',14,'Color','b');\r\ntext(1,28,'n*[HY1;HY2;1].*[dPY1 dPY2 dPY3 dPY4]=','Fontsize',14);\r\nstr='$$ n*\\left[\\matrix{ dPY1*HY1 \u0026 dPY2*HY1 \u0026 dPY3*HY1 \u0026 dPY4*HY1 \\cr dPY1*HY2 \u0026 dPY2*HY2 \u0026 dPY3*HY2 \u0026 dPY4*HY2 \\cr dPY1*1 \u0026 dPY2*1 \u0026 dPY3*1 \u0026 dPY4*1 } \\right]  $$'; \r\ntext(1,22,str,'Interpreter','latex','Fontsize',12);text(70,25,'=\\DeltaWP','Fontsize',14);\r\ntext(1,15,'The WP values affecting P1/PY1 adjusted by dPY1.  \\DeltaW=dWP','Fontsize',14);\r\n%text(1,15,'Cycle over all four cases','Fontsize',14);\r\ntext(1,11,'dWP=dWP+n*HY''.*dPY;  %Matlab combining single cases','Fontsize',14);\r\ntext(7,7,'Case1','Fontsize',13);text(36,7,'Case3','Fontsize',13);text(63,7,'Case4','Fontsize',13);\r\nstr='$$ \\left[\\matrix{ 0 \u0026 .0076 \u0026 -.0076 \u0026 0 \\cr 0 \u0026 .0356 \u0026 -.0354 \u0026 0 \\cr 0 \u0026 .0255 \u0026 -.0253 \u0026 0 } \\right]  $$'; \r\ntext(0,1,str,'Interpreter','latex','Fontsize',10);\r\nstr='$$ \\left[\\matrix{ 0 } \\right]  $$'; \r\ntext(22,1,str,'Interpreter','latex','Fontsize',10);\r\nstr='$$ \\left[\\matrix{ -.0010 \u0026 -.016 \u0026 -.0517 \u0026 .0741 \\cr -.0010 \u0026 -.016 \u0026 -.0157 \u0026 .0741 \\cr -.0021 \u0026 -.032 \u0026 -.1034 \u0026 .1481 } \\right]  $$'; \r\ntext(25,1,str,'Interpreter','latex','Fontsize',10);\r\nstr='$$ \\left[\\matrix{ .0437 \u0026 0 \u0026 -.0423 \u0026 0 \\cr .0135 \u0026 0 \u0026-.0130 \u0026 0 \\cr .0336 \u0026 0 \u0026 -.0325 \u0026 0 } \\right]  $$'; \r\ntext(56,1,str,'Interpreter','latex','Fontsize',10);\r\ntext(21,1,'+','Fontsize',13);text(24.5,1,'+','Fontsize',13);text(55,1,'+','Fontsize',13);\r\n\r\n\r\n% d_j=o_j(1-o_j)Sigma_k(WP_jk*d_k) if j is a hidden layer, d_k is from next layer\r\n%   next layer WP and d terms combined and scaled by Hidden layer Output function\r\n%   Generate a dHY to apply against WH terms\r\n% dHY=HY(1-HY)*SumdW  \r\n% dHY=HY.*(1-HY).*sum(WP.*dPY,2)' % Matlab per case\r\n% [HY_C1*(1-HY_C1)*SumdW_C1 HY_C2*(1-HY_C2)*SumdW_C2 HY_C3*(1-HY_C3)*SumdW_C3] where\r\n% SumdW_C1 = WP_11*dPY1+WP_12*dPY2+WP_13*dPY3+WP_14*dPY4   \r\n% SumdW_C2 = WP_21*dPY1+WP_22*dPY2   \r\n% SumdW_C3 = WP_31*dPY1+WP_32*dPY2 since HY_C3=1 this term is unused\r\n% dHY = [-.0420  -.0122 0  (9.5*0-1.9*.0255+6*-.0253+.5*0)=-.200 SumdW_11\r\n%                           (-.5*0+8*.0255+7.2*-.0253+.2*0)=.0218 SumdW_12\r\n%        -.0000 -0.0000 0\r\n%        -.1263 -0.2424 0\r\n%        -.0486  0.0602 0]\r\n%  -0.0420   -0.0122         0\r\n%  -0.7085   -0.7898         0  *1e-4\r\n%  -0.1263   -0.2424         0\r\n%  -0.0486   -0.0602         0\r\n\r\n%\r\ntext(82,80,'\\delta_{j}=o_{j}(1-o_{j})\\Sigma_{k}W_{jk}*\\delta_{k} if j is a hidden layer, d_k is from next layer','Fontsize',14);\r\ntext(81,76,'next layer WP, dPY combined and scaled by Hidden layer Output function','Fontsize',12);\r\ntext(82,72,'\\deltaHY=HY(1-HY)*SumdW','Fontsize',14);\r\ntext(82,68,'dHY=HY.*(1-HY).*sum(WP.*dPY,2)''     %Matlab per case','Fontsize',14,'Color','b');\r\ntext(61,64,'[HY_{C1}*(1-HY_{C1})*SumdW_{C1}   HY_{C2}*(1-HY_{C2})*SumdW_{C2}   HY_{C3}*(1-HY_{C3})*SumdW_{C3}] where','Fontsize',12);\r\ntext(80,60,'SumdW_{C1} = WP_{11}*dPY1+WP_{12}*dPY2+WP_{13}*dPY3+WP_{14}*dPY4','Fontsize',12);\r\ntext(80,56,'SumdW_{C2} = WP_{21}*dPY1+WP_{22}*dPY2+WP_{23}*dPY3+WP_{24}*dPY4','Fontsize',12);\r\ntext(80,52.5,'SumdW_{C3} = 0 since HY_{c3}=1','Fontsize',12);\r\ntext(77,49,'dHY = [-.0420  -.0122 0  %(9.5*0-1.9*.0255+6*-.0253+.5*0)= -.2   SumdW_{11}','Fontsize',12);\r\ntext(103,45.5,'%(-.5*0+8*.0255+7.2*-.0253+.2*0)=.0218 SumdW_{12}','Fontsize',12);\r\ntext(103,42.5,'%dHY_{11}=0.3*(.7)*(-.2)= -0.042','Fontsize',12);\r\ntext(103,39.5,'%dHY_{12}=1.4*(-.4)*(.0218)= -0.0122','Fontsize',12);\r\ntext(85,46,'-.0000 -.0000 0','Fontsize',12);\r\ntext(85,43,'-.1263 -.2424 0','Fontsize',12);\r\ntext(85,40,'-.0486 -.0602 0]','Fontsize',12);\r\n\r\n% n*xc'.*dHy  % xc is a single row of x\r\n% dWH=n*XC'.*dHY   %Matlab single case\r\n% n*[XC1;XC2;1].*[dHY1 dHY2 dHY3]=\r\n% n*[dHY1*XC1 dHY2*XC1 dHY3*XC1  =gtWH \r\n%    dHY1*XC2 dHY2*XC2 dHY3*XC2\r\n%    dHY1*1   dHY2*1   dHY3*1 ]  since dHY3=0 end col is 0\r\n% dWH=dWH+n*XC'.*dHY; % matlab for accumulating cases\r\n% The WH values affecting H1/HY1 adjusted by dHY1. gtw=dWH\r\n% The WH values affecting H2/HY2 adjusted by dHY2\r\n% dWH=\r\n%  [ 0         0   0       [-.1263 -.2424 0  [-.0486   -.0602 0\r\n%    0         0   0           0       0  0   -.0486   -.0602 0\r\n%   -.042   -0.0122 0]+[0]+ -.1263 -.2424 0]+ -.0486   -.0602 0]\r\n\r\ntext(85,36,'dWH=n*XC''.*dHY  %Matlab for a single case, n=1','Fontsize',14,'Color','b');\r\ntext(85,32,'n*[XC1;XC2;1].*[dHY1 dHY2 dHY3]=n*','Fontsize',14);\r\nstr='$$ \\left[\\matrix{ dHY1*XC1 \u0026 dHY2*XC1 \u0026 0 \\cr dHY1*XC2 \u0026 dHY2*XC2 \u0026 0 \\cr dHY1*1 \u0026 dHY2*1 \u0026 0 } \\right]  $$'; \r\ntext(91,25,str,'Interpreter','latex','Fontsize',12);text(145,25,'=\\DeltaWH','Fontsize',14);\r\ntext(81,19,'The WH values affecting H1/HY1 adjusted by dHY1. \\DeltaW=dWH','Fontsize',14);\r\ntext(81,15,'The WH values affecting H2/HY2 adjusted by dHY2. \\DeltaW=dWH','Fontsize',14);\r\n%text(71,15,'Cycle over all four cases','Fontsize',14);\r\ntext(81,11,'dWH=dWH+n*XC''.*dHY;  %Matlab combining cases','Fontsize',14);\r\nstr='$$ \\left[\\matrix{ 0 \u0026 0 \u0026 0 \\cr 0 \u0026 0 \u0026 0 \\cr -.042 \u0026 -.0122 \u0026 0 } \\right]  $$'; \r\ntext(82,3,str,'Interpreter','latex','Fontsize',11);\r\nstr='$$ \\left[\\matrix{ 0 \u0026 0 \u0026 0 \\cr 0 \u0026 0 \u0026 0 \\cr 0 \u0026 0 \u0026 0 } \\right]  $$'; \r\ntext(103,3,str,'Interpreter','latex','Fontsize',11);\r\nstr='$$ \\left[\\matrix{ -.1263 \u0026 -.2424 \u0026 0 \\cr 0 \u0026 0 \u0026 0 \\cr -.1263 \u0026 -.2424 \u0026 0 } \\right]  $$'; \r\ntext(114,3,str,'Interpreter','latex','Fontsize',11);\r\nstr='$$ \\left[\\matrix{ -.0486 \u0026 -.0602 \u0026 0 \\cr -.0486 \u0026 -.0602 \u0026 0 \\cr -.0486 \u0026 -.0602 \u0026 0 } \\right]  $$'; \r\ntext(136,3,str,'Interpreter','latex','Fontsize',11);\r\ntext(102.25,3,'+','Fontsize',14);text(113.25,3,'+','Fontsize',14);text(135.5,3,'+','Fontsize',14);\r\n\r\n\r\nend %Back_Propagation_ReLU_Soft\r\n%}","test_suite":"%%\r\nX=[0 0 1; %[x1 x2 1]\r\n   0 1 1;\r\n   1 0 1;\r\n   1 1 1];\r\nEPY=[0 1 0 0; % 0 0 : 1 Counter\r\n     0 0 1 0; % 0 1 : 2\r\n     0 0 0 1; % 1 0 : 3\r\n     1 0 0 0] % 1 1 : 4\r\nfor attempt=1:5  % ReLU not always successful with rand WP WH, get 5 tries\r\n fprintf('Attempt:%i\\n',attempt);\r\nWP=rand(3,4)\r\nWH=[rand(3,2) [0 0 1]']\r\nztic=tic;\r\nfor epoch=1:1000\r\n dWP=WP*0;\r\n dWH=WH*0;\r\n for i=1:4\r\n  [dWPi,dWHi]=Neural_Back_Propagation_ReLU(X(i,:),WH,WP,EPY(i,:));\r\n  dWP=dWP+dWPi;\r\n  dWH=dWH+dWHi;\r\n end\r\n WP=WP+dWP;\r\n WH=WH+dWH;\r\nend % epoch\r\nfprintf('Processing Time: %.3f\\n',toc(ztic));\r\nWH\r\nWP\r\n\r\n  H=X*WH;\r\n  %HY=1./(1+exp(-H)); %[HY1 HY2 1]  .6803 .6637 1 Sigmoid\r\n  %HY(:,end)=1; %Sigmoid\r\n  HY=max(0,H); % ReLU\r\n  \r\n  P=HY*WP;  %\r\n  PY=exp(P)./sum(exp(P),2) %Softmax [PY1 PY2 PY3 PY4]\r\n\r\n  [~,Pexp]=max(EPY,[],2);\r\n  [~,Pclass]=max(PY,[],2);\r\n if isequal(Pexp,Pclass),break;end\r\nend\r\n\r\nvalid=isequal(Pexp,Pclass);\r\nassert(valid)\r\n\r\n%%\r\n%2 Bit Mux 00:0 01:1 10:2 11:3\r\nX=[0 0 1; %[x1 x2 1]\r\n   0 1 1;\r\n   1 0 1;\r\n   1 1 1];\r\nEPY=[1 0 0 0; % 0 0 : 1 2 Bit Mux\r\n     0 1 0 0; % 0 1 : 2\r\n     0 0 1 0; % 1 0 : 3\r\n     0 0 0 1] % 1 1 : 4\r\nfor attempt=1:5  % ReLU not always successful with rand WP WH, get 5 tries\r\n fprintf('Attempt:%i\\n',attempt);\r\nWP=rand(3,4)\r\nWH=[rand(3,2) [0 0 1]']\r\nztic=tic;\r\nfor epoch=1:1000\r\n dWP=WP*0;\r\n dWH=WH*0;\r\n for i=1:4\r\n  [dWPi,dWHi]=Neural_Back_Propagation_ReLU(X(i,:),WH,WP,EPY(i,:));\r\n  dWP=dWP+dWPi;\r\n  dWH=dWH+dWHi;\r\n end\r\n WP=WP+dWP;\r\n WH=WH+dWH;\r\nend % epoch\r\nfprintf('Processing Time: %.3f\\n',toc(ztic));\r\nWH\r\nWP\r\n\r\n  H=X*WH;\r\n  %HY=1./(1+exp(-H)); %[HY1 HY2 1]  .6803 .6637 1 Sigmoid\r\n  %HY(:,end)=1; %Sigmoid\r\n  HY=max(0,H); % ReLU\r\n  \r\n  P=HY*WP;  %\r\n  PY=exp(P)./sum(exp(P),2) %Softmax [PY1 PY2 PY3 PY4]\r\n\r\n  [~,Pexp]=max(EPY,[],2);\r\n  [~,Pclass]=max(PY,[],2);\r\n if isequal(Pexp,Pclass),break;end\r\nend\r\n\r\nvalid=isequal(Pexp,Pclass);\r\nassert(valid)\r\n%%\r\n%Subtractor  3-X  00:3 01:2 10:1 11:0\r\nX=[0 0 1; %[x1 x2 1]\r\n   0 1 1;\r\n   1 0 1;\r\n   1 1 1];\r\nEPY=[0 0 0 1; % 0 0 : 4 3-X, subtract\r\n     0 0 1 0; % 0 1 : 3\r\n     0 1 0 0; % 1 0 : 2\r\n     1 0 0 0] % 1 1 : 1\r\nfor attempt=1:5  % ReLU not always successful with rand WP WH, get 5 tries\r\n fprintf('Attempt:%i\\n',attempt);\r\nWP=rand(3,4)\r\nWH=[rand(3,2) [0 0 1]']\r\nztic=tic;\r\nfor epoch=1:1000\r\n dWP=WP*0;\r\n dWH=WH*0;\r\n for i=1:4\r\n  [dWPi,dWHi]=Neural_Back_Propagation_ReLU(X(i,:),WH,WP,EPY(i,:));\r\n  dWP=dWP+dWPi;\r\n  dWH=dWH+dWHi;\r\n end\r\n WP=WP+dWP;\r\n WH=WH+dWH;\r\nend % epoch\r\nfprintf('Processing Time: %.3f\\n',toc(ztic));\r\nWH\r\nWP\r\n\r\n  H=X*WH;\r\n  %HY=1./(1+exp(-H)); %[HY1 HY2 1]  .6803 .6637 1 Sigmoid\r\n  %HY(:,end)=1; %Sigmoid\r\n  HY=max(0,H); % ReLU\r\n  \r\n  P=HY*WP;  %\r\n  PY=exp(P)./sum(exp(P),2) %Softmax [PY1 PY2 PY3 PY4]\r\n\r\n  [~,Pexp]=max(EPY,[],2);\r\n  [~,Pclass]=max(PY,[],2);\r\n if isequal(Pexp,Pclass),break;end\r\nend\r\n\r\nvalid=isequal(Pexp,Pclass);\r\nassert(valid)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":3097,"edited_by":3097,"edited_at":"2023-08-27T02:57:17.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-08-27T02:09:44.000Z","updated_at":"2023-08-27T02:57:18.000Z","published_at":"2023-08-27T02:57:18.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis challenge is to return the WH_delta and WP_delta, given X, WH, WP, EPY using ReLU on the hidden layer and Softmax on the output layer. Test Cases will accumulate dWP and dWH to solve neural nets for Counter, Subtractor,Mux. Test Cases will have four output cases. ReLU performs well on multiple output cases.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e[dWP,dWH]=Neural_Back_Propagation_ReLU(X,WH,WP,EPY)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"524\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"875\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e 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Puzzle - 039","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 113px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 56.5px; transform-origin: 407px 56.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGive an example of a number i where i\u0026gt;1000 that satisfies the following conditions:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 53px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 26.5px; text-align: left; transform-origin: 384px 26.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" 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data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eand N does not have the digit \"\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\" in it but the sum of the digits of N is equal to 2^3 or \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e8\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y=puzzle_039(n)\r\n  y=3939;\r\nend","test_suite":"%%\r\nn=2;\r\ny = num2str(puzzle_039(n)^3);\r\nassert(all(unique(y)~=num2str(n)))\r\nassert(puzzle_039(n)\u003e1000)\r\naa=0;\r\nfor i=1:length(y)\r\n    aa=aa+str2num(y(i));\r\nend\r\nassert(aa==n^3)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":180632,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":33,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-02-05T21:13:41.000Z","updated_at":"2024-11-18T01:20:53.000Z","published_at":"2021-02-05T21:13:41.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGive an example of a number i where i\u0026gt;1000 that satisfies the following conditions:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"47\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"105\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eand N does not have the digit 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data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eand N does not have the digit \"\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e4\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\" in it but the sum of the digits of N is equal to 4^3 or \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e64\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y=puzzle_041(n)\r\n  y=4141;\r\nend","test_suite":"%%\r\nn=4;\r\ny = num2str(puzzle_041(n)^3);\r\nassert(all(unique(y)~=num2str(n)))\r\nassert(puzzle_041(n)\u003e1000)\r\naa=0;\r\nfor i=1:length(y)\r\n    aa=aa+str2num(y(i));\r\nend\r\nassert(aa==n^3)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":180632,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":31,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-02-05T21:21:28.000Z","updated_at":"2021-02-05T21:21:28.000Z","published_at":"2021-02-05T21:21:28.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGive an example of a number i where i\u0026gt;1000 that satisfies the following conditions:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"47\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"105\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eand N does not have the digit 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data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = puzzle_045(x)\r\n  y = [123 345 678];\r\nend","test_suite":"%%\r\na=puzzle_045();\r\nassert(length(a)\u003e=3)\r\nassert(length(unique(a))\u003e=3)\r\nassert(sum(a)==1301)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":180632,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":33,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-02-10T22:44:58.000Z","updated_at":"2021-02-10T22:44:58.000Z","published_at":"2021-02-10T22:44:58.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document 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et mise à l'échelle avec des complexes","description":"Ecrire une fonction Zr=scale_rot(A,phi,Z) qui permet une mise à l'échelle d'un facteur A et une rotation d'un angle phi (en rad) d'un polygone. Vous utiliserez les nombres complexes, on considérera que le polygone est représenté par un vecteur complexe Z dont la partie réélle réprésente les abscisses de chaque sommet et la partie imaginaire les ordonnées.\r\nPar exemple prenons le trangle défini par le trois points A(1,0) B(2,1) et C(3,0) il sera repésenté dans Matlab par\r\nX=[1 2 3 1]; Y=[0 1 0 0]; % le 4 eme point =1 er point sert à fermer le contour lorsque l'on trace) \r\nZ=X+1i*Y;\r\nsi on veut par exemple appliquer une rotation de pi et une réduction d'échelle par un facteur 1/2, on appliquera\r\nZr=scale_rot(1/2,pi,Z); \r\nqui nous donne le triangle Ar, Br,Cr sur la figure d'illustration\r\n\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 708px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 354px; transform-origin: 407px 354px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eEcrire une fonction Zr=scale_rot(A,phi,Z) qui permet une mise à l'échelle d'un facteur A et une rotation d'un angle phi (en rad) d'un polygone. Vous utiliserez les nombres complexes, on considérera que le polygone est représenté par un vecteur complexe Z dont la partie réélle réprésente les abscisses de chaque sommet et la partie imaginaire les ordonnées.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ePar exemple prenons le trangle défini par le trois points A(1,0) B(2,1) et C(3,0) il sera repésenté dans Matlab par\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eX=[1 2 3 1]; Y=[0 1 0 0]; % le 4 eme point =1 er point sert à fermer le contour lorsque l'on trace) \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eZ=X+1i*Y;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003esi on veut par exemple appliquer une rotation de pi et une réduction d'échelle par un facteur 1/2, on appliquera\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eZr=scale_rot(1/2,pi,Z); \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003equi nous donne le triangle Ar, Br,Cr sur la figure d'illustration\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 426px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 213px; text-align: left; transform-origin: 384px 213px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"560\" height=\"420\" style=\"vertical-align: baseline;width: 560px;height: 420px\" 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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function Zr=scale_rot(A,phi,Z)\r\n  \r\nend","test_suite":"%%\r\nX=[1 2 3 1]; Y=[0 1 0 0];\r\nZ=X+1i*Y;\r\nZr_correct = 0.5*Z*exp(1i*pi);\r\nassert(isequal(scale_rot(0.5,pi,Z),Zr_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":63915,"edited_by":63915,"edited_at":"2024-09-27T07:22:47.000Z","deleted_by":null,"deleted_at":null,"solvers_count":12,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-10-27T13:53:33.000Z","updated_at":"2024-09-27T07:22:48.000Z","published_at":"2023-10-27T13:53:33.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eEcrire une fonction Zr=scale_rot(A,phi,Z) qui permet une mise à l'échelle d'un facteur A et une rotation d'un angle phi (en rad) d'un polygone. Vous utiliserez les nombres complexes, on considérera que le polygone est représenté par un vecteur complexe Z dont la partie réélle réprésente les abscisses de chaque sommet et la partie imaginaire les ordonnées.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePar exemple prenons le trangle défini par le trois points A(1,0) B(2,1) et C(3,0) il sera repésenté dans Matlab par\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eX=[1 2 3 1]; Y=[0 1 0 0]; % le 4 eme point =1 er point sert à fermer le contour lorsque l'on trace) \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eZ=X+1i*Y;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003esi on veut par exemple appliquer une rotation de pi et une réduction d'échelle par un facteur 1/2, on appliquera\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eZr=scale_rot(1/2,pi,Z); \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003equi nous donne le triangle Ar, Br,Cr sur la figure d'illustration\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":59349,"title":"Determine ground distance from an aircraft to a DME station","description":"In aviation, distance measuring equipment (DME) uses radio signals to determine slant distance from an aircraft to a ground station. Given the altitude of an aircraft in feet (ft) and a DME readout in nautical miles (NM), determine the ground distance in nautical miles from the aircraft to the DME ground station. Assume that 1 NM = 6076 ft and round solutions to the nearest tenth.\r\nFor example, if an aircraft is at 10000 ft and the DME readout is 5 NM, then the ground distance is 4.7 NM.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440001px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 114px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 57px; transform-origin: 407px 57px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eIn aviation, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Distance_measuring_equipment\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003edistance measuring equipment (DME)\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e uses radio signals to determine \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eslant distance\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e from an aircraft to a ground station. Given the altitude of an aircraft in feet (ft) and a DME readout in nautical miles (NM), determine the ground distance in nautical miles from the aircraft to the DME ground station. Assume that 1 NM = 6076 ft and round solutions to the nearest tenth.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFor example, if an aircraft is at 10000 ft and the DME readout is 5 NM, then the ground distance is 4.7 NM.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function d = groundDistance(alt,DME)\r\n    d = [];\r\nend","test_suite":"%%\r\nalt = 18000;\r\nDME = 10;\r\nd_correct = 9.6;\r\nassert(isequal(groundDistance(alt,DME),d_correct))\r\n%%\r\nalt = 29000;\r\nDME = 45.2;\r\nd_correct = 44.9;\r\nassert(isequal(groundDistance(alt,DME),d_correct))\r\n%%\r\nalt = 0;\r\nDME = 1;\r\nd_correct = 1;\r\nassert(isequal(groundDistance(alt,DME),d_correct))\r\n%%\r\nalt = 30380;\r\nDME = 5;\r\nd_correct = 0;\r\nassert(isequal(groundDistance(alt,DME),d_correct))","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":48615,"edited_by":48615,"edited_at":"2023-12-07T22:54:26.000Z","deleted_by":null,"deleted_at":null,"solvers_count":19,"test_suite_updated_at":"2023-12-07T22:54:26.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2023-12-07T22:50:51.000Z","updated_at":"2024-11-18T23:14:53.000Z","published_at":"2023-12-07T22:54:26.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn aviation, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Distance_measuring_equipment\\\"\u003e\u003cw:r\u003e\u003cw:t\u003edistance measuring equipment (DME)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e uses radio signals to determine \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eslant distance\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e from an aircraft to a ground station. Given the altitude of an aircraft in feet (ft) and a DME readout in nautical miles (NM), determine the ground distance in nautical miles from the aircraft to the DME ground station. Assume that 1 NM = 6076 ft and round solutions to the nearest tenth.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, if an aircraft is at 10000 ft and the DME readout is 5 NM, then the ground distance is 4.7 NM.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":59409,"title":"Determine pressure altitude using field elevation and altimeter setting","description":"Given an airfield's elevation in feet (ft) and the current altimeter setting in inches of mercury (inHg), calculate the pressure altitude of the airfield. Use 29.92 inHg as standard pressure and round solutions to the nearest tens of feet.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440001px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 21px; transform-origin: 407px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGiven an airfield's elevation in feet (ft) and the current altimeter setting in inches of mercury (inHg), calculate the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Pressure_altitude#QNE\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003epressure altitude\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e of the airfield. Use 29.92 inHg as standard pressure and round solutions to the nearest tens of feet.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function a = pressureAlt(elevation,altSetting)\r\n  a = [];\r\nend","test_suite":"%%\r\nelevation = 4831;\r\naltSetting = 30.00;\r\na_correct = 4750;\r\nassert(isequal(pressureAlt(elevation,altSetting),a_correct))\r\n%%\r\nelevation = 1602;\r\naltSetting = 29.83;\r\na_correct = 1690;\r\nassert(isequal(pressureAlt(elevation,altSetting),a_correct))\r\n%%\r\nelevation = 0;\r\naltSetting = 29.92;\r\na_correct = 0;\r\nassert(isequal(pressureAlt(elevation,altSetting),a_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":48615,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":14,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-12-08T01:14:46.000Z","updated_at":"2023-12-08T01:14:46.000Z","published_at":"2023-12-08T01:14:46.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven an airfield's elevation in feet (ft) and the current altimeter setting in inches of mercury (inHg), calculate the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Pressure_altitude#QNE\\\"\u003e\u003cw:r\u003e\u003cw:t\u003epressure altitude\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e of the airfield. Use 29.92 inHg as standard pressure and round solutions to the nearest tens of feet.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":59546,"title":"Getting values from a vector","description":"This exercise is for finding the values that meet your criteria.\r\na = [-5 28 7 83 73];\r\nb = 23 ;\r\nc = (a \u003e b)\r\nThen :\r\nc = \r\n   0   1   0   1   1\r\nWhat we are looking for now is how to get the values :\r\ny =     \r\n    28    83    73\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 287.062px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 143.525px; transform-origin: 407px 143.531px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThis exercise is for finding the values that meet your criteria.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 61.3125px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 30.65px; transform-origin: 404px 30.6562px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.8px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.8px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.8px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.8px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2125px; text-wrap: nowrap; transform-origin: 404px 10.2188px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003ea = [-5 28 7 83 73];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.8px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.8px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.8px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.8px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2125px; text-wrap: nowrap; transform-origin: 404px 10.2188px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eb = 23 ;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.8px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.8px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.8px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.8px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2125px; text-wrap: nowrap; transform-origin: 404px 10.2188px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003ec = (a \u0026gt; b)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThen :\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 40.875px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 20.4375px; transform-origin: 404px 20.4375px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.8px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.8px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.8px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.8px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2125px; text-wrap: nowrap; transform-origin: 404px 10.2188px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003ec = \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.8px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.8px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.8px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.8px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2125px; text-wrap: nowrap; transform-origin: 404px 10.2188px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e   0   1   0   1   1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eWhat we are looking for now is how to get the values :\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 40.875px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 20.4375px; transform-origin: 404px 20.4375px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.8px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.8px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.8px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.8px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2125px; text-wrap: nowrap; transform-origin: 404px 10.2188px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003ey =     \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.8px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.8px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.8px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.8px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2125px; text-wrap: nowrap; transform-origin: 404px 10.2188px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    28    83    73\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = your_fcn_name(x)\r\n  \r\nend","test_suite":"%%\r\nx = [17 85 -20 99];\r\ny_correct = [85 99];\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n%%\r\nx = [-5 28 7 83 73];\r\ny_correct = [28 83 73];\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n%%\r\nx = [55 0 7 53];\r\ny_correct = [55 53];\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n%%\r\nx = [80 0 -90];\r\ny_correct = [80];\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n%%\r\nx = [10 14 -80 30 -95];\r\ny_correct = [30];\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n%%","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":4033021,"edited_by":4033021,"edited_at":"2024-01-10T06:33:06.000Z","deleted_by":null,"deleted_at":null,"solvers_count":34,"test_suite_updated_at":"2024-01-10T06:33:06.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2024-01-09T17:51:26.000Z","updated_at":"2024-11-18T01:17:46.000Z","published_at":"2024-01-09T18:04:51.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis exercise is for finding the values that meet your criteria.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[a = [-5 28 7 83 73];\\nb = 23 ;\\nc = (a \u003e b)]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThen :\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[c = \\n   0   1   0   1   1]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWhat we are looking for now is how to get the values :\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[y =     \\n    28    83    73]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":50524,"title":"Calculate the structural rank of a 2-by-4 matrix.","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 51px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 25.5px; transform-origin: 407px 25.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 10px; transform-origin: 404px 10px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003ex=[1 0 2 0 ;2 0 4 0]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; 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The challenge is to write a code that can take some arbitrary function, f(t,x), and use Euler's method to integrate over  equally-spaced points ( equal intervals) between times  and . You must implement the boundary condition . 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src=\"data:image/png;base64,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\" width=\"44.5\" height=\"18\" style=\"width: 44.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. The challenge is to write a code that can take some arbitrary function, f(t,x), and use Euler's method to integrate over \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eN\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e equally-spaced points (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"39.5\" height=\"18\" style=\"width: 39.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e equal intervals) between times \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABgAAAAoCAYAAADkDTpVAAAAAXNSR0IArs4c6QAAAgdJREFUWEft1UuoTXEUx/HPjcTEAEVKJIUBMjIwESUSIwOvyCuFCQYoMbiJlDDD1CslMvIsrzwmSgZSTEyIIq+8UvxX/bd217lnn3vaZ3b2ZO/2/u/1/a/f+q3179Hhq6fD8XUBlQp3JepKVKlA5YJWXTQOE3CvMmKfBa0ARuAwbuJM3YAIfhBzsBRP6wJEZjNxAPNxARvwqQ7AJBxPes9rEOwxluFlq6BmNZiM85iRs7jRatDyumaAJUmmyyn4A6zAqzoBg9CL3TiFLfhSJ2BUDrwA23GkneDxT38STc/OGYOFuF83YCVOJ//fRjy/rhMwJDfXtizNLvyqEzA2j4To3lXtjIcqm87GFXzF4tRYz5NF1+Ic3g80k0ZF3pQ7+WoOvBpPcL3BoJyCRfiBablmF5O9fxZr+wKG5sm5GddSBjEaPuAYfpcAw1Jf7EiZzsJOPEsZFp0fc2s//jSyaTTYVuxN7nmBo9mu5eCDc/A1WI+HGTwy1ytMshxvm/VBM6mL6Rrw2GkhR2GOz9iId+0AQpro6rmI2jwq7aQwx4kk554C3MqJVs5mPM7iWwa8yR9D2n35XUh3p78iV7mwKGScbOUBODXb+BIOpcJ/bxcwHCcRhVyHjxiNkCVMESdguO7fNVCJ4seJWePw/q18tMb9btn/7WZQJeF/39vJYECQLqBSro5L9BfiqV4prbLMRwAAAABJRU5ErkJggg==\" width=\"12\" height=\"20\" style=\"width: 12px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"14\" height=\"20\" style=\"width: 14px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. You must implement the boundary condition \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"63\" height=\"19\" style=\"width: 63px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [t,x] = EulerIntegration(t0,tf,N,x0,func)\r\n  t = 0;\r\n  x = 0;\r\nend","test_suite":"%%\r\nt0=0; tf=1.5; \r\nfunc = @(t,x) 2*x*t;\r\nN=50;\r\nt = linspace(t0,tf,N);\r\nh = (tf-t0)/N;\r\nnum_steps = length(t) - 1;\r\nx = zeros(1,num_steps + 1);\r\nx(1) = 1;\r\nfor i = 1:num_steps\r\n    x(i+1) = x(i) + h*func(t(i),x(i));\r\nend\r\n\r\nx0=1;\r\n[t2,x2] = EulerIntegration(t0,tf,N,x0,func)\r\n\r\nassert(isequal(x(1),x2(1)))\r\nn1 = length(x);\r\nn2 = length(x2);\r\nassert(isequal(x(n1),x2(n2)))\r\nassert(isequal(n1,n2))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":5,"created_by":4078801,"edited_by":4078801,"edited_at":"2024-02-29T18:51:13.000Z","deleted_by":null,"deleted_at":null,"solvers_count":11,"test_suite_updated_at":"2024-02-29T18:51:13.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2024-02-28T23:15:52.000Z","updated_at":"2024-10-29T13:31:26.000Z","published_at":"2024-02-28T23:15:52.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eEuler's method approximates the solution to a differential equation as\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex(t+\\\\Delta t) = x(t) + h \\\\cdot f(x, t )\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh = \\\\Delta t\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. The challenge is to write a code that can take some arbitrary function, f(t,x), and use Euler's method to integrate over \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e equally-spaced points (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eN-1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e equal intervals) between times \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et_o\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et_f\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. You must implement the boundary condition \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex(0)=x0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":59736,"title":"Counting the occurrences of a digit in a book","description":"The printer has printed a book with 'p' pages. How many times did they use the character 'd'? In other words, how many times does the digit 'd' appear when writing numbers from 1 to 'p'?","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 343.5px 21px; transform-origin: 343.5px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320.5px 21px; text-align: left; transform-origin: 320.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThe printer has printed a book with '\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep'\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e pages. How many times did they use the character 'd'? In other words, how many times does the digit 'd' appear when writing numbers from 1 to '\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep'\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e?\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function count = printer(d,p)\r\n  \r\nend","test_suite":"%%\r\nd = 4 ;\r\np = 1234 ;\r\ny_correct = 344;\r\nassert(isequal(printer(d,p),y_correct))\r\n%%\r\nd = randi([5, 9]);\r\np = d-1 ;\r\ny_correct = 0;\r\nassert(isequal(printer(d,p),y_correct))\r\n%%\r\nd = randi([1, 8]);\r\np = d ;\r\ny_correct = 1;\r\nassert(isequal(printer(d,p),y_correct))\r\n%%\r\nd = randi([3, 9]);\r\np = 9+d ;\r\ny_correct = 1;\r\nassert(isequal(printer(d,p),y_correct))\r\n%%\r\nd = randi([2, 9]);\r\np = 108+d ;\r\ny_correct = 21;\r\nassert(isequal(printer(d,p),y_correct))\r\n%%\r\nd = randi([2, 9]);\r\np = 1107+d ;\r\ny_correct = 321;\r\nassert(isequal(printer(d,p),y_correct))\r\n%%\r\nd = randi([2, 9]);\r\np = 11106+d ;\r\ny_correct = 4321;\r\nassert(isequal(printer(d,p),y_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":208445,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-03-30T09:24:59.000Z","updated_at":"2024-03-30T09:24:59.000Z","published_at":"2024-03-30T09:24:59.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe printer has printed a book with '\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e pages. How many times did they use the character 'd'? In other words, how many times does the digit 'd' appear when writing numbers from 1 to '\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":59741,"title":"Pivot index","description":"Let L be a vector of numbers. We are searching for the index n of the pivot element defined as follows: the dot product of the elements in the sub-vector to the left by their distance to the pivot element is equal to the dot product of the elements in the sub-vector to the right by their distance to the pivot element. \r\nExample 1: \r\nIf L = [6,1,10,5,4], then n = 3 since :\r\nLeft sub-vector: L(1:n-1) = [6,1] and distances = [2,1] so dot product = \r\nRight sub-vector: L(n+1:end) = [5,4] and distances = [1,2] so dot product =  \r\nExample 2:\r\nIf L = [10,3,3,2,1], then n = 2 since :\r\nLeft sub-vector: L(1:n-1) = [10] and distances = [1] so dot product = \r\nRight sub-vector: L(n+1:end) = [3,2,1] and distances = [1,2,3] so dot product =  \r\n\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 432.062px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 216.025px; transform-origin: 407px 216.031px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eLet \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eL\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e be a vector of numbers. We are searching for the index n of the pivot element defined as follows: the dot product of the elements in the sub-vector to the left by their distance to the pivot element is equal to the dot product of the elements in the sub-vector to the right by their distance to the pivot element. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eExample 1: \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eIf L = [\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e6\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e10\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e5\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e4\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e], then n = 3 since :\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 83.35px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 41.675px; transform-origin: 391px 41.675px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 41.675px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.8375px; text-align: left; transform-origin: 363px 20.8375px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eLeft sub-vector: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eL(1:n-1) = [6,1] and distances = [\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e] so dot product = \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"116\" height=\"18\" style=\"width: 116px; height: 18px;\"\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 41.675px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.8375px; text-align: left; transform-origin: 363px 20.8375px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eRight sub-vector: L(n+1:end) = [5,4] and distances = [\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e] so dot product =  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"116\" height=\"18\" style=\"width: 116px; height: 18px;\"\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eExample 2:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eIf L = [10,3,3,2,1], then n = 2 since :\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 62.9125px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 31.45px; transform-origin: 391px 31.4562px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 21.2375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.6125px; text-align: left; transform-origin: 363px 10.6187px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eLeft sub-vector: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eL(1:n-1) = [10] and distances = [1] so dot product = \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"75.5\" height=\"18\" style=\"width: 75.5px; height: 18px;\"\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 41.675px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.8375px; text-align: left; transform-origin: 363px 20.8375px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eRight sub-vector: L(n+1:end) = [3,2,1] and distances = [\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e2,3] so dot product =  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"164\" height=\"18\" style=\"width: 164px; height: 18px;\"\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.9px; text-align: left; transform-origin: 384px 10.9px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function n = pivot(L)\r\n\r\nend","test_suite":"%%\r\nL = [6 1 10 5 4];\r\ny_correct = 3;\r\nassert(isequal(pivot(L),y_correct))\r\n%%\r\nL = [10 3 3 2 1];\r\ny_correct = 2;\r\nassert(isequal(pivot(L),y_correct))\r\n%%\r\nx = randi([5,9]);\r\nL = [1:x, x-1:-1:1]\r\ny_correct = x;\r\nassert(isequal(pivot(L),y_correct))\r\n%%\r\nx = randi([20,30]);\r\nL = [x:-1:1, 2:x]\r\ny_correct = x;\r\nassert(isequal(pivot(L),y_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":208445,"edited_by":208445,"edited_at":"2024-03-30T11:44:59.000Z","deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-03-30T10:20:09.000Z","updated_at":"2024-03-30T11:44:59.000Z","published_at":"2024-03-30T10:20:09.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLet \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eL\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e be a vector of numbers. We are searching for the index n of the pivot element defined as follows: the dot product of the elements in the sub-vector to the left by their distance to the pivot element is equal to the dot product of the elements in the sub-vector to the right by their distance to the pivot element. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample 1: \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf L = [\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e6\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e10\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e5\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e4\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e], then n = 3 since :\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eLeft sub-vector: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eL(1:n-1) = [6,1] and distances = [\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e] so dot product = \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e6\\\\times2+1\\\\times1=13\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eRight sub-vector: L(n+1:end) = [5,4] and distances = [\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e] so dot product =  \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e5\\\\times1+4\\\\times2=13\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample 2:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf L = [10,3,3,2,1], then n = 2 since :\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eLeft sub-vector: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eL(1:n-1) = [10] and distances = [1] so dot product = \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e10\\\\times1=10\\n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eRight sub-vector: L(n+1:end) = [3,2,1] and distances = [\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2,3] so dot product =  \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e3\\\\times1+2\\\\times2+1\\\\times3=10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":59761,"title":"Digits eliminate","description":"Complete the function my_f(n,b) to return, for a given integer, the number obtained by removing the digits '0' and 'b'. If there are no other digits, it should return -1.\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 72.8px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 343.5px 36.4px; transform-origin: 343.5px 36.4px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320.5px 21px; text-align: left; transform-origin: 320.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eComplete the function my_f(n,b) to return, for a given integer, the number obtained by removing the digits '0' and 'b'. If there are no other digits, it should return -1.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320.5px 10.9px; text-align: left; transform-origin: 320.5px 10.9px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = my_f(n,b)\r\n\r\nend","test_suite":"%%\r\nn = 203456789\r\nb = 1\r\ny_correct = 23456789;\r\nassert(isequal(my_f(n,b),y_correct))\r\n%%\r\nn = 3300303003\r\nb = 3\r\ny_correct = -1;\r\nassert(isequal(my_f(n,b),y_correct))\r\n%%\r\nb = randi([7, 9])\r\nn = b*10^randi([2, 5])\r\ny_correct = -1;\r\nassert(isequal(my_f(n,b),y_correct))\r\n%%\r\ny_correct = randi([1, 6]);\r\nb = randi([7, 9])\r\nn = b*10^randi([2, 5])+y_correct\r\nassert(isequal(my_f(n,b),y_correct))\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":208445,"edited_by":208445,"edited_at":"2024-03-31T10:03:42.000Z","deleted_by":null,"deleted_at":null,"solvers_count":16,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-03-31T09:37:36.000Z","updated_at":"2024-11-12T07:42:17.000Z","published_at":"2024-03-31T10:03:42.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eComplete the function my_f(n,b) to return, for a given integer, the number obtained by removing the digits '0' and 'b'. If there are no other digits, it should return -1.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":59786,"title":"Missing Number (arithmetic progression)","description":"Given a list of integers forming an arithmetic progression (where the difference between consecutive elements is constant), your task is to find the missing element. However, the sequence provided is unsorted.\r\nComplete the missing_number function. This function should take an unsorted list L as input and return the missing element in the sequence.\r\nFor example, if the input list is [4, 2, 6, 10, 12], the missing element is 8.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 125px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 428px 62.5px; transform-origin: 428px 62.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 405px 21px; text-align: left; transform-origin: 405px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGiven a list of integers forming an arithmetic progression (where the difference between consecutive elements is constant), your task is to find the missing element. However, the sequence provided is unsorted.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 43px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 405px 21.5px; text-align: left; transform-origin: 405px 21.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eComplete the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003emissing_number\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e function. This function should take an unsorted list \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eL\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e as input and return the missing element in the sequence.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 405px 11px; text-align: left; transform-origin: 405px 11px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFor example, if the input list is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e[4, 2, 6, 10, 12]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, the missing element is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e8\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function n = missing_number(L)\r\n\r\nend","test_suite":"%%\r\nL = [4, 2, 6, 10, 12];\r\nn_correct = 8;\r\nassert(isequal(missing_number(L),n_correct))\r\n%%\r\nk_init = randi([1, 100]); \r\ndelta = randi([2, 20]); \r\nnum_elements = randi([10, 15]); \r\nL = k_init:k_init + (num_elements - 1) * delta;\r\nidx_to_remove = randi([2, num_elements - 1]); \r\nn_correct = L(idx_to_remove);\r\nL(idx_to_remove) = [];\r\nL = L(randperm(length(L)));\r\nassert(isequal(missing_number(L),n_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":208445,"edited_by":208445,"edited_at":"2024-05-19T08:08:32.000Z","deleted_by":null,"deleted_at":null,"solvers_count":13,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-03-31T12:27:31.000Z","updated_at":"2024-11-01T14:06:25.000Z","published_at":"2024-03-31T12:27:31.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a list of integers forming an arithmetic progression (where the difference between consecutive elements is constant), your task is to find the missing element. However, the sequence provided is unsorted.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eComplete the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emissing_number\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e function. This function should take an unsorted list \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eL\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e as input and return the missing element in the sequence.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, if the input list is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[4, 2, 6, 10, 12]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, the missing element is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e8\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":59801,"title":"Limiting Element Occurrences","description":"You are given a list 'v' of numbers. This list may contain repeated numbers. Your objective is to create a new list that maintains the same elements in the same order as the original list. However, if a number appears more than 'k times in the original list, only the first 'k' occurences of that number will be included in the new list. Any additional instances of that number beyond the k-th occurrence will be discarded. Note that, if k equals 0, the resulting list would be empty.\r\nExample: if v = [ 1, 3, 5, 3, 1, 3, 5, 3, 1 ] and k = 2, the function should output [ 1, 3, 5, 3, 1,  5 ].","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 117.67px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.989px 58.8352px; transform-origin: 406.996px 58.8352px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 87.6705px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.991px 43.8352px; text-align: left; transform-origin: 383.999px 43.8352px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou are given a list 'v' of numbers. This list may contain repeated numbers. Your objective is to create a new list that maintains the same elements in the same order as the original list. However, if a number appears more than\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e '\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ek\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003etimes in the original list, only the first\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e 'k' occurences of that number will be included in the new list. Any additional instances of that number beyond the\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e k\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e-\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth occurrence will be discarded. Note that, if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ek\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e equals 0, the resulting list would be empty.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0085px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.991px 10.4972px; text-align: left; transform-origin: 383.999px 10.5043px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eExample: if v = [ 1, 3, 5, 3, 1, 3, 5, 3, 1 ] and k = 2, the function should output [ 1, 3, 5, 3, 1,  5 ].\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function L = remove_after_kth(v, k)\r\n\r\nend","test_suite":"%%\r\nk = 2\r\nv =  [ 1, 3, 5, 3, 1, 3, 5, 3, 1 ] \r\nL_correct = [ 1, 3, 5, 3, 1,  5 ]\r\nassert(isequal(remove_after_kth(v, k),L_correct))\r\n%%\r\nk = randi([3,7])\r\nr = k+randi([1,10 ]);\r\nval = randi([40,70]);\r\nv = val*ones(1,r)\r\nL_correct = val*ones(1,k)\r\nassert(isequal(remove_after_kth(v, k),L_correct))\r\n%%\r\nk = 3\r\nv = [1:5,4:-1:1,2:5,4:-1:1,2:5]\r\nL_correct = [1:5,4:-1:1,2:5,1,5]\r\nassert(isequal(remove_after_kth(v, k),L_correct))\r\n%%\r\nk = randi([5,10])\r\nv = [1, 1, 1, 2, 2, 2]\r\nL_correct = v\r\nassert(isequal(remove_after_kth(v, k),L_correct))\r\n%%\r\nk = 0\r\nv = randi([1,5],1,20)\r\n% L_correct = []\r\n% assert(isequal(remove_after_kth(v, k),L_correct))\r\nassert(isempty(remove_after_kth(v, k)))\r\n%%\r\nk = randi([3,7])\r\nr = k+randi([1,10 ]);\r\nval = 1:5;\r\nv = repmat(val,1,k+5) \r\nL_correct = repmat(val,1,k)  \r\nassert(isequal(remove_after_kth(v, k),L_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":4,"created_by":208445,"edited_by":208445,"edited_at":"2024-05-13T15:52:54.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":"2024-05-13T15:52:54.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2024-04-01T07:36:09.000Z","updated_at":"2024-11-01T14:30:43.000Z","published_at":"2024-04-01T07:36:15.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou are given a list 'v' of numbers. This list may contain repeated numbers. Your objective is to create a new list that maintains the same elements in the same order as the original list. However, if a number appears more than\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e '\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003etimes in the original list, only the first\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e 'k' occurences of that number will be included in the new list. Any additional instances of that number beyond the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e k\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e-\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eth occurrence will be discarded. Note that, if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e equals 0, the resulting list would be empty.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample: if v = [ 1, 3, 5, 3, 1, 3, 5, 3, 1 ] and k = 2, the function should output [ 1, 3, 5, 3, 1,  5 ].\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":59811,"title":"Sort by absolute value","description":"Given a list of numbers, arrange them in ascending order based on their absolute values. \r\nFor example, for the list [-30, -5, 11, 14], the sorted list would be [-5, 11, 14, -30].","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 51px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 428px 25.5px; transform-origin: 428px 25.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 405px 10.5px; text-align: left; transform-origin: 405px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGiven a list of numbers, arrange them in ascending order based on their absolute values. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 405px 10.5px; text-align: left; transform-origin: 405px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFor example, for the list [-30, -5, 11, 14], the sorted list would be [-5, 11, 14, -30].\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = sortAbsolute(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = [-30, -5, 11, 14]\r\ny_correct = [-5, 11, 14, -30]\r\ny = sortAbsolute(x)\r\nassert(isequal(y,y_correct))\r\n%%\r\nx = [46, -83, 43, 28, -96, -84, -4, -21, 50, -65, -47]\r\ny_correct = [-4, -21, 28, 43, 46, -47, 50, -65, -83, -84, -96]\r\ny = sortAbsolute(x)\r\nassert(isequal(y,y_correct))\r\n%%\r\nk = randi([3,10]);\r\nx = [1:k,0]\r\ny_correct = [0,1:k]\r\ny = sortAbsolute(x)\r\nassert(isequal(y,y_correct))\r\n%%\r\nk = randi([3,10]);\r\nx = -[0:k]\r\ny_correct = x\r\ny = sortAbsolute(x)\r\nassert(isequal(y,y_correct))\r\n%%\r\nk = randi([7,15]);\r\nx = -[k:-1:1]\r\ny_correct = -[1:k]\r\ny = sortAbsolute(x)\r\nassert(isequal(y,y_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":208445,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":22,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-04-01T08:33:44.000Z","updated_at":"2024-11-20T13:07:15.000Z","published_at":"2024-04-01T08:33:44.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a list of numbers, arrange them in ascending order based on their absolute values. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, for the list [-30, -5, 11, 14], the sorted list would be [-5, 11, 14, -30].\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":59816,"title":"Sun angle","description":"Determine the angle of the sun above the horizon based on the time of day. \r\nAssumptions: the sun rises in the East at 6h00, corresponding to an angle of 0° degrees; reaches its zenith at 12h00, with an angle of 90° degrees; and sets at 18h00, with an angle of 180° degrees.\r\n\r\nInput: The time of day represented as a list [hh, mm], where  and . \r\nOutput: The angle of the sun above the horizon, in degrees, rounded to 2 decimal places. If the input time falls within the night hours (before 6h00 or after 18h00), your function should return 'Night'.\r\nExample:\r\nsun_angle([7,0]) should return 15.00\r\nsun_angle([12,15]) should return 93.75","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 389.875px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 194.938px; transform-origin: 407px 194.938px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eDetermine the angle of the sun above the horizon based on the time of day. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAssumptions: the sun rises in the East at 6h00, corresponding to an angle of 0° degrees; reaches its zenith at 12h00, with an angle of 90° degrees; and sets at 18h00, with an angle of 180° degrees.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 147px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 73.5px; text-align: left; transform-origin: 384px 73.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"264\" height=\"147\" style=\"vertical-align: middle;width: 264px;height: 147px\" 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data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eInput: The time of day represented as a list [hh, mm], where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"77.5\" height=\"18\" style=\"width: 77.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"86\" height=\"18\" style=\"width: 86px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eOutput: The angle of the sun above the horizon, in degrees, rounded to 2 decimal places. If the input time falls within the night hours (before 6h00 or after 18h00), your function should return 'Night'.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eExample:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 40.875px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 20.4375px; transform-origin: 391px 20.4375px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003esun_angle([7,0]) should return 15.00\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003esun_angle([12,15]) should return 93.75\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function angle = sun_angle(time)\r\n\r\nend","test_suite":"%%\r\ntime = [6,0]\r\nangle = sun_angle(time)\r\nangle_correct = 0\r\nassert(isequal(angle,angle_correct))\r\n%%\r\ntime = [12,0]\r\nangle = sun_angle(time)\r\nangle_correct = 90\r\nassert(isequal(angle,angle_correct))\r\n%%\r\ntime = [18,0]\r\nangle = sun_angle(time)\r\nangle_correct = 180\r\nassert(isequal(angle,angle_correct))\r\n%%\r\nnn = [0:5,18:23];\r\nhh = nn(randi([1,numel(nn)]));\r\nmm = randi([1,59]);\r\ntime = [hh,mm]\r\nangle = sun_angle(time)\r\nangle_correct = 'Night'\r\nassert(isequal(angle,angle_correct))\r\n%%\r\ntime = [7,0]\r\nangle = sun_angle(time)\r\nangle_correct = 15\r\nassert(isequal(angle,angle_correct))\r\n%%\r\ntime = [17,0]\r\nangle = sun_angle(time)\r\nangle_correct = 165\r\nassert(isequal(angle,angle_correct))\r\n%%\r\ntime = [7,20]\r\nangle = sun_angle(time)\r\nangle_correct = 20\r\nassert(isequal(angle,angle_correct))\r\n%%\r\ntime = [12,15]\r\nangle = sun_angle(time)\r\nangle_correct = 93.75\r\nassert(isequal(angle,angle_correct))\r\n%%\r\ntmp = randi([0,180]);\r\ntime = [6+floor(tmp/15),0];\r\ntime(2) =  round((tmp - (time(1)-6) * 15) * 4);\r\ntime\r\nangle = sun_angle(time)\r\nangle_correct = tmp\r\nassert(isequal(angle,angle_correct))\r\n%%\r\ntime = [randi(5),0]\r\nangle = sun_angle(time)\r\nangle_correct = 'Night'\r\nassert(isequal(angle,angle_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":208445,"edited_by":208445,"edited_at":"2024-07-01T17:28:03.000Z","deleted_by":null,"deleted_at":null,"solvers_count":13,"test_suite_updated_at":"2024-07-01T17:28:03.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2024-04-01T08:56:06.000Z","updated_at":"2024-11-06T00:07:48.000Z","published_at":"2024-04-01T09:17:29.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDetermine the angle of the sun above the horizon based on the time of day. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAssumptions: the sun rises in the East at 6h00, corresponding to an angle of 0° degrees; reaches its zenith at 12h00, with an angle of 90° degrees; and sets at 18h00, with an angle of 180° degrees.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"147\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"264\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"middle\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInput: The time of day represented as a list [hh, mm], where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e0 \\\\le \\\\text{hh} \\\\le 23\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e0 \\\\le \\\\text{mm} \\\\le 59\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOutput: The angle of the sun above the horizon, in degrees, rounded to 2 decimal places. If the input time falls within the night hours (before 6h00 or after 18h00), your function should return 'Night'.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003esun_angle([7,0]) should return 15.00\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003esun_angle([12,15]) should return 93.75\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.png\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAhAAAAElCAIAAAA6PUxdAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAgAElEQVR4nO3deVxVZcIH8B+rCCiooCI7SgQK6giCIqJpaprLSPGmZpOaZZpjZfO6NNnYO6nlmJlLKjoziaKDUrmHpQKKSOKoOICJIrEki8IFAfFyuef94zhXZD3cheXy+376g7M9z7kk53fP8zznOQaCIICIiKgphq19AkS6pFSgqlwP6yJqDQwM0mvVj7B7OJSK5h0VY4AYg2bXlbQdNw43+yii9oOBQXrNxAKeIUiJ1HlFFYU49yn6h+q8IqLWw8AgfRe0EvGf6byx6OQShB6CobFuayFqVQwM0neGxghchtMrdVhFwXVUFMIxUIdVELUBDAzqALxnIjMGskxdlf/tq5gcpqvCidoMBgZ1DNP34uh8nZR8PQIuo2DtopPCidoSBgZ1DD29YW6L7HgtF6tUIP4zjFmj5WKJ2iQGBnUYU8IQ+VKzh9g27twaBC6DiYU2yyRqqxgY1GGYWCDoQ20OsZVlIi2KQ2mp42BgUEfiuwCnlmptiO3plZi0jUNpqeNgYFBHYmiMKbtxRBu932J3CIfSUkfCwKAOxn0iClM0HWKrVOD4QrywSTunRNROMDCo43nlMA5MbXCrUoFKoBKNtVylRMIzBOa2ujg7ojbLgNObU0f0wxL0HQ/3iY8XC64jdTuSIlAug6czqn6FIWDkjKx8lFfC72UMeAd2Qx6Phqoqx+7hePMyey+oo2FgUPsnKKB8BKPmjG2tKsdX/bDkDs6vROxGDDbHMxWwa+CWuxDIAa5bolcAxobh4kbY+8N7pm7PkKjtYWBQ+5cfgbRZcFkN55UwkPatX6nAD4tway8CKuAhuWm2EDjZCVUmWJTXjGcvSuKR8hJMe8L3mtRDiNok9mFQ+2dsDdPeyPwYCY64f6Lp/SsKET4Yxjvxhwp4NuePwBZ47REmlGGTDbLimt6/MhPXnseVEZDnwXoUBK0+M0jU4niHQXqhuhzZG5D5MQBY+mDAYZi51L+n7DZ2DcKLZbDXoLoK4KQlPD+E//IGz+fOSuR8BQDdxsIjrMHzIWo/GBikRyozkbESBfsBoOcMeITV7jbIv4pwf8yWw1zjupTAD2bo/UcEf/bUekGBgkjcXgp5Hkx7w2M3ekxsoAiidoaBQXqnJB7pC1GWDADum9FnweOOjYpC/NMLIfe0kBYiJfCtKUbsh/v0Jqom0gsMDNJH4tf8tFkAYNob/Q+hiz929MXoLI1aoupSAmGmmJ0IK+smbm6I2j8GBumvmh0JhU7olYXBOqilAojsggEPYNBU9wlRO8fAIH1XmYmUuTh9Fm/pbFRgAlBmhcBt6NWchzOI2hsOqyV9Z+aCgj4Yr8t/7L5ARjVsOc856TkGBum7qnJkHIabLqswAYaW4fYRXdZB1PoYGKTvMs/Au0zntXgACf+n81qIWhUDg/RdejgcdF+LOVBwQ8vvfyVqYxgYpO9Sj6NlpiH3qURuYovURNQ6GBik1yoK4dRSb62wBoqTWqguotbAwCC9Ji+H8tcWqqsP8LCkheoiag0MDNJr8ge6HR9VS/a5FqyMqKXxwT1qP1YbqHPUC4Cnts+kXiVAJPCg+Qd+zL9Bah8YGKTXZJlIdtXJjCB1lQDXX8cL/2iRyohaAZukSN/dtW6hiuSA/aAWqouoNTAwSK91dYCBVQvVdQ8w6NpCdRG1BgYG6TVDY2Tdh7JF6sozRy/fFqmJqHUwMEjf+b6Gu7qvRQncNERPb93XRNRqGBik77wW4Ka23rHXsPtA/6k6r4WoVTEwSN/ZeCKnC6p0XMslM/R/U8d1ELUyBgbpO0NjBP4FOp2zowS4ZwWnkbqsg6j1MTBIrwkK5G5B0du4Ah3eZJwDnPOROhNVhTqrg6j1MTBIf90/gQRHpC9Gp96Y8BEOm+qklgzAcAR6+6BgP+J7IvMTCJzknPQTn/QmfVSZiV/mo/gnAHD4I1zXwMgCMe9DvhHDtFpRCXDAEu8Xw9AY+RG4vRTyPJj2Rt8NfL836R8GBumX6nLcWYmcrwCg21h4hMHM5fEmpQLhwzAoSWvTEVYA4aZYmAPz/86gLijw6xpkfgwAlj7w3AsLDrQl/cHAIH0hKFAQibRZAGDaG/0PwSqw9j5V5QjzgG+uFqYjLAEOmCL0x3r6uqsKkb4EBfsBoOcMeITByELj+ohaHwOD9EJJPFJegjwPADz3oWcoDIzr31OpwLcvwPQCgivU78LLBY5ZYmHGk3uLek8pfSHKkgHAfTP6LGjwlIjaCQYGtX+ZnzxuBZL+dT5xHZJWY0wl7JtZVwVwxhRVXphxHiZNVSTe9Kg6Nvxv8VaD2jUGBrV/4nf5AYefdFdIcWAq5Nl4kIYXKtFDwoDBCuAacMsO1eZYcK3ptFCpLkf2BlTcgFdEM06PqO1hYFCHJMvE0fmY/SNkmbjwv0g9iWeUeKYCloAJIM4kogQeAHLgFpBuiS79MOwj9J2ClEgU3ULwqlb+CEQtjoFBHdL2gXjlMKxdnqwpuI68M7gZDaEEORfwCOg7HAbmcAyC3SjYDXnqlqLu4UQdAAODOp7rEchNxIRNDe4QYwAAoxr+0yi4jnNrEcImJupY+KQ3dTBKBU4txZg1GhUiTmOeHa+VMyJqLxgY1MGcW4NxG5rRZd2QFzYh8iUoOQsIdSAMDOpIKgqRFoX+oVooytwWvm8jJVILRRG1EwwM6khOLsGkbTDU0gN0QStxaimqyrVTGlGbx8CgDqPgOgA41pkvRG2GxpiyG6dXaq1AoraNgUEdg1KBb1/VtK+7LveJyIyBLFPLxRK1SQwM6hhSIuEZopMnJ145jAN8mzd1CAwM6gCqyhH/GYYv1Unh1i6w7Y/0EzopnKgtYWBQB3BhAwKXaWEobUOmhOHIPA6xJb3HwCB9J8tEWhS8dfn+OxMLBH2IpO06rIKoDWBgkL47Oh/T9+q8Ft8FOPcph9iSfmNgkF6rKIS57eOZPHTK0Bihh3Bhg84rImo9nHyQiIgk4R0GERFJwsAgIiJJGBhERCQJA4OIiCRhYBARkSQMDGp/8vPzv/3229Y+C6nKy8vnz5/v7+8/bdq03Nzc1j4dIvVxWC21vsLCwujo6AkTJtjY2NRcX1RUdO7cuYKCgmeeeSYoKMjQ0BDA119/vWHDhtu3bzfyT7esrCw+Pr6oqCgoKMjBwaHmJoVCcfny5Rs3bvj6+vbv31+Ns01NTU1OTu7WrdvQoUO7detWc1NeXl5cXJylpWVgYKCVlZW48oMPPnB3d3/rrbfOnz+/du3a48ePq1EpUVvAOwxqTRs3bgwMDOzbt+/s2bNrffv++9///txzzyUkJOTm5r7yyiv+/v4ymQzA22+/vWLFikbKTE5O9vLyio6OzsnJGTFixM6dO1WbiouLR48evW7dugcPHsybN2/OnDkKRTMmgLp///6UKVMWLFiQn59/6NAhd3f3mlf/iIgIPz+/27dvx8XFeXl5JSYmiusvX748e/ZsACNGjLh375706ojaHIGo9cTFxeXl5R07dgzA1atXVevv379vZGT017/+VVxMS0szMjJasmSJuLhr166G/unK5XIHB4dVq1aJi5cuXQKQkJAgLoaGho4aNaq6uloQBJlMZm9vv3btWulnGxISMnToUIVCIS5+9NFH3bp1KyoqEgQhJSXFwMDgzJkz4qb169d37969vLxcEIQVK1asX79eoVAcO3ZsypQp0qsjamsYGNT66gbGw4cPn3vuucjISNUaDw8Pf39/8WdVYFRXV9+4cePevXuq3fbt2wcgMzNTtcbb2zs0NFQQhF9//dXIyOibb75RbVq8eLG9vX1VVZWUkywoKACwdetW1Zrs7GwA//jHPwRBmD9/vqurq2pTYWGhoaHhtm3bxM/y3nvvDRs27NVXXy0oKJD2KyFqi9gkRW2RmZnZ6dOnX375ZdWaoqIiV1fXmvt8/vnnHh4egwYNsrOzCw8PF1fGxsba2dk5OzurdvP394+NjQUQHx9fXV0dEBBQc1Nubu6tW7eknNIvv/wCoGfPnqo1Dg4OnTp1Sk9PF+utWbKNjY2bm5tYr5mZ2RdffHHhwoXw8HBbW9tm/BaI2hgGBrUDly5dKiwsnDFjRs2VgYGB6enpMpksODj4r3/9q7gyKyurVs+5jY1NQUHBo0ePsrKyxMWamwCINwpNcnR0BHDz5k3VGvE7V9euXcVC6tYrsWSi9oKBQW2dXC6fP3/+a6+9NmXKlJrrAwMDAXTq1GncuHGqS3NxcbG5uXnN3czNzQVBkMlkxcXF4mLNTQCKioqknIazs/OYMWM2b96syoz4+Hi5XO7t7V1ZWfnw4cO69Uosmai9MG7tEyBqTHV19dy5c/v06bNjx46G9jE1NRX+O8TWzs5ObDtSKSkpMTY2trW1tbOzA1BaWmpmZqbaBKBPnz51yzQwqGfEeXh4+BtvvOHj4/PMM8+Ym5s/evSoS5cuAQEBZmZm1tbWpaWlteqtt2Si9ouBQW1XVVXVrFmzFArF999/b2pqKuUQJyenuLi4mmvy8vIcHBwMDQ2dnJzERVU/RF5enniIxPOxs7M7fvx4eXl5SUmJjY3NgAEDVq5c2b17d7EQsbSa9Xp76/49HEQtiE1S1EYVFRWNHz++b9++hw4dEtNi/fr1NbsQ6hUSElJUVHT16lXVmpiYmJCQEABjx47t2rXrmTNnVJvOnj07ZMiQmj3kUlhYWPTp02fBggVmZmbvvvuuqt7Y2Njq6mpxMT09PTc3V6yXSG8wMKj1KZVKADWbgG7cuDF06NDu3bv7+vp+9913UVFRUVFRu3btevDgQeNFjRw5MjAwcM2aNeLinj17ZDLZ4sWLAXTp0mXx4sVbt24VW6LS0tIOHz68fPny5p5tRUXF7NmzU1NTY2JiVK1bb7/9tlKpVLWbrV271sfHZ9KkSc0tnKhNa70RvUTC4cOHVbN3eHp6jh07NiMjQxCEDz74oN5/rklJSeHh4c8++yyAyZMnl5WVff/99/369QMwbdo08SmH4uLiCRMm+Pn5TZw40cPD4+eff1ZVp1Qqly5d6uHhERIS4ubmFhYW1tCJNfSn8d1333l6es6dO/fBgwe1NiUnJw8YMGD8+PHDhg0LDg7mIxekfziXFOmnkpKS0tJScSxsLXK5PCsry83NTZycql71dnrfvXv3vffe+8tf/iImVr1+++23zp0715pjikg/MDCI6lFvYBB1cOzDICIiSRgYREQkCQODiIgkYWAQEZEkDAwiIpKEgUFERJIwMIiISBIGBhERScLAICIiSRgYREQkCQODiIgkYWAQEZEkDAwiIpKEgUFERJIwMIiISBIGBhERScLAICIiSRgYREQkCQODiIgkYWAQEZEkDAwiIpKEgUFERJIwMIiISBIGBhERScLAICIiSRgYREQkCQODiIgkYWAQEZEkDAwiIpKEgUFERJIwMIiISBIGBhERScLAICIiSRgYREQkCQODiIgkYWAQEZEkDAwiIpKEgUFERJIwMIiISBIGBhERScLAICIiSRgYREQkCQODiIgkYWAQEZEkDAwiIpKEgUFERJIwMIiISBIGBhERScLAICIiSRgYREQkCQODiIgkYWAQEZEkDAwiIpKEgUFERJIwMIiISBIGBhERScLAICIiSRgYREQkCQODiIgkYWAQEZEkDAwiIpKEgUFERJIwMIiISBIGBhERScLAICIiSRgYREQkCQODiIgkYWAQEZEkDAwiIpKEgUFERJIwMIiISBIGBhERScLAICIiSRgYREQkCQODiIgkYWAQEZEkDAwiIpKEgUFERJIwMIiISBIGBhERScLAICIiSRgYREQkCQODiIgkYWAQEZEkDAwiIpKEgUFERJIwMIiISBIGBhERScLAICIiSRgYREQkCQODiIgkYWAQEZEkDAwiIpKEgUFERJIwMIiISBIGBhERScLAICIiSRgYREQkCQODiIgkYWAQEZEkDAwiIpKEgUFERJIwMIiISBIGBhERScLAICIiSRgYREQkCQODiIgkYWAQEZEkDAwiIpKEgUFERJIwMIiISBIGBhERScLAICIiSRgYREQkCQODiIgkYWAQEZEkDAwiIpKEgUFERJIwMIiISBIGBhERScLAICIiSRgYREQkCQODiIgkYWAQEZEkDAwiIpKEgUFERJIwMIiISBIGBhERScLAICIiSRgYREQkCQODiIgkYWAQEZEkDAwiIpKEgUFERJIwMIiISBIGBhERScLAICIiSRgYREQkCQODiIgkYWAQEZEkDAwiIpKEgUFERJKoGxhKBdJPqHNgjEHL1UVE1C7IMlFR2OyjYgzUuaKqVxcA9QPD0BgXN0KWqebhzZISid+SWqIiIqLWEjWzJWpRKnBgqtpHa9AkNTlMk4qlqipH/GcYvlTnFRERtRZrF5jbtkRTSkokPENgbqve0RoEhrULXEbp/BNe2IDAZTCx0G0tRESta0oYjsyDUqHDKqrKcWopglaqXYBmnd5j1uj2E8oykRaF/qG6Kp+IqI0wsUDQh0jarsMqTq/EuA0wNFa7AM0Cw8QC4zbg3BqNCmnE6ZWYvleTj0dE1G74LsC5T1FVrpPCZZnIjIG3Rj0lGg+r7R+KpK/V7nNvTHY8APT01n7JRERtkKExQg/hyHydFH50Pqbv1bAMjQND/IQnl2haTi1KBSJfwgubtFwsEVFb5hiIikLtD0DNjoe5rebfv7Xx4J5jIAAUXNdCUSopkfB9W+2ufCKi9krrA1DF799TwjQvSUtPeo9Zg29f1U5R0EJXPhFReyUOQL0eobUCk7Yj6EOtjDXVUmBYu8AzRGuf8PRKTNnNvm4i6qDGrMGppdoZgFpVjnOfwneBForS5lxSw5ci/jMt9O+LXfnuE7VxTkRE7ZAWB6Aema/F79/aCwwTCwQuw4UNmpZzdD5eOayNEwKA8vLykydPFhbqYBAXEXUwN27cOHv2bAtV1j8UaVGaDkAVp43S3vdvrc5WK37Cuv37SgVkmZBlIv0E7gHZ8Y8X60o/AXNbWLuoV/+1a9dWrVo1evTo3bt3A4iLixs7duzEiRNTU1MbOkShUCQmJn7zzTcpKSl1t964cWPPnj3x8fFyuVy9UyKitkmpVCYkJBw/frzupry8vAMHDmzduvXcuXOqlW+++WZQUNAnn3zSSJl5eXmRkZEnTpwoKSmptamsrCw6Onr//v05OTmSzs/QGJO21T8AtaocskwUXEchkI/Hl9N6W3cOTMVkLfR1PzkpLZYFQ2NM34vT/+2sripH+rfYMxhfdEH0YPzsiuJJcALujkCcK04Nw98scCIUWXGPP6pSgSPz1OvKVyqV69at+/3vf9+3b9+wsLA5c+YAGDly5N69jY07Li4uHj169Lp16x48eDBv3rw5c+YoFApVgYsXL54xY4ZMJtuyZcvw4cMLCgrUODEiamtSUlLmzp3r5OQUHBy8a9euWlujoqIGDRp048aNTp06LV26dOrUqUqlEsDOnTsnTJjQSLERERF+fn63b9+Oi4vz8vJKTExUbUpOTvby8oqOjs7JyRkxYsTOnTslnag4AFV8Ig1AwXXELMI2B+zrhx9ckekDZ8AVSHZFtCf29cM2BySue/JdPP0EXEap/f27fkLj7h0XlFVN7FPLoRlCxk/CwbHCFkshFkIehNKG/7sNIRrCenPh7HvCxU1C4ubm1aUoE+4dFwRh4cKFXl5epaWltbbfunULQExMTL1Hh4aGjho1qrq6WhAEmUxmb2+/du1acdO2bdt69OhRUFAgLr744ovjx49v3rlRe9b0nwa1WxkZGdeuXZPL5b6+vtOmTau5qbKyskuXLjt37hQXi4qKLCwsDh48KC6++uqro0aNqrfMlJQUAwODM2fOiIvr16/v3r17eXm5IAhyudzBwWHVqlXCwzvCwzuXLl0CkJCQIOlci+8IX/sImWeE9ZbCYXMhDYKs4cvpfQhXIRwwE7Y5CZlnhL/1FuRlzfvVlCUL8oJGtjd6h1ESj+uTkOCIkvjGdqtJqUBXKxx4HgN+wmtlGAyYN7q/LTAMmF8B8404/x46mUmtSFAgPwKJ/XB9Uuq/T+zYsWP//v1dunRp5Ijs7OzMzEzVYlZWVlRU1Jw5cwwNDQFYWVlNnz59y5YtCoVCEIQvv/xyypQptraPHwSZM2dOdHR0I01bRNReuLq6+vj4mJiY1N2UkZHx4MEDLy8vcbFbt27Ozs63b9+utdujR49SUlIqKipUa7788ksXF5fRo0eLi6+//rpMJvvmm28AHDx4MCcnZ+7cufjPVFx09bUOH/q7/hs3bpR0ro9kePgrLkzA3DKMroB9o61CJoAbMLESk7MQPw49uqFcchdIVSFSZ+KSD9Ibewq70cCwHISeMyDPw5URSJ2JyswmqqwoxHYXWG3HQgH2Us/z8Vl4AnOU+HU+vvFrejBZ+XVcHoK0WZDnwX3zh/+3ffDgwU5OTkePHg0LC7ty5Uqt3Y8ePern5+ft7e3q6rpgwePhZfHx8dXV1QEBAard/P39c3Nzb926lZeXd/PmzVqbAMTFxTXnUxFRO+Pu7m5lZfXFF19UVVUBuHfv3s2bN8eMGaPaoaioaNGiRW5ubgMHDnR2dv7Pf/4jro+Nja15xbCxsXFzc4uNjRU32dnZOTs7w30bTHsj56vEDSndFdEQmrrQJW/HoSC8XIIX5agn3RpmBUxWYGwadnkgq6mrlqBA5ieI74mC/bD0gfOKRvZtNDCMLOAVgYA7sPRBwX5cdEXmJ6huYOBs/lX80wvP5cJT3Z4RE2A04JmE7S4Njg1QxWBZMnrOQGAB7N9JSrpSWVkZGhp69OjREydO+Pn5vfnmmzUP6tmz54ULF2Qy2UcffbRjx467d+8CyMrKAmBjY6PaTfw5Ozu7kU1qfTAiah+MjY137dr1448/Dh069MCBAzNmzIiIiPD19VXt8OjRo/fffz83Nzc7O9vAwGDz5s3i+uzs7JpXDAA2NjbiFSMrK+vxJqtADMuG5z4AXy8uUV5waLDxRqlAzPu4vASvlsFK3Q9jBcyV4/TziF3W4D73TyDBEZkfw7Q3PPfB9xosGps+RMKl3cwFvtfgfRymvZH5MRL7IT+idjbKbiPcHyH3mndjUS9P4LlcbHOr3elfKwb9kuEVARPb8vLy3NzcqVOnnjp1aufOnd99993+/fvDwsLCw8NVh/r7+4u3n5MnT8Z/r/vFxcUAzM2fNJmJPxcVFdXd1KlTJyMjo6KiIo0/HhG1aebm5p6ent7e3vPmzbt27dq9e/dqbrWzs+vbt6/4g5+fn3gxqaysfPjwYc0rhliOeMUoLi5+ssnAGL1mrov/81dRMKzKx5URuPZ8PY030a9DvhEvyTUdlmQCTJcj76t6MqMyE0kDcX0S5HlwWQ3/W+jV9ES2kk+nx0QMy4b7ZsjzkDYLl4eg/L+TR1UUYtcgzJY30V0hnT3wYhn2j3jSNpUf0VAM5ufnC4LQq1cv1dEvv/yyi4vL0aNH6xZsamoKQBAEAHZ2dgBKS0tVW8WRcH369Km7qaysrLq6uk+fPlr6hETUFkVHR//hD3+IjIzcs2dPTk7OzJkzFy5cuGZN/Q/QmZqaihcTMzMza2vrmlcMACUlJeIVw87Ortame8UPl243Vg69DUsfFP9Uu/EmeTtKozBMSx/JEJhQiYwvn7RNVZcjdSYuuj5upwm4A5dVMJI0cUhz8svAGPbvILAAPWegLBmXfJA6E4/u4uBzeLFMa2khsgd6X0X0649jUOyucFmNYdm1YtDR0dHIyKjWo3l2dnYymazxGpycnADk5eWp1og/Ozk5NbJJ089FRG3Yjh07nn/+eWdnZwDdunX78ssvX3755S1btjR5oJOTU80rBoC8vDzxiuHk5JSfn19rk4ODg6G5Wz2NN3lJOPcnTKjU5qcyBKbKEfk8in9B7hacs3zcTjP4PLwiYObSrJKaycQWXhHwS37csXGkD+z+o4WWqLqGAXf/hZinY9Cg9gPuJiYmv/vd72oOeVYoFOnp6TWbHes1duzYrl27njlzRrXm7NmzQ4YMcXZ27tat2+jRo2ttMjMzmziRE5YQ6TMjI6Nao6dcXV3NzJoevRkSEhIbG1tdXS0upqen5+bmhoSEiJuKioquXr2q2jkmJkbcBDzdeJM6C/8ajpfKtPuAHACYAK/I8c/+SF8MAJ77MOQyrAKbW4y652XhDd9reHYPMgzQxJVZA+MUyDRrMgY/+eSTn376KT7+cffRxo0bDQwM3nvvvcbL7tKly+LFi7du3Sq2RKWlpR0+fHj58uXi1uXLl586dUoccFVRUfHVV1+98cYbqlG2RKQHlEql2KakEhISEhUVpZr34f79+//6179mz57dZFFvv/22UqncsWOHuLh27VofH59JkyYBGDlyZGBgoKpda8+ePTKZbPHixU8OVjXeyP3hWaXl1hoVK6B3NTqFIKgMvWbW/fItSfMe66jl4mohsdHn8jT/74CZ8GtskycSERHh6Og4derU0aNHjxgxIjU1VRCEpKSk4OBgAH5+fklJSb/88ktgYCCAgICAuLg4QRCUSuXSpUs9PDxCQkLc3NzCwsJqlrl//343N7fp06d7enouWLBAfD6DOghN/zSobfv973/v7+9vZGRkYWERHBy8evVq1abPP//c1tb2xRdffOWVV+zt7f/0pz+Jf/srVqzo0aOHubn5smXLBEH49NNPraysxO+d4oHJyckDBgwYP378sGHDgoODVY/9CoJQXFw8YcIEPz+/iRMnenh4/Pzzz/WcU3WVsN5SuK/Ly2kehK32mvzeDISnA7Z5/tYF83Vw91RTIfDvYLwU0+SOgiBkZGTY2NhYWTVvGJpcLs/KynJzcxOf4Ktbpr29vZR7UtInBgaa/WlQe1ZZWZmeni6Xy5999lkLi+a9RuK3337r3Llzt27d6m4qKSkpLS11dHSs/8isONwI1lpfd0POmiPgouJMo7EAAAyiSURBVNqv3tPgr6LgOi4GYHRF03tqaIc53i/h6zGoJTEwqKWdCMWzB6HrZu9cIG8hRm1V72gN7g7uHIez7tMCgE8Fci60REVERK1CqUDqcZ2nBQA7IGmP2kdrEBhZR9HArZWW9QMyvm+RmoiIWkNpDnxa5Pu3IWADtV+zoUFgpF5o3vQmajMFChOb3o2IqJ16kAvrlqqrTxnkar4aVYPAsG2pz6f2VCpERO1CcVLL1WUNPMhV71B1A6OiEDYteCFPZR8GEemvhyVoyYmH1M0nA0EQsNpAnUPtgBnqVdp8X6h74Mf1D3RRKBT1zoZPRCRFY4Po1LiimgGzWqo1JQOIBh42/8CPNXkO4592CMlrejet+HYA/nC96d2IiNqj5E0Q3oVbi9SVBnQ7AvfJahyqQR/Gry2VFhWAedcWqouIqOV1dsOjlqqrErBV88E9DQLDZQCU6h/dDFWApWuL1ERE1BpsvdHE/Nrac1f98UoaBIbzSNxV/+hmyAD6TW+RmoiIWoOFLdItW6iuGzJYu6h3qAaB4bUAWeof3QzXLeEyvkVqIiJqDSYW6NIPLfDoXiHg97LaR2sQGDaeSNbRPLw1VABd+sGkefN/1VVWVhYdHb1///6cnJya6//2t78FBAQEBQVduMCRu0QdmlKpTEhIOH78eN1NKSkpf//733fv3n3jxo1amxQKRWJi4jfffKOaFF0UHR09fPjwgICAsLAwSdUP+wi/qHvq0t0CBryj9tEaBIahMbwmQc3nPyS7Bgz+o4ZlJCcne3l5RUdH5+TkjBgxYufOneL6Y8eOXb9+PS4u7uDBg4sWLaqoaJFH84mojUlJSZk7d66Tk1NwcPCuXbtqbV22bNnUqVMfPnxYWlo6duzYzz//XLWpuLh49OjR69ate/Dgwbx58+bMmaNQKAAUFBSsWrXq6NGjZ8+ePXbsWM03vDXIZTx+NtNtx3AVcKsXHIarX4Imc6MLpSnCZ4aCTGezt9+H8JmxIJdpco5yudzBwWHVqlXi4qVLlwAkJCQIgvDnP/85OjpaXD9//vxr165p9NsgovYpIyPj2rVrcrnc19d32rRpNTeJbQ+//PKLuHjq1ClDQ8P8/HxxMTQ0dNSoUdXV1YIgyGQye3v7tWvXCoLw008/rVixQtxn3759mzZtavoklFXC8Rd0+4ahaAgX3tXkF6XuHUZ1OW4tweX+sFPq8DbqBwN4KBBvjfwICAr1yjh48GBOTs7cuXPFRV9fX29v740bNwIICgratWvXgwcPbt++fenSJXd3d62dORG1H66urj4+PvU+zHv16tVOnTr17dtXXBw0aJBSqbxz5w6ArKysqKioOXPmiK/SsbKymj59+pYtWxQKxcCBA3/88cfs7Ozi4uLw8HDx1W2NKYnH5SHodBIXoaubjCrgClD5JZIGojJTvTKaHxiCAvkRSOyHnK9g2hvjohBnqZO+mlygygcB+wAgbRYSHFESr0YxsbGxdnZ24lvdRf7+/rGxsQDGjRs3ZsyYSZMmLVy4cPfu3Z07d9bSqRORnvDz83v06NGmTZvExfPnz/fs2dPb2xtAfHx8dXV1QECAamd/f//c3Nxbt27Z2Nh88cUXr7/++rRp01577bUhQ4Y0WEFVIVJn4soIlCXDbgaCv8YPOnhdmxI4bIqZx9FrBsqScdEVqTNR3ewpCJv5VqKSeKQvRFkyALhvRp8FMDDGGwOxywtz5dqcvLYCOGaJJfEwsYDNVNxZiZyvcGUEuo2FR1gj7/euKysry8bGpuYaGxubgoKCR48ederU6a233nrrrbe0d95EpFeGDBmyYsWKDz744Ny5c7NmzVq/fv3p06fNzc0BZGVlAah5eRF/zs7OfvbZZ4OCgk6fPt1Y0YICv65B5scAYOkDz72w8AaA384jYZ+WX72XCLi9C8eJwETYL0L6QhTsR8H+J5dxaSTfYVRmPonBnjMQVAb7dx5XY90XU/fjsKnW7qQqgHBTvHH18eAoIwv024SAO+g2FsU/4aIrbi2Rno3FxcXi/10Vc3NzscFRS6dLRPqsR48eQUFBlZWV//M///Pw4cPCwscvkyguLgZQ8/Ii/lxUVNR0ofkRSHBE5scw7Q3PffC99jgtAIz/J/IGaXM80RXgri+CP3u8aBWIIZfhuQ8A0hc3q/FGQmAICmR+gouuKNgPSx8E3IFXBIyeHufqPh1eq/GdNtqmCoFwU4T+COu+T603c8HAH+F9HKa9kfMVEvtJ7Niws7MrLS2tuaakpMTY2NjWtgXebkVE7dtHH3303Xff/fDDDydPnkxNTe3du/e4cePi4uIA2NnZAah5eSkpKQHQp0+jE8+WX0fSQKTNgjwPLqsxLBu9Zj61g6ExZpxH4gBc0fjslUACcMcXsxOeWm9gjF4zEVQGhz9CnocrI3DteSkdG00FRt0YbKg5yH85njuOKGuo+SonAEAG8K0lFubAaWT9O/SYiGHZcN8MeR7SZuHykCaz0cnJKT8/v+aavLw8BwcHsZ+KiKgR27Zte+2118QOTg8Pj2PHjvXq1Wv79u0AnJycAOTlPZlVT/xZXF+P6nKkzsQln8ftNIEFcFlVf3OQiQVmX0H5LJzQYKBtFfCtKTr9L/5wCYb11dL8xptGL5r3TzQWg3U5jcTrNxHtiCMGzb7VKAH+YYD0F/B+Mcwb/e5vYAz7dxBUhp4zUJaMKyNQ3thEtiEhIUVFRVevXlWtiYmJCQkJaeb5EVFHZGRkVHP0lKmpqb29vZmZGYCxY8d27dr1zJkzqq1nz54dMmRIzSE2T0ns97idZvB5eEXApNELnaExXtgLz43YYYK0Zg6dUgJpQIQVRux/0hLVELHxZvD5x403Vxp7SqPRwOg+Dg5/bCwG6zK3hdcbsP8zouyRgKbvNpRALnDCDKcHoOdkDHyn/iSsy8gCXhEIuAOX1U/a/uozcuTIwMDANWvWiIt79uyRyWSLFy+WVAsRdSRKpVJ4+o0PISEhmzZtEtuaACQmJl69enXWrFkAunTpsnjx4q1bt4pb09LSDh8+vHz58gZL99gNz30YchlWTY2yVfGcjS4eKHsHey2Rgaa/iFcAV4AwMyg+xKPO6DtFakVWgY8bbzz3NrKXBu/DqJcsEwem4s3LAJBzAf/ZgksHMdgcvSvQCejx391+AwDcMUO2MXxfg9cC9PRGVTm+6of3sqVmhvSTkslmzJhx//59W1vb27dvh4eH+/n5abcKImrXpk+f/ttvvyUlJZmZmfn6+j733HOrVq0CUFFRsWjRoujo6JEjR1ZUVPz73/9eu3bt7NmzxaMEQfjTn/507NixAQMGXLlyZcWKFW+88YY2Tyv2E3TvB++ZqCrHvzfjxj6UZcK7DGaADWAKAJAD94BK4LoluvTDsI/gMh4mFvh5Czp3h3dTLUPNoe3AiJqJoYvg+HR+yjKRfQ5CEYp+xc2NGLgana3Q2R22XrUnTbwegYdFGKr+VCeNKCkpKS0tdXR01EXhRKTHZDJZenq6paVlv3796j7fJ5fLs7Ky3NzctNwzKn7/XnDtqZVV5ci7iuLrwCNcfBemwO++hEFX9PJFN7enpt1TKrDREX+8pflcfCpaDYzsePy8FSERje0TY4BRDdeog09IRNQuhT+P8V+gZ8NN7jEGABq7oqafQPLeJq7JzaG9PFQqcHwhXtikUSGGxgg9hCPztXRORETtU3Y8zG0bSwsp3CeiMAWyTO2ckjYDIyUSniFNDHCSwjEQFYUo4Bu8iaijUioQ+ZKm379FrxzGgalaKAeA1gKjqhzxnyFopXZKmxyGb1/VTlFERO1OSiSCPtTC928A1i5wGYX0E1ooSmuBcXolApdpbXST+Amva63djYio3agqx6ml8F2gtQLHrMGReVCqOeF3TdoIDFkmMmO0O3gLY9Yg/jOtfEIiovbk9EpM2a3NpwtMLDBuA86t0bwkbQTG0fmY3tizHuowsUDgMq18QiKidkP8/u0+UcvF9g9F0teo0GTiJkALgaGVrvx69Q9FWpQW+/eJiNq6A1PxymHtFysOQD25RNNiNDpa7MqfIu0V581laIxJ23BaSx3pRERtXPoJ2Pav/TiztmhjAKpmgZG0HUEf6vAhO/GJ8Wx1XrRHRNSeKBU4Mk9X379FGg9A1SAwqspx7lNtduXXa8waHF/I3m8i0nNJ2zFug24nubB2gWeIJgNQNQiMI/O13JVfL/ETpkTqthYiolZUUYhzn6J/qM4rGr4U8Z+hqtlv8xapGxhKBSxstd+VX6+glSi61RIVERG1ivs3MfuUzr9/AzCxwJi1KM5Q72htz1ZLRER66v8BDkQE8rEwo5cAAAAASUVORK5CYII=\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":59846,"title":"Sequencing Odd Even numbers ","description":"Given an input value n, create a vector which contains all odd numbers  \u0026 even numbers centered around mean of vector. If the mean is even/decimal number, round and rescale the even values of vecto. Similarly if the mean of vector is odd, rescale the odd numbers and present it as Odd-Even format ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 62.9883px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.484px 31.4844px; transform-origin: 406.494px 31.4941px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.496px 31.4844px; text-align: left; transform-origin: 383.506px 31.4941px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven an input value n, create a vector which contains all odd numbers  \u0026amp; even numbers centered around mean of vector. If the mean is even/decimal number, round and rescale the even values of vecto. Similarly if the mean of vector is odd, rescale the odd numbers and present it as Odd-Even format \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [odd m even] = odd_even_num(n)\r\n  y = 1:n;\r\n  odd = y(1:2:end);\r\n  even = y(2:2:end);\r\n  m = round(mean(y));\r\n  if mod(m,2) == 0\r\n      even = rescale(even);\r\n       y = [even m odd]\r\n  elseif mod(m,3)== 0 \r\n      odd = rescale(odd);\r\n      y = [odd m even] \r\n  end  \r\nend","test_suite":"%%\r\nn = 10;\r\ny_correct = [1.0000    3.0000    5.0000    7.0000    9.0000    6.0000         0    0.2500    0.5000    0.7500    1.0000]\r\nassert(isequal(odd_even_num(n),y_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":584788,"edited_by":584788,"edited_at":"2024-04-06T10:01:03.000Z","deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":"2024-04-06T07:54:10.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2024-04-06T07:42:57.000Z","updated_at":"2024-11-01T22:33:34.000Z","published_at":"2024-04-06T07:42:57.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven an input value n, create a vector which contains all odd numbers  \u0026amp; even numbers centered around mean of vector. If the mean is even/decimal number, round and rescale the even values of vecto. Similarly if the mean of vector is odd, rescale the odd numbers and present it as Odd-Even format \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60176,"title":"Find the number of diagonals in a n sided polygon.","description":"Find the number of diagonals in a n sided polygon.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 21px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 10.5px; transform-origin: 407px 10.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFind the number of diagonals in a n sided polygon.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = count_diagonals(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx =12;\r\ny_correct =54;\r\nassert(isequal(count_diagonals(x),y_correct))\r\n\r\nx =4;\r\ny_correct =2;\r\nassert(isequal(count_diagonals(x),y_correct))\r\n\r\nx =3;\r\ny_correct =0;\r\nassert(isequal(count_diagonals(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":3469688,"edited_by":3469688,"edited_at":"2024-05-02T19:23:51.000Z","deleted_by":null,"deleted_at":null,"solvers_count":15,"test_suite_updated_at":"2024-05-02T19:23:51.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2024-05-02T18:52:26.000Z","updated_at":"2024-11-04T22:23:28.000Z","published_at":"2024-05-02T19:23:51.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the number of diagonals in a n sided polygon.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":51173,"title":"Squares inside a square! ","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 99.7778px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.5px 49.8889px; transform-origin: 406.5px 49.8889px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 40.8889px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 20.4444px; text-align: left; transform-origin: 383.5px 20.4444px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eIf you have a square has a side (x) that is divided into four squares. Two of those squares carries smaller squares inside them. Each side carries 5 squares. Find the area of one of these small squares. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.4444px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 10.2222px; text-align: left; transform-origin: 383.5px 10.2222px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.4444px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 10.2222px; text-align: left; transform-origin: 383.5px 10.2222px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = squares_inside_square(x)\r\n  y = ;\r\nend","test_suite":"%%\r\nx = 500;\r\ny_correct = 2500;\r\nassert(isequal(squares_inside_square(x),y_correct))\r\n\r\n%%\r\nx = 100;\r\ny_correct = 100;\r\nassert(isequal(squares_inside_square(x),y_correct))\r\n\r\n%%\r\nx = 50;\r\ny_correct = 25;\r\nassert(isequal(squares_inside_square(x),y_correct))\r\n\r\n%%\r\nx = 30;\r\ny_correct = 9;\r\nassert(isequal(squares_inside_square(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":3,"created_by":995198,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":54,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-03-24T11:45:55.000Z","updated_at":"2024-11-05T19:25:27.000Z","published_at":"2021-03-24T11:45:55.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf you have a square has a side (x) that is divided into four squares. Two of those squares carries smaller squares inside them. Each side carries 5 squares. Find the area of one of these small squares. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60181,"title":"Integer Persistence, Product","description":"Let's construct a sequence  as follows:  is a given natural number, and  is the product of the digits of . The persistence of  is defined as the smallest index  such that . \r\nComplete the function persistance(u0) which, for a given , returns its persistence.\r\n\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 137.159px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 386.491px 68.5795px; transform-origin: 386.499px 68.5795px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 43.5227px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 363.494px 21.7614px; text-align: left; transform-origin: 363.501px 21.7614px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eLet's construct a sequence \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"46\" height=\"18.5\" style=\"width: 46px; height: 18.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e as follows: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"15.5\" height=\"18.5\" style=\"width: 15.5px; height: 18.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is a given natural number, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"28.5\" height=\"18.5\" style=\"width: 28.5px; height: 18.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the product of the digits of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB8AAAAlCAYAAAC6TzLyAAAAAXNSR0IArs4c6QAAAmZJREFUWEft1l/ojncYBvAPWspmB8NioiihjaIMOVBSGi20LAfKn5oSsbK1WjjyL4TIUGQpB/60lcaBwqkkB0gciOLA35a1YZn43nW/9fb2/vbr93r4nbzfeuvt6fne131f131f99NDN54e3YitDd4t7Ldpb9P+XhloN9x7pbsG9n+0f4wx+LL8TuNmQ4afYARe4nIr2TcDH4bvsRh98Rqf4nEDwDasxnlMqwq8FmcLfsRVjG0I3gv3MBBrsKFq8N8xB7uxsiH4LPyRzybjQpXgIcdD9C+Vf1Mq/60h+El8jb8Q2r+qEvyLpLuZ3p/jCnoikpjdCnDc6ajbVyTdzfSuyRH3V5XKd1UNfiLpbtR7OpZnLwRmsHC9SvCO9O6DA9nlMQX3MahV4I5oj2quNZnvoPdgGa99mFQM5ggW1IF/gB8wrvTC+DL/U8sY/lc84pf8vxHb65NtpvmyvFCv96KscieelrkOoIU4jCUImaLze2fi8c5XZQrWYgfO5PRM6Qz81wx8KAPHrIfbzcWEupkegpH5bHMGDfA/sRUf4Wf8iwc5Gd91Bl7r5rhwqXR9P8zIymYWsFMZIGT4DPPr5jxs9mzKsx53CjvDcSvfO9oZeJhH6PQis11XbPafvPQhzmFU6fTj6XzP6gJuwk/p+UF3nKXYm/vhSWfgb9PAwdTgrPZ5Bookh2JiY+Aqv2TCZh8VrWPbRfVxwgXj2Z5cPrExb9SSqBJ8Ho5lhRcTIMYudn30xehM7O93Ab4/fT6MJ3ZCnAG5I24XJ/wWd9+l5l3qlypp7xJwR/ba5SCtXmhX3ipzb3XvDRG8cSbnMUYnAAAAAElFTkSuQmCC\" width=\"15.5\" height=\"18.5\" style=\"width: 15.5px; height: 18.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The persistence of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB8AAAAlCAYAAAC6TzLyAAAAAXNSR0IArs4c6QAAApZJREFUWEftllmoTWEUx3+XRIQyhRIeRBneCOXBFJGQB4oyPd2uaxaZyjyEzHkgUl4QJTwowwvdJAop7zIlQoZCrL/W1udr79252veeB/ur83D22Xv91/oPa58aqnhqqohNCV4V9kvaS9qblYHScM1KdwKWR3sHYDAwzD5XgadRh52AfsA34P6/dJ8G3hdYCswH2gM/gW7AmwhgD7ACuAmMKQo8qbMbWAU8AoZExVsCz4DuwHpgW9HgF4FpwCFgcVR8MnDZr40AGooElxyvgS42+Qyb/EJU/BIwBfgASPsfwe9dgX0uVzvgs0m2CHgfN5hluEFOd5reA4GHQAtATUwNinZ0D8igkkNH3hgJTDCPfAwbyAJXp6I7Te9EDtVZYpMfDAoeBhbYs52BL35d0791X2yuBPy80x3rPQ6ocy+ojlh44gVbAy+MiQfA2Iji20BvoI8x8j0v51l6twWOu8uVgpdAjwBkvNF7zeK5F1gZgYudeuAvc6bRrmkep+RbBU5YvI4Bw23BnAHmBCALvbl1wPYIfBOwEZgJnM2bvNaWytFI73k+5X53bStgLnDaNZZM0l+ayi9HIvBlngAxImZ+n7TJT3nhk15YWde2mw4MDTLdC+jv13YCa91U8oSaD4/2xAFgDbArDzxx8yvgnjtXMVGmJxnYFX9YMvQEZnnOE9rVxI4IfIOzkrCVObmWhzr/6jmWVp+C2NwABpjTz/nm0xLR0X6/Dmgtr47AtXRE/WjgVt7k0XMVf5UPxNZdk2Zi9JQa1vtB6dBbMHPyitFSblQSZvvKTUDamBnfeVJkxj+n6L9RegXf8ThtcZSt/h4Y5b5pMnAVVgq0z+UZ7X/JsRx4HjNV9OSNkqwEbxRdRd38/9L+C782fiZdt1vKAAAAAElFTkSuQmCC\" width=\"15.5\" height=\"18.5\" style=\"width: 15.5px; height: 18.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is defined as the smallest index \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e such that \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"49\" height=\"18.5\" style=\"width: 49px; height: 18.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22.8267px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 363.494px 11.4062px; text-align: left; transform-origin: 363.501px 11.4134px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eComplete the function \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003epersistance(u0)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e which, for a given \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"15.5\" height=\"18.5\" style=\"width: 15.5px; height: 18.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, returns its persistence.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22.8267px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 363.494px 11.4062px; text-align: left; transform-origin: 363.501px 11.4134px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0085px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 363.494px 10.4972px; text-align: left; transform-origin: 363.501px 10.5043px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function idx = persistance(n)\r\n\r\nend","test_suite":"%% Test Case 1: n = 7\r\nassert(persistance(7) == 0);\r\n\r\n%% Test Case 2: n = 18\r\nassert(persistance(18) == 1);\r\n\r\n%% Test Case 3: n = 23\r\nassert(persistance(23) == 1);\r\n\r\n%% Test Case 4: n = 97\r\nassert(persistance(97) == 3);\r\n\r\n%% Test Case 5: n = 1009\r\nassert(persistance(1009) == 1);\r\n\r\n%% Test Case 6: n = 12345\r\nassert(persistance(12345) == 2);\r\n\r\n%% Random Test Case 1\r\nn = randi([1, 9])\r\nassert(persistance(n) == 0);\r\n\r\n%% Random Test Case 2\r\nL = [10:24,100:111,200:211,300:311,1000:1111];\r\nn = L(randi([1, numel(L)]))\r\nassert(persistance(n) == 1);\r\n\r\n%% Random Test Case 3\r\nL = [679, 688, 697, 769, 796, 868, 886, 967, 976, 9969, 9996];\r\nn = L(randi([1, numel(L)]))\r\nassert(persistance(n) == 5);\r\n\r\n%% Random Test Case 4\r\nn = randi([93, 98])\r\nassert(persistance(n) == 3);\r\n\r\n%% Random Test Case 5\r\nformat long\r\nnbDig = randi([5, 10]);\r\nnb = randi([0, 1], 1, nbDig);\r\nn = str2double(strrep(num2str(nb), ' ', ''))\r\nassert(persistance(n) == 1);\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":3,"created_by":208445,"edited_by":208445,"edited_at":"2024-05-03T17:21:46.000Z","deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":"2024-05-03T17:21:46.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2024-05-03T16:44:48.000Z","updated_at":"2024-05-03T17:21:46.000Z","published_at":"2024-05-03T17:21:46.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLet's construct a sequence \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e(u_n)_{n\\\\in\\\\mathbb{N}}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e as follows: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eu_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is a given natural number, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eu_{n+1}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the product of the digits of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eu_n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. The persistence of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eu_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is defined as the smallest index \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e such that \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eu_n\u0026lt;10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eComplete the function \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003epersistance(u0)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e which, for a given \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eu_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, returns its persistence.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60201,"title":"Find the largest sum of any contiguous subarray","description":"Given an array of N integers, find the contiguous subarray (which must contain at least one number) with the maximum sum and return its sum. \r\nHere are some examples:\r\nmax_subarray([1,2,3,-2,5]) should return 9 because the sum of the subarray [1,2,3,-2,5] is 9, and the sum of any other subarray is always less.\r\nmax_subarray([-1,-2,-3,-4]) should return -1 because the maximum sum subarray is [-1].\r\nmax_subarray([5,-1,6,-2,7]) should return 15 because the maximum sum subarray is [5, -1, 6, -2, 7].\r\nmax_subarray([-2, 1, -3, 4, -1, 2, 1, -5, 4]) should return 6 because the maximum sum subarray is [4, -1, 2, 1].\r\nmax_subarray([-2, -5, 6, -2, -3, 1, 5, -6]) should return 7 because the maximum sum subarray is [6, -2, -3, 1, 5].","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 273.253px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 386.491px 136.619px; transform-origin: 386.499px 136.626px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42.017px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 363.494px 21.0085px; text-align: left; transform-origin: 363.501px 21.0085px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven an array of N integers, find the contiguous subarray (which must contain at least one number) with the maximum sum and return its sum. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0085px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 363.494px 10.4972px; text-align: left; transform-origin: 363.501px 10.5043px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHere are some examples:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003col style=\"block-size: 191.236px; font-family: Helvetica, Arial, sans-serif; list-style-type: decimal; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 370.497px 95.6108px; transform-origin: 370.497px 95.6179px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 41.7898px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 342.5px 20.8949px; text-align: left; transform-origin: 342.5px 20.8949px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003emax_subarray([1,2,3,-2,5])\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e should return \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e9\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e because the sum of the subarray \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e[1,2,3,-2,5]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e9\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and the sum of any other subarray is always less.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 21.3494px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 342.5px 10.6676px; text-align: left; transform-origin: 342.5px 10.6747px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003emax_subarray([-1,-2,-3,-4])\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e should return \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e-1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e because the maximum sum subarray is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e[-1]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 42.6989px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 342.5px 21.3494px; text-align: left; transform-origin: 342.5px 21.3494px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003emax_subarray([5,-1,6,-2,7])\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e should return \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e15\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e because the maximum sum subarray is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e[5, -1, 6, -2, 7]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 42.6989px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 342.5px 21.3494px; text-align: left; transform-origin: 342.5px 21.3494px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003emax_subarray([-2, 1, -3, 4, -1, 2, 1, -5, 4])\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e should return \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e6\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e because the maximum sum subarray is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e[4, -1, 2, 1]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 42.6989px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 342.5px 21.3494px; text-align: left; transform-origin: 342.5px 21.3494px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003emax_subarray([-2, -5, 6, -2, -3, 1, 5, -6])\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e should return \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e7\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e because the maximum sum subarray is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e[6, -2, -3, 1, 5]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = max_subarray(x)\r\n  \r\nend","test_suite":"%% \r\nassert(isequal(max_subarray([5,-1,6,-2,7]),15))\r\n\r\n%% \r\nassert(isequal(max_subarray([-2, 1, -3, 4, -1, 2, 1, -5, 4]),6))\r\n\r\n%% \r\nassert(isequal(max_subarray([-2, -5, 6, -2, -3, 1, 5, -6]),7))\r\n\r\n%% If the array contains all non-negative numbers, a maximum subarray is the entire array.\r\nx = randi([0,100],1,30)\r\ny_correct = sum(x)\r\nassert(isequal(max_subarray(x),y_correct))\r\n\r\n%% If the array contains all non-positive numbers, then a solution is any subarray of size 1 containing the maximal value of the array\r\nx = -randi([0,100],1,30)\r\ny_correct = max(x)\r\nassert(isequal(max_subarray(x),y_correct))\r\n\r\n%%\r\nell1 = randi([10,30]);\r\nx1 = -randi([0,100],1,ell1);\r\nell2 = randi([5,76]);\r\nx2 = randi([0,100],1,ell2);\r\nx = [x1,x2]\r\ny_correct = sum(x2)\r\nassert(isequal(max_subarray(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":208445,"edited_by":208445,"edited_at":"2024-05-04T14:13:44.000Z","deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":"2024-05-04T14:13:44.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2024-05-04T14:09:16.000Z","updated_at":"2024-11-20T07:56:33.000Z","published_at":"2024-05-04T14:13:44.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven an array of N integers, find the contiguous subarray (which must contain at least one number) with the maximum sum and return its sum. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHere are some examples:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emax_subarray([1,2,3,-2,5])\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e should return \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e9\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e because the sum of the subarray \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[1,2,3,-2,5]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e9\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and the sum of any other subarray is always less.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emax_subarray([-1,-2,-3,-4])\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e should return \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e-1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e because the maximum sum subarray is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[-1]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emax_subarray([5,-1,6,-2,7])\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e should return \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e15\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e because the maximum sum subarray is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[5, -1, 6, -2, 7]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emax_subarray([-2, 1, -3, 4, -1, 2, 1, -5, 4])\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e should return \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e6\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e because the maximum sum subarray is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[4, -1, 2, 1]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emax_subarray([-2, -5, 6, -2, -3, 1, 5, -6])\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e should return \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e7\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e because the maximum sum subarray is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[6, -2, -3, 1, 5]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60216,"title":"Perfect shuffle","description":"We call \"perfect shuffle\" the process of cutting a deck of cards into two equal halves, and then perfectly interleaving them: one card from the left stack, one card from the right stack, one card from the left stack, and so on.\r\nLet \"deck\" be an array with an even number of elements. Write a function \"perfect_shuffle(deck)\" that returns a new array constructed according to this shuffle.\r\nFor example, perfect_shuffle([1, 2, 3, 4, 5, 6]) should return [1, 4, 2, 5, 3, 6].\r\nRemark: For an array of 1024 elements, after 10 shuffles, we get back to the initial arrangement.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 153.026px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 441.989px 76.5057px; transform-origin: 441.996px 76.5128px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42.017px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 418.991px 21.0085px; text-align: left; transform-origin: 418.999px 21.0085px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWe call \"perfect shuffle\" the process of cutting a deck of cards into two equal halves, and then perfectly interleaving them: one card from the left stack, one card from the right stack, one card from the left stack, and so on.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42.017px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 418.991px 21.0085px; text-align: left; transform-origin: 418.999px 21.0085px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eLet \"deck\" be an array with an even number of elements. Write a function \"perfect_shuffle(deck)\" that returns a new array constructed according to this shuffle.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0085px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 418.991px 10.4972px; text-align: left; transform-origin: 418.999px 10.5043px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example, perfect_shuffle([1, 2, 3, 4, 5, 6]) should return [1, 4, 2, 5, 3, 6].\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0085px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 418.991px 10.4972px; text-align: left; transform-origin: 418.999px 10.5043px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eRemark: For an array of 1024 elements, after 10 shuffles, we get back to the initial arrangement.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = perfect_shuffle(x)\r\n  \r\nend","test_suite":"%%  \r\nx = [1, 2, 3, 4, 5, 6];\r\ny_correct = [1, 4, 2, 5, 3, 6];\r\ny = perfect_shuffle(x);\r\nassert(isequal(y, y_correct));\r\n\r\n%%  \r\nx = [1, 4, 2, 5, 3, 6];\r\ny_correct = [1, 5, 4, 3, 2, 6];\r\ny = perfect_shuffle(x);\r\nassert(isequal(y, y_correct));\r\n\r\n%%  \r\nx = [10, 20, 30, 40, 50, 60, 70, 80];\r\ny_correct = [10, 50, 20, 60, 30, 70, 40, 80];\r\ny = perfect_shuffle(x);\r\nassert(isequal(y, y_correct));\r\n\r\n%% \r\nx = randperm(6);\r\ny_correct = x;\r\nfor i = 1:4\r\n    y_correct = perfect_shuffle(y_correct);\r\nend\r\nassert(isequal(y_correct, x));\r\n\r\n%% \r\nx = randperm(1024);\r\ny_correct = x;\r\nfor i = 1:10\r\n    y_correct = perfect_shuffle(y_correct);\r\nend\r\nassert(isequal(y_correct, x));\r\n\r\n\r\n%% \r\nnn = [6, 30, 22, 126, 16, 124, 120, 118, 116, 114, 112, 110, 100, 98];\r\nii = [4, 28,  6, 100,  4,  20,  24,  12,  44,  28,  36,  36,  30, 48];\r\nidx = randi(length(nn)); % random index\r\nn = nn(idx) % number of elements\r\nj = ii(idx) % number of shuffles to get back to the initial arrangement for n elements\r\nx = randperm(n); % array of n elements\r\ny_correct = x;\r\nfor i = 1:j\r\n    y_correct = perfect_shuffle(y_correct);\r\nend\r\nassert(isequal(y_correct, x));\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":208445,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":12,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-05-05T08:41:11.000Z","updated_at":"2024-05-05T08:41:11.000Z","published_at":"2024-05-05T08:41:11.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWe call \\\"perfect shuffle\\\" the process of cutting a deck of cards into two equal halves, and then perfectly interleaving them: one card from the left stack, one card from the right stack, one card from the left stack, and so on.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLet \\\"deck\\\" be an array with an even number of elements. Write a function \\\"perfect_shuffle(deck)\\\" that returns a new array constructed according to this shuffle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, perfect_shuffle([1, 2, 3, 4, 5, 6]) should return [1, 4, 2, 5, 3, 6].\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRemark: For an array of 1024 elements, after 10 shuffles, we get back to the initial arrangement.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60221,"title":"Battery Charge Indicator","description":"Write a function called battery_charge that visually represents the charge of a battery.\r\nThe function takes an integer parameter percentage between 0 and 100 representing the battery charge percentage. It returns an array bars where each element contains a single character (visually representing the battery charge). \r\nThe array starts with '[', ends with ']', and contains from 0 to 10 characters '❚' or ' ' (space) to visually represent the battery charge. The number of '❚' characters is rounded, meaning that for percentages like 9% and 11%, only one ❚ will be used.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 132.116px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 441.989px 66.0511px; transform-origin: 441.996px 66.0582px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 22.8267px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 418.991px 11.4062px; text-align: left; transform-origin: 418.999px 11.4134px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function called \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ebattery_charge\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e that visually represents the charge of a battery.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 45.6534px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 418.991px 22.8267px; text-align: left; transform-origin: 418.999px 22.8267px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe function takes an integer parameter \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003epercentage\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e between 0 and 100 representing the battery charge percentage. It returns an array \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ebars\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e where each element contains a single character (visually representing the battery charge). \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 45.6534px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 418.991px 22.8267px; text-align: left; transform-origin: 418.999px 22.8267px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe array starts with '\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e['\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, ends with '\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e]'\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and contains from 0 to 10 characters '\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e❚' or ' '\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (space) to visually represent the battery charge. The number of '\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e❚'\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e characters is rounded, meaning that for percentages like 9% and 11%, only one \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e❚\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e will be used.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function bars = battery_charge(percentage)\r\n  \r\nend","test_suite":"%% Verify the charge bar for 9%\r\nexpected_result = [ '[', '❚', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ']' ]\r\nobtained_result = battery_charge(9) \r\nassert(isequal(obtained_result, expected_result));\r\n\r\n%% Verify the charge bar for 11%\r\nexpected_result = [ '[', '❚', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ']' ]\r\nobtained_result = battery_charge(11) \r\nassert(isequal(obtained_result, expected_result));\r\n\r\n%% Verify the charge bar for 16%\r\nexpected_result = [ '[', '❚', '❚', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ']' ]\r\nobtained_result = battery_charge(16) \r\nassert(isequal(obtained_result, expected_result));\r\n\r\n%% Verify the charge bar for 99%\r\nexpected_result = [ '[', '❚', '❚', '❚', '❚', '❚', '❚', '❚', '❚', '❚', '❚', ']' ]\r\nobtained_result = battery_charge(99) \r\nassert(isequal(obtained_result, expected_result));\r\n\r\n%% Verify the charge bar for 4%\r\nexpected_result = [ '[', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ']' ]\r\nobtained_result = battery_charge(4) \r\nassert(isequal(obtained_result, expected_result));\r\n\r\n%% Random test case\r\npercentage = randi([6, 87]); \r\nobtained_result = battery_charge(percentage);\r\nassert(length(obtained_result) == 12, 'Incorrect length');\r\nassert(obtained_result(1) == '[', 'Missing opening bracket');\r\nassert(obtained_result(end) == ']', 'Missing closing bracket');\r\nexpected_bars = min(round(percentage/10), 10);\r\nobtained_bars = sum(obtained_result == '❚');\r\nassert(obtained_bars == expected_bars, 'Incorrect number of bars');\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":208445,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":12,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-05-05T09:20:21.000Z","updated_at":"2024-11-16T11:33:39.000Z","published_at":"2024-05-05T09:20:21.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function called \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ebattery_charge\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e that visually represents the charge of a battery.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe function takes an integer parameter \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003epercentage\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e between 0 and 100 representing the battery charge percentage. It returns an array \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ebars\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e where each element contains a single character (visually representing the battery charge). \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe array starts with '\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e['\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, ends with '\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e]'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and contains from 0 to 10 characters '\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e❚' or ' '\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (space) to visually represent the battery charge. The number of '\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e❚'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e characters is rounded, meaning that for percentages like 9% and 11%, only one \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e❚\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e will be used.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":42778,"title":"GJam March 2016 IOW: Polynesiaglot Medium","description":"This Challenge is derived from GJam March 2016 Annual I/O for Polynesiaglot. This is a subset of small set 2. The max Qraw is 2^50 (\u003c1.1259e15) for C[1,50], V[1,50], L[1,15].\r\nThe GJam story goes that words are such that consonants are always followed by a vowel. Determine the number of possible words of length L using C consonants and V vowels. The final Q is to be modulo of the prime 1E9+7.\r\nInput: [C V L] , C[1,50], V[1,50], 1\u003c=L\u003c=15\r\nOutput: [Q] max Qraw is 2^50 (\u003c1.1259e15); Q=mod(Qraw,1E9+7)\r\nExamples: [C V L] [Q]\r\n[1 1 4] [5] {aaaa,aaba,abaa,baaa,baba}  invalid are {bbaa, aaab} \r\n[1 2 2] [6] {aa,ae,ba,be,ee,ea} invalid are {ab,eb,bb}\r\nGoogle Code Jam 2016 Open Qualifier: April 8, 2016\r\nTheory: This is a large value problem, on the order of (C+V)^L, thus brute force will not work. This is also a probability tree type problem. Tree calculations can be reduced to a linear in L evaluation. Inspection shows Q(1)=V, Q(2)=V^2, L=3 Q(3)=V^3+V*C*V+C*V^2 = V*Q(L-1)+V*C*Q(L-2)+C*Q(L-1). There are no Cs at the Q1 level since can not end in a C. Qnext=f(Q(-1),Q(-2)). Qfinal=Q+C*Q(-1)\r\nQ3    V          C\r\nQ2  V   C       V\r\nQ1 V   V       V\r\n\r\nThis medium challenge has eps(Qraw) \u003c0.25 so normal matlab doubles work. For the unbounded case a solution method is to convert this Challenge algorithm to Matlab BigInteger java calls. Solution sizes are on the order of (C+V)^L with the large case being C=50,V=50,L=500.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 522.625px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407.5px 261.312px; transform-origin: 407.5px 261.312px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 21px; text-align: left; transform-origin: 384.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThis Challenge is derived from\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"/#null\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eGJam March 2016 Annual I/O for Polynesiaglot\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. This is a subset of small set 2. The max Qraw is 2^50 (\u0026lt;1.1259e15) for C[1,50], V[1,50], L[1,15].\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 21px; text-align: left; transform-origin: 384.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThe GJam story goes that words are such that consonants are always followed by a vowel. Determine the number of possible words of length L using C consonants and V vowels. The final Q is to be modulo of the prime 1E9+7.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.5px; text-align: left; transform-origin: 384.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eInput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e [C V L] , C[1,50], V[1,50], 1\u0026lt;=L\u0026lt;=15\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.5px; text-align: left; transform-origin: 384.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eOutput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e [Q] max Qraw is 2^50 (\u0026lt;1.1259e15); Q=mod(Qraw,1E9+7)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.5px; text-align: left; transform-origin: 384.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExamples:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e [C V L] [Q]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 40.875px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404.5px 20.4375px; transform-origin: 404.5px 20.4375px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.666667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.666667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.666667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.666667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404.5px 10.2188px; text-wrap: nowrap; transform-origin: 404.5px 10.2188px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e[1 1 4] [5] {aaaa,aaba,abaa,baaa,baba}  invalid \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003eare {bbaa, aaab} \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.666667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.666667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.666667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.666667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404.5px 10.2188px; text-wrap: nowrap; transform-origin: 404.5px 10.2188px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e[1 2 2] [6] {aa,ae,ba,be,ee,ea} invalid \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003eare {ab,eb,bb}\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384.5px 10.5px; text-align: left; transform-origin: 384.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"/#null\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"font-weight: 700; \"\u003eGoogle Code Jam 2016 Open Qualifier: April 8, 2016\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 42px; text-align: left; transform-origin: 384.5px 42px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eTheory:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e This is a large value problem, on the order of (C+V)^L, thus brute force will not work. This is also a probability tree type problem. Tree calculations can be reduced to a linear in L evaluation. Inspection shows Q(1)=V, Q(2)=V^2, L=3 Q(3)=V^3+V*C*V+C*V^2 = V*Q(L-1)+V*C*Q(L-2)+C*Q(L-1). There are no Cs at the Q1 level since can not end in a C. Qnext=f(Q(-1),Q(-2)). Qfinal=Q+C*Q(-1)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 81.75px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404.5px 40.875px; transform-origin: 404.5px 40.875px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.666667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.666667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.666667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.666667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404.5px 10.2188px; text-wrap: nowrap; transform-origin: 404.5px 10.2188px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eQ3    \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003eV\u003c/span\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e          \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003eC\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.666667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.666667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.666667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.666667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404.5px 10.2188px; text-wrap: nowrap; transform-origin: 404.5px 10.2188px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eQ2  \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003eV\u003c/span\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e   \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003eC\u003c/span\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e       \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003eV\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.666667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.666667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.666667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.666667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404.5px 10.2188px; text-wrap: nowrap; transform-origin: 404.5px 10.2188px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eQ1 \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003eV\u003c/span\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e   \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003eV\u003c/span\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e       \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003eV\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.666667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.666667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.666667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.666667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404.5px 10.2188px; text-wrap: nowrap; transform-origin: 404.5px 10.2188px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384.5px 31.5px; text-align: left; transform-origin: 384.5px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThis medium challenge has eps(Qraw) \u0026lt;0.25 so normal matlab doubles work. For the unbounded case a solution method is to convert this Challenge algorithm to Matlab BigInteger java calls. Solution sizes are on the order of (C+V)^L with the large case being C=50,V=50,L=500.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function Q=Polyglot(m)\r\n% Q total words of length L using C consonants and V vowels\r\n% Q is modulo 1E9+7\r\n C=m(1); V=m(2);L=m(3); %\r\n Q=0;\r\n\r\nend","test_suite":"%%\r\ntic\r\nm=[2 8 15 ];\r\nv=Polyglot(m);\r\nvexp=[6938704 ];\r\nassert(isequal(vexp,v))\r\n%%\r\nm=[2 7 15 ];\r\nv=Polyglot(m);\r\nvexp=[853390015];\r\nassert(isequal(vexp,v))\r\n%%\r\nm=[2 2 2 ];\r\nv=Polyglot(m);\r\nvexp=[8];\r\nassert(isequal(vexp,v))\r\n%%\r\nm=[2 2 3 ];\r\nv=Polyglot(m);\r\nvexp=[24];\r\nassert(isequal(vexp,v))\r\n%%\r\nm=[2 2 15];\r\nv=Polyglot(m);\r\nvexp=[32342016 ];\r\nassert(isequal(vexp,v))\r\n%%\r\nm=[4 2 2];\r\nv=Polyglot(m);\r\nvexp=[12];\r\nassert(isequal(vexp,v))\r\n%%\r\nm=[4 2 3];\r\nv=Polyglot(m);\r\nvexp=[40];\r\nassert(isequal(vexp,v))\r\n%%\r\nm=[4 2 4];\r\nv=Polyglot(m);\r\nvexp=[176];\r\nassert(isequal(vexp,v))\r\n%%\r\nm=[44 2 15];\r\nv=Polyglot(m);\r\nvexp=[916593151];\r\nassert(isequal(vexp,v))\r\n%%\r\nm=[1 3 15];\r\nv=Polyglot(m);\r\nvexp=[397629405];\r\nassert(isequal(vexp,v))\r\n%%\r\nm=[2 3 15];\r\nv=Polyglot(m);\r\nvexp=[105078522];\r\nassert(isequal(vexp,v))\r\n%%\r\nm=[2 4 15];\r\nv=Polyglot(m);\r\nvexp=[133836675];\r\nassert(isequal(vexp,v))\r\n%%\r\nm=[2 8 15];\r\nv=Polyglot(m);\r\nvexp=[6938704];\r\nassert(isequal(vexp,v))\r\n%%\r\nm=[2 8 14];\r\nv=Polyglot(m);\r\nvexp=[624439943];\r\nassert(isequal(vexp,v))\r\n%%\r\nm=[50 50 2];\r\nv=Polyglot(m);\r\nvexp=[5000];\r\nassert(isequal(vexp,v))\r\n%%\r\nm=[50 50 3];\r\nv=Polyglot(m);\r\nvexp=[375000];\r\nassert(isequal(vexp,v))\r\n%%\r\nm=[50 50 7];\r\nv=Polyglot(m);\r\nvexp=[249885158];\r\nassert(isequal(vexp,v))\r\n%%\r\nm=[10 20 10];\r\nv=Polyglot(m);\r\nvexp=[998720967];\r\nassert(isequal(vexp,v))\r\n%%\r\nm=[5 10 13];\r\nv=Polyglot(m);\r\nvexp=[746816099];\r\nassert(isequal(vexp,v))\r\n%%\r\nm=[1 1 13 ];\r\nv=Polyglot(m);\r\nvexp=[377 ];\r\nassert(isequal(vexp,v))\r\n\r\n\r\ntoc\r\n","published":true,"deleted":false,"likes_count":8,"comments_count":1,"created_by":3097,"edited_by":7,"edited_at":"2023-07-14T16:27:46.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2016-03-19T18:33:48.000Z","updated_at":"2024-11-07T10:33:15.000Z","published_at":"2016-03-19T20:24:10.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis Challenge is derived from\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eGJam March 2016 Annual I/O for Polynesiaglot\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. This is a subset of small set 2. The max Qraw is 2^50 (\u0026lt;1.1259e15) for C[1,50], V[1,50], L[1,15].\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe GJam story goes that words are such that consonants are always followed by a vowel. Determine the number of possible words of length L using C consonants and V vowels. The final Q is to be modulo of the prime 1E9+7.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e [C V L] , C[1,50], V[1,50], 1\u0026lt;=L\u0026lt;=15\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e [Q] max Qraw is 2^50 (\u0026lt;1.1259e15); Q=mod(Qraw,1E9+7)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExamples:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e [C V L] [Q]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[[1 1 4] [5] {aaaa,aaba,abaa,baaa,baba}  invalid are {bbaa, aaab} \\n[1 2 2] [6] {aa,ae,ba,be,ee,ea} invalid are {ab,eb,bb}]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGoogle Code Jam 2016 Open Qualifier: April 8, 2016\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eTheory:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e This is a large value problem, on the order of (C+V)^L, thus brute force will not work. This is also a probability tree type problem. Tree calculations can be reduced to a linear in L evaluation. Inspection shows Q(1)=V, Q(2)=V^2, L=3 Q(3)=V^3+V*C*V+C*V^2 = V*Q(L-1)+V*C*Q(L-2)+C*Q(L-1). There are no Cs at the Q1 level since can not end in a C. Qnext=f(Q(-1),Q(-2)). Qfinal=Q+C*Q(-1)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[Q3    V          C\\nQ2  V   C       V\\nQ1 V   V       V\\n]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis medium challenge has eps(Qraw) \u0026lt;0.25 so normal matlab doubles work. For the unbounded case a solution method is to convert this Challenge algorithm to Matlab BigInteger java calls. Solution sizes are on the order of (C+V)^L with the large case being C=50,V=50,L=500.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":2390,"title":"Fair Scoring for Cody","description":"The length-based scoring system for Cody has a few well-known loopholes that allow clever programmers to hide complex code inside certain functions so that it doesn't register in the score.  This problem represents an attempt to generate a fairer Cody scoring function.  It doesn't try to replace the length-based criterion with something more elegant; merely to eliminate places where longer code can be hidden and remain undetected by the scoring function.\r\n\r\nI have included a few examples that I consider abusive to start with.  These are just my own opinions.  Please feel free to add your suggestions for others in the comments section for this problem, and I will add good ideas to the test suite when I have the time.  Thanks for playing!\r\n\r\n* regexp:  count number of nodes inside (?@cmd) and add to total\r\n* regexprep:  count number of nodes inside {$cmd} and add to total\r\n\r\nUsing this scoring function, it might even be possible to allow use of eval.\r\n\r\n* eval:  count number of nodes inside argument to be evaluated and add to total\r\n\r\nOther possibilities -- should str2num count the numbers inside its argument?  Suggestions welcome!  And if you support the idea of changing the scoring function along these lines, please 'like' this problem.  Thanks!\r\n\r\nSee also http://www.mathworks.com/matlabcentral/cody/problems/2033-poll-would-you-like-the-regexp-cmd-functionality-to-be-banned-in-cody","description_html":"\u003cp\u003eThe length-based scoring system for Cody has a few well-known loopholes that allow clever programmers to hide complex code inside certain functions so that it doesn't register in the score.  This problem represents an attempt to generate a fairer Cody scoring function.  It doesn't try to replace the length-based criterion with something more elegant; merely to eliminate places where longer code can be hidden and remain undetected by the scoring function.\u003c/p\u003e\u003cp\u003eI have included a few examples that I consider abusive to start with.  These are just my own opinions.  Please feel free to add your suggestions for others in the comments section for this problem, and I will add good ideas to the test suite when I have the time.  Thanks for playing!\u003c/p\u003e\u003cul\u003e\u003cli\u003eregexp:  count number of nodes inside (?@cmd) and add to total\u003c/li\u003e\u003cli\u003eregexprep:  count number of nodes inside {$cmd} and add to total\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eUsing this scoring function, it might even be possible to allow use of eval.\u003c/p\u003e\u003cul\u003e\u003cli\u003eeval:  count number of nodes inside argument to be evaluated and add to total\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eOther possibilities -- should str2num count the numbers inside its argument?  Suggestions welcome!  And if you support the idea of changing the scoring function along these lines, please 'like' this problem.  Thanks!\u003c/p\u003e\u003cp\u003eSee also \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/2033-poll-would-you-like-the-regexp-cmd-functionality-to-be-banned-in-cody\"\u003ehttp://www.mathworks.com/matlabcentral/cody/problems/2033-poll-would-you-like-the-regexp-cmd-functionality-to-be-banned-in-cody\u003c/a\u003e\u003c/p\u003e","function_template":"function y = fair_score(prog)\r\n  y = 0;\r\nend","test_suite":"%%\r\nnewline = char(10);\r\ns = ['function testStr2Num(s)' newline...\r\n'str2num(''1'')'];\r\ny_correct = 9;\r\nassert(isequal(fair_score(s),y_correct))\r\n\r\n%% should this be added?\r\n% newline = char(10);\r\n%s = ['function testStr2Num(s)' newline...\r\n%'str2num(''1 2 3'')'];\r\n%y_correct = 11;\r\n%assert(isequal(fair_score(s),y_correct))\r\n\r\n%%\r\nnewline = char(10);\r\ns = ['function testRegexp(s)' newline...\r\n'regexp(s,''(\\d)'');'];\r\ny_correct = 10;\r\nassert(isequal(fair_score(s),y_correct))\r\n\r\n%%\r\nnewline = char(10);\r\ns = ['function testRegexp(s)' newline...\r\n'regexp(s,''(.{2,}).?(??@fliplr($1))'');'];\r\ny_correct = 14;\r\nassert(isequal(fair_score(s),y_correct))\r\n\r\n%%\r\nnewline = char(10);\r\ns = ['function ans = testRegexprep(s)' newline...\r\n'regexprep(s,''(\\d)'',''A'');'];\r\ny_correct = 12;\r\nassert(isequal(fair_score(s),y_correct))\r\n\r\n%%\r\nnewline = char(10);\r\ns = ['function ans = cellSourceIndex(C)' newline...\r\n'str2num(regexprep(num2str(1:numel(C)),''(\\d)'',''${num2str(repmat(str2num($1),1,length(C{str2num($1)})))}''));'];\r\ny_correct = 36;\r\nassert(isequal(fair_score(s),y_correct))","published":true,"deleted":false,"likes_count":4,"comments_count":12,"created_by":3117,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":"2014-06-26T11:53:06.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2014-06-25T20:27:27.000Z","updated_at":"2024-11-13T11:22:05.000Z","published_at":"2014-06-25T21:05:13.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe length-based scoring system for Cody has a few well-known loopholes that allow clever programmers to hide complex code inside certain functions so that it doesn't register in the score. This problem represents an attempt to generate a fairer Cody scoring function. It doesn't try to replace the length-based criterion with something more elegant; merely to eliminate places where longer code can be hidden and remain undetected by the scoring function.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eI have included a few examples that I consider abusive to start with. These are just my own opinions. Please feel free to add your suggestions for others in the comments section for this problem, and I will add good ideas to the test suite when I have the time. Thanks for playing!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eregexp: count number of nodes inside (?@cmd) and add to total\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eregexprep: count number of nodes inside {$cmd} and add to total\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eUsing this scoring function, it might even be possible to allow use of eval.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eeval: count number of nodes inside argument to be evaluated and add to total\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOther possibilities -- should str2num count the numbers inside its argument? Suggestions welcome! And if you support the idea of changing the scoring function along these lines, please 'like' this problem. Thanks!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSee also\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/2033-poll-would-you-like-the-regexp-cmd-functionality-to-be-banned-in-cody\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ehttp://www.mathworks.com/matlabcentral/cody/problems/2033-poll-would-you-like-the-regexp-cmd-functionality-to-be-banned-in-cody\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":2907,"title":"Collaborative Fun : Nomination","description":"Series of problems have been presented in Cody aiming at collaborative fun. This problem is based on Alfonso's problem #2825 - Pay it Forward. This one encourages more directed collaboration.\r\n\r\nYou can solve this problem only if you are nominated by some other player. Once you are nominated, you can solve it by returning anything. You can nominate a player to solve this problem by returning his player ID.\r\n\r\nThis is not a hacking problem. You should hack only when you are not interested in collaboration.\r\n\r\nExample - I have nominated Alfonso by returning his player ID 1379371. (Since test suite of this problem uses codes from his problem, it is fair to nominate Alfonso)","description_html":"\u003cp\u003eSeries of problems have been presented in Cody aiming at collaborative fun. This problem is based on Alfonso's problem #2825 - Pay it Forward. This one encourages more directed collaboration.\u003c/p\u003e\u003cp\u003eYou can solve this problem only if you are nominated by some other player. Once you are nominated, you can solve it by returning anything. You can nominate a player to solve this problem by returning his player ID.\u003c/p\u003e\u003cp\u003eThis is not a hacking problem. You should hack only when you are not interested in collaboration.\u003c/p\u003e\u003cp\u003eExample - I have nominated Alfonso by returning his player ID 1379371. (Since test suite of this problem uses codes from his problem, it is fair to nominate Alfonso)\u003c/p\u003e","function_template":"function y = nomination(x)\r\n  y = ;\r\nend","test_suite":"lines=textread('nomination.m','%s');\r\nid_own=str2num(regexp(lines{end},'\\d+','match','once'));\r\n\r\nx=uint64(nomination());\r\n\r\nif x == uint64(id_own)\r\n    assignin('caller','score',-1);\r\n    error('Funny! You tried to nominate yourself!')\r\nend\r\n\r\nassignin('caller','score',x);\r\n\r\nproblem=2907;\r\nhtml=urlread(sprintf('http://www.mathworks.com/matlabcentral/cody/problems/%d/solutions?term=size:%d',problem,id_own));\r\nn=numel(regexpi(html,'solution \\d+'));\r\n\r\nif n \u003c 1\r\n    error('Sorry. You are nominated by none.');\r\nend\r\n\r\n\r\n%_______\r\n\r\nurl = sprintf('https://www.mathworks.com/matlabcentral/cody/players/%d',x);\r\nhtml = urlread(url);\r\n\r\nc = regexp(html,'h1.+h1','match');\r\nname = c{1}(4:end-4);\r\n\r\ns = sprintf('____________________\\n\\nYou have nominated %s !!!',name);\r\ndisp(s)","published":true,"deleted":false,"likes_count":3,"comments_count":6,"created_by":17203,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":"2015-02-01T12:49:00.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2015-01-31T09:55:23.000Z","updated_at":"2024-11-08T13:06:23.000Z","published_at":"2015-01-31T09:55:23.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSeries of problems have been presented in Cody aiming at collaborative fun. This problem is based on Alfonso's problem #2825 - Pay it Forward. This one encourages more directed collaboration.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou can solve this problem only if you are nominated by some other player. Once you are nominated, you can solve it by returning anything. You can nominate a player to solve this problem by returning his player ID.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis is not a hacking problem. You should hack only when you are not interested in collaboration.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample - I have nominated Alfonso by returning his player ID 1379371. (Since test suite of this problem uses codes from his problem, it is fair to nominate Alfonso)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":1752,"title":"Get me! v4   (Cody hacking challenge)","description":"The latest version of the anti-hack test-suite.\r\n","description_html":"\u003cp\u003eThe latest version of the anti-hack test-suite.\u003c/p\u003e","function_template":"function y = get_me()\r\n  y = 42;\r\nend","test_suite":"%%\r\n\r\n% Clean workspace\r\n\r\n!/bin/cp get_me.m safe\r\n!/bin/rm *.*\r\n!/bin/mv safe get_me.m\r\n!/bin/rm @*\r\n\r\n% Clean user's function from some known jailbreaking mechanisms\r\nfunctions = {'!','feval','str2func','regex','system','dos','unix','perl','java','fopen','write','save','setenv','path'};\r\n\r\nfid = fopen('get_me.m');\r\n  st = char(fread(fid)');\r\n  for n = 1:numel(functions)\r\n    st = regexprep(st, functions{n}, 'error(''No fancy functions!''); %', 'ignorecase');\r\n  end\r\nfclose(fid)\r\n\r\n% Force a function header, and comment first code's line (the supposedly users' function header)\r\nst = sprintf('function y = get_me()\\n%%%s', st);\r\n\r\nfid = fopen('get_me.m' , 'w');\r\n  fwrite(fid,st);\r\nfclose(fid)\r\n\r\n% Release the Kraken!\r\nget_me()\r\n\r\n% Try to cleanup the mess\r\n!/bin/cp get_me.m safe\r\n!/bin/rm *.*\r\n!/bin/mv safe get_me.m\r\n!/bin/rm @*\r\n\r\npath(pathdef) % undo any change on search path\r\n\r\nassert(isequal(ans,now))","published":true,"deleted":false,"likes_count":4,"comments_count":7,"created_by":3359,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":17,"test_suite_updated_at":"2013-07-26T15:59:47.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2013-07-26T15:00:58.000Z","updated_at":"2024-11-13T12:17:55.000Z","published_at":"2013-07-26T15:00:58.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe latest version of the anti-hack test-suite.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":1875,"title":"GJam: 2013 China Event: Cannon Angle","description":"This Challenge is derived from \u003chttp://code.google.com/codejam/contest/2933486/dashboard#s=p1 GJam 2013 China Captain Hammer\u003e. The problem is modified to fit within Cody dimensions.\r\n\r\nThe Challenge is to return the lower angle of a cannon given a target distance and an initial cannonball velocity. Gravity is a constant at 9.8m/sec^2, A valid solution is assured. (Error tolerance 2e-6).\r\n\r\n*Input:* [v d]  Velocity and Distance in meters.\r\n\r\n*Output:* theta  in units of degrees with an accuracy of 2e-6\r\n\r\n\r\n*Competition Summary:*  Best Time of 8 minutes,  755/1070 completed\r\n\r\nThe winner completed all three GJam China Challenges in 26 minutes with second at 43 minutes.\r\n","description_html":"\u003cp\u003eThis Challenge is derived from \u003ca href = \"http://code.google.com/codejam/contest/2933486/dashboard#s=p1\"\u003eGJam 2013 China Captain Hammer\u003c/a\u003e. The problem is modified to fit within Cody dimensions.\u003c/p\u003e\u003cp\u003eThe Challenge is to return the lower angle of a cannon given a target distance and an initial cannonball velocity. Gravity is a constant at 9.8m/sec^2, A valid solution is assured. (Error tolerance 2e-6).\u003c/p\u003e\u003cp\u003e\u003cb\u003eInput:\u003c/b\u003e [v d]  Velocity and Distance in meters.\u003c/p\u003e\u003cp\u003e\u003cb\u003eOutput:\u003c/b\u003e theta  in units of degrees with an accuracy of 2e-6\u003c/p\u003e\u003cp\u003e\u003cb\u003eCompetition Summary:\u003c/b\u003e  Best Time of 8 minutes,  755/1070 completed\u003c/p\u003e\u003cp\u003eThe winner completed all three GJam China Challenges in 26 minutes with second at 43 minutes.\u003c/p\u003e","function_template":"function theta=Cannon(v,d)\r\n  theta=0;\r\nend","test_suite":"%%\r\ntic\r\nvd=[249 6326 ];\r\nexp=44.5948575;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[77 41 ];\r\nexp=1.9429163;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[28 11 ];\r\nexp=3.9516039;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[105 21 ];\r\nexp=0.5347917;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[147 51 ];\r\nexp=0.6626633;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 3210 ];\r\nexp=10.2293872;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[219 61 ];\r\nexp=0.3570850;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[240 41 ];\r\nexp=0.1998405;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[179 3269 ];\r\nexp=44.5041154;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 3480 ];\r\nexp=11.1338133;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[102 81 ];\r\nexp=2.1878908;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[121 51 ];\r\nexp=0.9781434;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[138 31 ];\r\nexp=0.4570257;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[210 4500 ];\r\nexp=45.0000000;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[192 3761 ];\r\nexp=44.4745779;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[37 41 ];\r\nexp=8.5337735;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[32 41 ];\r\nexp=11.5514232;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[199 81 ];\r\nexp=0.5742839;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 3360 ];\r\nexp=10.7304643;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[233 71 ];\r\nexp=0.3671784;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[266 81 ];\r\nexp=0.3214027;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[27 21 ];\r\nexp=8.1988972;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[279 21 ];\r\nexp=0.0757408;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 5230 ];\r\nexp=17.3572961;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[279 51 ];\r\nexp=0.1839431;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[218 21 ];\r\nexp=0.1240585;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 7690 ];\r\nexp=28.4309587;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[89 31 ];\r\nexp=1.0990234;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[141 2028 ];\r\nexp=44.2618026;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[178 81 ];\r\nexp=0.7178094;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[132 71 ];\r\nexp=1.1443126;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 690 ];\r\nexp=2.1544417;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 6970 ];\r\nexp=24.6861041;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[41 1 ];\r\nexp=0.1670142;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[123 21 ];\r\nexp=0.3897097;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[48 61 ];\r\nexp=7.5190650;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[77 81 ];\r\nexp=3.8470546;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[152 71 ];\r\nexp=0.8628902;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[267 11 ];\r\nexp=0.0433201;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[164 21 ];\r\nexp=0.2192071;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 4310 ];\r\nexp=13.9947943;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[256 71 ];\r\nexp=0.3041622;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[192 41 ];\r\nexp=0.3122545;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 7110 ];\r\nexp=25.3662790;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[98 31 ];\r\nexp=0.9063600;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[286 21 ];\r\nexp=0.0720786;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[44 91 ];\r\nexp=13.7142226;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 8360 ];\r\nexp=32.7741901;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 5060 ];\r\nexp=16.7170592;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[194 81 ];\r\nexp=0.6042720;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[96 61 ];\r\nexp=1.8595639;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[190 1 ];\r\nexp=0.0077770;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[237 51 ];\r\nexp=0.2549165;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[52 31 ];\r\nexp=3.2254600;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[250 71 ];\r\nexp=0.3189378;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[29 61 ];\r\nexp=22.6508544;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 4030 ];\r\nexp=13.0143792;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[39 31 ];\r\nexp=5.7607904;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[62 61 ];\r\nexp=4.4733355;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[246 61 ];\r\nexp=0.2829993;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[86 51 ];\r\nexp=1.9374169;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[252 91 ];\r\nexp=0.4023216;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[275 11 ];\r\nexp=0.0408363;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[49 81 ];\r\nexp=9.6529702;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[127 11 ];\r\nexp=0.1914728;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[223 61 ];\r\nexp=0.3443890;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[160 21 ];\r\nexp=0.2303047;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[196 31 ];\r\nexp=0.2265546;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[55 91 ];\r\nexp=8.5730698;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[110 1234 ];\r\nexp=44.0395169;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[274 61 ];\r\nexp=0.2281140;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 6800 ];\r\nexp=23.8846446;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 3310 ];\r\nexp=10.5630642;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[44 31 ];\r\nexp=4.5141266;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[295 1 ];\r\nexp=0.0032261;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[64 11 ];\r\nexp=0.7540525;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[240 21 ];\r\nexp=0.1023567;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[91 21 ];\r\nexp=0.7120327;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 1870 ];\r\nexp=5.8744286;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 1730 ];\r\nexp=5.4290641;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[259 51 ];\r\nexp=0.2134486;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[51 91 ];\r\nexp=10.0258563;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 4200 ];\r\nexp=13.6075829;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[262 81 ];\r\nexp=0.3312919;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[74 81 ];\r\nexp=4.1674764;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[88 81 ];\r\nexp=2.9417237;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[255 91 ];\r\nexp=0.3929103;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[72 41 ];\r\nexp=2.2226617;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 7900 ];\r\nexp=29.6707716;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 1620 ];\r\nexp=5.0800699;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[253 71 ];\r\nexp=0.3114186;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[265 91 ];\r\nexp=0.3638145;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[248 1 ];\r\nexp=0.0045647;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 6090 ];\r\nexp=20.7696393;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[158 71 ];\r\nexp=0.7985813;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 2170 ];\r\nexp=6.8338053;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 1500 ];\r\nexp=4.7002140;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[163 31 ];\r\nexp=0.3275780;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[139 31 ];\r\nexp=0.4504729;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[271 21 ];\r\nexp=0.0802786;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[113 41 ];\r\nexp=0.9016072;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[156 81 ];\r\nexp=0.9346125;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[100 61 ];\r\nexp=1.7135925;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[85 91 ];\r\nexp=3.5451226;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[43 61 ];\r\nexp=9.4316060;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[57 61 ];\r\nexp=5.3012744;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[136 61 ];\r\nexp=0.9260755;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 5200 ];\r\nexp=17.2436039;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[159 71 ];\r\nexp=0.7885653;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[86 61 ];\r\nexp=2.3180653;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 8140 ];\r\nexp=31.2094004;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 5190 ];\r\nexp=17.2057754;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[259 6845 ];\r\nexp=45.0000000;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 6570 ];\r\nexp=22.8379951;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[285 71 ];\r\nexp=0.2454102;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 6460 ];\r\nexp=22.3511092;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[75 573 ];\r\nexp=43.3260450;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[46 41 ];\r\nexp=5.4730826;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[52 21 ];\r\nexp=2.1824862;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 5950 ];\r\nexp=20.1913108;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[68 91 ];\r\nexp=5.5599659;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[64 21 ];\r\nexp=1.4399949;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[36 11 ];\r\nexp=2.3856596;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[134 21 ];\r\nexp=0.3283507;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[9 1 ];\r\nexp=3.4745532;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[143 31 ];\r\nexp=0.4256222;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[116 91 ];\r\nexp=1.9000393;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[23 41 ];\r\nexp=24.7121091;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 8390 ];\r\nexp=33.0022766;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[200 51 ];\r\nexp=0.3579647;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[66 91 ];\r\nexp=5.9068209;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[203 21 ];\r\nexp=0.1430697;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 230 ];\r\nexp=0.7175455;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 7250 ];\r\nexp=26.0668121;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[81 71 ];\r\nexp=3.0438586;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[184 91 ];\r\nexp=0.7547006;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[273 41 ];\r\nexp=0.1544470;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[224 91 ];\r\nexp=0.5091983;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[25 1 ];\r\nexp=0.4492173;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[243 51 ];\r\nexp=0.2424831;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 4920 ];\r\nexp=16.1968290;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 840 ];\r\nexp=2.6239945;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 2740 ];\r\nexp=8.6794304;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[49 91 ];\r\nexp=10.9018740;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[244 81 ];\r\nexp=0.3819768;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[197 31 ];\r\nexp=0.2242603;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[186 31 ];\r\nexp=0.2515707;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[278 71 ];\r\nexp=0.2579249;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[258 1 ];\r\nexp=0.0042177;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 2990 ];\r\nexp=9.5002916;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[10 1 ];\r\nexp=2.8120066;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 7390 ];\r\nexp=26.7901102;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 430 ];\r\nexp=1.3418485;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[46 215 ];\r\nexp=42.3568299;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 6250 ];\r\nexp=21.4435357;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[109 1 ];\r\nexp=0.0236301;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[152 31 ];\r\nexp=0.3767088;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[290 41 ];\r\nexp=0.1368700;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[277 21 ];\r\nexp=0.0768385;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[136 81 ];\r\nexp=1.2298703;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 910 ];\r\nexp=2.8433535;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[224 21 ];\r\nexp=0.1175014;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 2440 ];\r\nexp=7.7039453;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[119 71 ];\r\nexp=1.4081796;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[20 31 ];\r\nexp=24.7100694;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 5120 ];\r\nexp=16.9419243;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 1940 ];\r\nexp=6.0976449;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[119 1445 ];\r\nexp=45.0000000;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[255 6635 ];\r\nexp=44.7753101;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 280 ];\r\nexp=0.8735777;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[219 41 ];\r\nexp=0.2400045;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[262 61 ];\r\nexp=0.2494890;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 970 ];\r\nexp=3.0315083;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 7720 ];\r\nexp=28.6029416;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[189 31 ];\r\nexp=0.2436475;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[110 51 ];\r\nexp=1.1836603;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[298 61 ];\r\nexp=0.1928498;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[231 5445 ];\r\nexp=44.9999996;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[69 81 ];\r\nexp=4.7988649;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[107 11 ];\r\nexp=0.2697430;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[114 21 ];\r\nexp=0.4536767;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[47 225 ];\r\nexp=43.2757298;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[17 1 ];\r\nexp=0.9716372;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[130 81 ];\r\nexp=1.3460985;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 4630 ];\r\nexp=15.1376561;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[121 91 ];\r\nexp=1.7460565;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[82 41 ];\r\nexp=1.7129065;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[199 31 ];\r\nexp=0.2197751;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[93 71 ];\r\nexp=2.3071761;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 5540 ];\r\nexp=18.5513095;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[126 41 ];\r\nexp=0.7251166;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 4260 ];\r\nexp=13.8184496;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 440 ];\r\nexp=1.3730779;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 3130 ];\r\nexp=9.9634881;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[145 61 ];\r\nexp=0.8146500;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 1170 ];\r\nexp=3.6596870;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[200 4081 ];\r\nexp=44.4955953;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[271 41 ];\r\nexp=0.1567351;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 1490 ];\r\nexp=4.6685979;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[291 21 ];\r\nexp=0.0696230;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[139 51 ];\r\nexp=0.7411528;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[53 51 ];\r\nexp=5.1245500;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[42 71 ];\r\nexp=11.6156650;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[243 91 ];\r\nexp=0.4326773;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 4430 ];\r\nexp=14.4204070;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[210 11 ];\r\nexp=0.0700282;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[112 61 ];\r\nexp=1.3657683;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[219 31 ];\r\nexp=0.1814659;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 4910 ];\r\nexp=16.1599009;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[44 11 ];\r\nexp=1.5959920;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[192 11 ];\r\nexp=0.0837741;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[276 71 ];\r\nexp=0.2616766;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[75 91 ];\r\nexp=4.5611459;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[166 21 ];\r\nexp=0.2139567;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[195 41 ];\r\nexp=0.3027202;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[116 81 ];\r\nexp=1.6909858;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[282 8114 ];\r\nexp=44.6253583;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[37 11 ];\r\nexp=2.2581760;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 1910 ];\r\nexp=6.0019356;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[182 1 ];\r\nexp=0.0084757;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[176 21 ];\r\nexp=0.1903338;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[120 1 ];\r\nexp=0.0194965;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 1320 ];\r\nexp=4.1319681;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[298 9061 ];\r\nexp=44.6614758;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 7700 ];\r\nexp=28.4881098;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[79 636 ];\r\nexp=43.5312934;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 5280 ];\r\nexp=17.5474818;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[227 31 ];\r\nexp=0.1689006;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[275 41 ];\r\nexp=0.1522086;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[171 1 ];\r\nexp=0.0096012;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[229 91 ];\r\nexp=0.4872031;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[200 1 ];\r\nexp=0.0070187;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[147 41 ];\r\nexp=0.5327126;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[169 31 ];\r\nexp=0.3047300;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[133 41 ];\r\nexp=0.6507837;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 1150 ];\r\nexp=3.5967945;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[147 1 ];\r\nexp=0.0129922;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[144 51 ];\r\nexp=0.6905672;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[30 51 ];\r\nexp=16.8668385;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[217 4805 ];\r\nexp=45.0000000;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[131 1 ];\r\nexp=0.0163597;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[58 41 ];\r\nexp=3.4299252;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[116 61 ];\r\nexp=1.2731382;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[43 1 ];\r\nexp=0.1518392;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[167 21 ];\r\nexp=0.2114020;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[295 31 ];\r\nexp=0.1000086;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[217 51 ];\r\nexp=0.3040728;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 7220 ];\r\nexp=25.9148699;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[25 51 ];\r\nexp=26.5497777;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 3620 ];\r\nexp=11.6073520;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[67 31 ];\r\nexp=1.9402732;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 31 ];\r\nexp=0.0967027;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 8610 ];\r\nexp=34.8206771;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[81 91 ];\r\nexp=3.9060385;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[57 31 ];\r\nexp=2.6826598;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 180 ];\r\nexp=0.5615346;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[73 81 ];\r\nexp=4.2832883;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[201 21 ];\r\nexp=0.1459311;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[68 11 ];\r\nexp=0.6679330;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[159 51 ];\r\nexp=0.5663996;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[204 1 ];\r\nexp=0.0067462;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[189 81 ];\r\nexp=0.6366722;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 590 ];\r\nexp=1.8417362;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[149 61 ];\r\nexp=0.7714868;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 8980 ];\r\nexp=38.9553303;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[216 11 ];\r\nexp=0.0661918;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[119 91 ];\r\nexp=1.8053178;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[125 81 ];\r\nexp=1.4560313;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 6750 ];\r\nexp=23.6536081;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 790 ];\r\nexp=2.4674046;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 4520 ];\r\nexp=14.7419107;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 6830 ];\r\nexp=24.0242561;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[94 51 ];\r\nexp=1.6213062;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[75 21 ];\r\nexp=1.0483648;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 5630 ];\r\nexp=18.9049816;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[86 71 ];\r\nexp=2.6991243;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[43 31 ];\r\nexp=4.7284323;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[193 31 ];\r\nexp=0.2336526;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[259 31 ];\r\nexp=0.1297425;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[287 21 ];\r\nexp=0.0715772;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 6870 ];\r\nexp=24.2115915;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[57 41 ];\r\nexp=3.5519442;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[239 11 ];\r\nexp=0.0540650;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[192 71 ];\r\nexp=0.5407548;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 8470 ];\r\nexp=33.6315148;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[77 61 ];\r\nexp=2.8933815;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[105 1125 ];\r\nexp=45.0000000;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 9183 ];\r\nexp=44.6530547;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 7170 ];\r\nexp=25.6638839;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 5560 ];\r\nexp=18.6296154;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 980 ];\r\nexp=3.0628800;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[145 91 ];\r\nexp=1.2154985;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 5820 ];\r\nexp=19.6630507;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[32 61 ];\r\nexp=17.8587444;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 5270 ];\r\nexp=17.5093740;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[237 31 ];\r\nexp=0.1549479;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[168 1 ];\r\nexp=0.0099472;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[41 71 ];\r\nexp=12.2256701;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[207 11 ];\r\nexp=0.0720728;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[250 61 ];\r\nexp=0.2740155;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 51 ];\r\nexp=0.1590921;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[161 51 ];\r\nexp=0.5524132;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[265 1 ];\r\nexp=0.0039979;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[246 21 ];\r\nexp=0.0974246;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[195 61 ];\r\nexp=0.4503988;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[160 2612 ];\r\nexp=44.6077195;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 6150 ];\r\nexp=21.0206716;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[83 21 ];\r\nexp=0.8559461;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[160 61 ];\r\nexp=0.6690338;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[156 61 ];\r\nexp=0.7037899;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[162 1 ];\r\nexp=0.0106977;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[166 61 ];\r\nexp=0.6215362;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[107 51 ];\r\nexp=1.2510059;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[215 41 ];\r\nexp=0.2490182;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[212 91 ];\r\nexp=0.5684822;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[84 61 ];\r\nexp=2.4300259;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 6630 ];\r\nexp=23.1071658;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[119 61 ];\r\nexp=1.2097168;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[7 1 ];\r\nexp=5.7684795;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 6730 ];\r\nexp=23.5617578;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 2860 ];\r\nexp=9.0724806;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[274 21 ];\r\nexp=0.0785303;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 1510 ];\r\nexp=4.7318359;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[42 21 ];\r\nexp=3.3498826;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 5220 ];\r\nexp=17.3193640;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 8670 ];\r\nexp=35.3730578;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[18 31 ];\r\nexp=34.8306447;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 8540 ];\r\nexp=34.2104815;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[256 21 ];\r\nexp=0.0899619;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[91 71 ];\r\nexp=2.4099422;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[247 51 ];\r\nexp=0.2346928;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[56 21 ];\r\nexp=1.8813698;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[135 91 ];\r\nexp=1.4023810;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 3930 ];\r\nexp=12.6682378;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[97 41 ];\r\nexp=1.2237457;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[280 8000 ];\r\nexp=45.0000000;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[280 41 ];\r\nexp=0.1468211;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[147 21 ];\r\nexp=0.2728412;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[23 11 ];\r\nexp=5.8790664;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[139 1 ];\r\nexp=0.0145308;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[78 620 ];\r\nexp=43.5307164;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[250 41 ];\r\nexp=0.1841728;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[69 41 ];\r\nexp=2.4205902;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 2730 ];\r\nexp=8.6467533;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[141 91 ];\r\nexp=1.2854868;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 3800 ];\r\nexp=12.2211854;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[290 11 ];\r\nexp=0.0367211;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[276 21 ];\r\nexp=0.0773963;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[105 11 ];\r\nexp=0.2801172;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[238 81 ];\r\nexp=0.4014801;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[200 91 ];\r\nexp=0.6387576;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[293 41 ];\r\nexp=0.1340815;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[299 9122 ];\r\nexp=44.6851269;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[21 1 ];\r\nexp=0.6366722;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[36 91 ];\r\nexp=21.7406299;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[270 7438 ];\r\nexp=44.5863296;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 5870 ];\r\nexp=19.8652679;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[125 21 ];\r\nexp=0.3773380;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[132 81 ];\r\nexp=1.3055882;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 4510 ];\r\nexp=14.7060881;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[111 91 ];\r\nexp=2.0753631;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[176 11 ];\r\nexp=0.0996981;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[76 81 ];\r\nexp=3.9496009;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[183 51 ];\r\nexp=0.4275657;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[144 41 ];\r\nexp=0.5551429;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[111 11 ];\r\nexp=0.2506519;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[232 21 ];\r\nexp=0.1095376;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[153 2388 ];\r\nexp=44.3197033;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[264 41 ];\r\nexp=0.1651571;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[203 1 ];\r\nexp=0.0068128;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[206 1 ];\r\nexp=0.0066158;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[190 41 ];\r\nexp=0.3188632;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[67 51 ];\r\nexp=3.1962494;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[59 21 ];\r\nexp=1.6946784;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 8380 ];\r\nexp=32.9257979;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[108 51 ];\r\nexp=1.2279321;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[267 7274 ];\r\nexp=44.7042055;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[298 21 ];\r\nexp=0.0663905;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 9070 ];\r\nexp=40.4879078;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[247 31 ];\r\nexp=0.1426554;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 1580 ];\r\nexp=4.9533543;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 310 ];\r\nexp=0.9672092;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[246 91 ];\r\nexp=0.4221877;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[110 81 ];\r\nexp=1.8807470;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[189 1 ];\r\nexp=0.0078595;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[299 91 ];\r\nexp=0.2857755;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 4820 ];\r\nexp=15.8288860;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[184 41 ];\r\nexp=0.3399986;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[173 81 ];\r\nexp=0.7599105;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[201 61 ];\r\nexp=0.4239087;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 1820 ];\r\nexp=5.7152103;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[130 41 ];\r\nexp=0.6811720;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[65 71 ];\r\nexp=4.7395084;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[192 91 ];\r\nexp=0.6931066;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[136 1887 ];\r\nexp=44.4506934;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[171 51 ];\r\nexp=0.4896861;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[236 91 ];\r\nexp=0.4587274;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[173 31 ];\r\nexp=0.2908008;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[35 41 ];\r\nexp=9.5737143;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 9020 ];\r\nexp=39.5832887;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[296 91 ];\r\nexp=0.2915978;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[33 41 ];\r\nexp=10.8258185;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 4110 ];\r\nexp=13.2927675;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[277 1 ];\r\nexp=0.0036590;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[254 31 ];\r\nexp=0.1349008;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[82 81 ];\r\nexp=3.3899244;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[54 21 ];\r\nexp=2.0235395;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[54 91 ];\r\nexp=8.9040499;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[85 71 ];\r\nexp=2.7632032;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[14 1 ];\r\nexp=1.4329920;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[170 81 ];\r\nexp=0.7869742;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[42 51 ];\r\nexp=8.2296248;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[35 125 ];\r\nexp=45.0000000;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 3390 ];\r\nexp=10.8310888;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[122 81 ];\r\nexp=1.5285870;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[74 31 ];\r\nexp=1.5901570;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 8170 ];\r\nexp=31.4129069;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 1660 ];\r\nexp=5.2068859;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[134 41 ];\r\nexp=0.6411051;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[184 3454 ];\r\nexp=44.4258154;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[143 81 ];\r\nexp=1.1123483;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[67 91 ];\r\nexp=5.7294046;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[208 41 ];\r\nexp=0.2660616;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[169 81 ];\r\nexp=0.7963175;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[213 11 ];\r\nexp=0.0680695;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[152 61 ];\r\nexp=0.7413270;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[259 21 ];\r\nexp=0.0878899;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[174 71 ];\r\nexp=0.6584409;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[242 41 ];\r\nexp=0.1965510;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[265 31 ];\r\nexp=0.1239339;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 6930 ];\r\nexp=24.4952155;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[177 1 ];\r\nexp=0.0089613;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 8630 ];\r\nexp=35.0015489;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[281 8057 ];\r\nexp=44.7766386;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 4450 ];\r\nexp=14.4916789;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[257 51 ];\r\nexp=0.2167838;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 7210 ];\r\nexp=25.8644501;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 8110 ];\r\nexp=31.0086245;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[120 31 ];\r\nexp=0.6044357;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 4010 ];\r\nexp=12.9449893;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[85 737 ];\r\nexp=44.2615751;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[287 1 ];\r\nexp=0.0034084;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 6900 ];\r\nexp=24.3530039;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[107 81 ];\r\nexp=1.9878552;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[73 91 ];\r\nexp=4.8168446;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 5830 ];\r\nexp=19.7034001;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[125 51 ];\r\nexp=0.9165221;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[174 31 ];\r\nexp=0.2874678;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[258 91 ];\r\nexp=0.3838254;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[88 51 ];\r\nexp=1.8502291;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 890 ];\r\nexp=2.7806630;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[131 71 ];\r\nexp=1.1618593;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 5890 ];\r\nexp=19.9464871;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[275 81 ];\r\nexp=0.3007089;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[201 31 ];\r\nexp=0.2154232;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[103 61 ];\r\nexp=1.6151178;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[169 11 ];\r\nexp=0.1081282;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[234 81 ];\r\nexp=0.4153242;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[127 41 ];\r\nexp=0.7137400;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[45 61 ];\r\nexp=8.5850615;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[268 71 ];\r\nexp=0.2775328;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[120 81 ];\r\nexp=1.5800158;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 2520 ];\r\nexp=7.9631306;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[39 91 ];\r\nexp=17.9483177;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[113 31 ];\r\nexp=0.6816548;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[152 91 ];\r\nexp=1.1060655;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 1260 ];\r\nexp=3.9429273;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 6980 ];\r\nexp=24.7340581;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[212 61 ];\r\nexp=0.3810567;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[8 1 ];\r\nexp=4.4040343;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[153 61 ];\r\nexp=0.7316660;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[55 1 ];\r\nexp=0.0928099;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 3080 ];\r\nexp=9.7977560;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[108 81 ];\r\nexp=1.9511562;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[81 41 ];\r\nexp=1.7555143;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[242 71 ];\r\nexp=0.3403741;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[46 81 ];\r\nexp=11.0165379;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[221 1 ];\r\nexp=0.0057482;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[249 71 ];\r\nexp=0.3215048;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 7440 ];\r\nexp=27.0544802;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[45 21 ];\r\nexp=2.9165098;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[289 21 ];\r\nexp=0.0705899;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 7520 ];\r\nexp=27.4846425;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[235 1 ];\r\nexp=0.0050837;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[299 1234 ];\r\nexp=3.8870928;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[250 1 ];\r\nexp=0.0044920;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[176 51 ];\r\nexp=0.4622558;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 8510 ];\r\nexp=33.9588221;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[151 31 ];\r\nexp=0.3817151;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[61 1 ];\r\nexp=0.0754501;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[132 31 ];\r\nexp=0.4995219;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[238 21 ];\r\nexp=0.1040843;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[238 91 ];\r\nexp=0.4510494;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[101 31 ];\r\nexp=0.8533003;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[252 1 ];\r\nexp=0.0044210;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[101 41 ];\r\nexp=1.1286835;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[152 51 ];\r\nexp=0.6197772;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 8830 ];\r\nexp=37.0236469;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[240 31 ];\r\nexp=0.1510984;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[134 51 ];\r\nexp=0.7975086;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 1020 ];\r\nexp=3.1884039;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[257 91 ];\r\nexp=0.3868183;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[128 11 ];\r\nexp=0.1884927;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 6160 ];\r\nexp=21.0627029;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[213 31 ];\r\nexp=0.1918335;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[255 51 ];\r\nexp=0.2201977;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[126 11 ];\r\nexp=0.1945242;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[280 51 ];\r\nexp=0.1826315;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[150 41 ];\r\nexp=0.5116148;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 7480 ];\r\nexp=27.2684278;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 4140 ];\r\nexp=13.3975114;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[133 51 ];\r\nexp=0.8095495;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[168 41 ];\r\nexp=0.4078483;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[281 71 ];\r\nexp=0.2524469;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[147 2205 ];\r\nexp=45.0000000;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[113 1 ];\r\nexp=0.0219868;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[242 61 ];\r\nexp=0.2924323;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[56 91 ];\r\nexp=8.2607465;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[260 21 ];\r\nexp=0.0872152;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[22 31 ];\r\nexp=19.4398009;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[165 71 ];\r\nexp=0.7322451;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 2190 ];\r\nexp=6.8980297;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 7570 ];\r\nexp=27.7582308;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[141 41 ];\r\nexp=0.5790205;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 4840 ];\r\nexp=15.9022391;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[142 11 ];\r\nexp=0.1531570;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 7750 ];\r\nexp=28.7765421;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[232 81 ];\r\nexp=0.4225163;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[53 21 ];\r\nexp=2.1007558;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[123 81 ];\r\nexp=1.5038100;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[210 51 ];\r\nexp=0.3246830;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[273 1 ];\r\nexp=0.0037670;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[50 81 ];\r\nexp=9.2565056;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[298 1 ];\r\nexp=0.0031614;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[166 11 ];\r\nexp=0.1120718;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 6260 ];\r\nexp=21.4861399;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[253 81 ];\r\nexp=0.3552825;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[144 91 ];\r\nexp=1.2324494;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[288 8463 ];\r\nexp=44.6385985;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[268 7328 ];\r\nexp=44.5316039;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[297 61 ];\r\nexp=0.1941507;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[62 41 ];\r\nexp=2.9999445;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[223 5074 ];\r\nexp=44.6458418;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[248 91 ];\r\nexp=0.4154052;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[106 61 ];\r\nexp=1.5249020;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[211 41 ];\r\nexp=0.2585494;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[120 21 ];\r\nexp=0.4094400;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[210 1 ];\r\nexp=0.0063662;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 4660 ];\r\nexp=15.2461386;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[172 71 ];\r\nexp=0.6738453;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[214 91 ];\r\nexp=0.5579047;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[131 11 ];\r\nexp=0.1799582;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[50 255 ];\r\nexp=44.1896883;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[227 51 ];\r\nexp=0.2778715;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 4330 ];\r\nexp=14.0654935;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[115 1 ];\r\nexp=0.0212287;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[80 91 ];\r\nexp=4.0049368;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[228 21 ];\r\nexp=0.1134147;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[104 11 ];\r\nexp=0.2855301;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[260 61 ];\r\nexp=0.2533422;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[290 1 ];\r\nexp=0.0033383;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[105 81 ];\r\nexp=2.0644344;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[57 71 ];\r\nexp=6.1830728;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[43 188 ];\r\nexp=42.5787456;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[214 71 ];\r\nexp=0.4352775;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[284 11 ];\r\nexp=0.0382891;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[267 41 ];\r\nexp=0.1614665;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[270 31 ];\r\nexp=0.1193862;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[131 51 ];\r\nexp=0.8344642;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[70 71 ];\r\nexp=4.0817971;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[21 41 ];\r\nexp=32.8296766;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[282 91 ];\r\nexp=0.3212706;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[24 11 ];\r\nexp=5.3933350;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[226 21 ];\r\nexp=0.1154310;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[227 11 ];\r\nexp=0.0599322;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 4800 ];\r\nexp=15.7556484;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[134 81 ];\r\nexp=1.2668806;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[256 61 ];\r\nexp=0.2613212;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 8860 ];\r\nexp=37.3715407;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[230 81 ];\r\nexp=0.4298969;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[182 91 ];\r\nexp=0.7713825;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[142 2057 ];\r\nexp=44.3369812;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[32 71 ];\r\nexp=21.4019868;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[142 61 ];\r\nexp=0.8494455;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 3170 ];\r\nexp=10.0963242;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[191 61 ];\r\nexp=0.4694629;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[190 71 ];\r\nexp=0.5522004;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[205 71 ];\r\nexp=0.4743394;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[248 71 ];\r\nexp=0.3241029;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[166 31 ];\r\nexp=0.3158443;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[145 51 ];\r\nexp=0.6810732;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 6050 ];\r\nexp=20.6033628;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[254 71 ];\r\nexp=0.3089712;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[185 71 ];\r\nexp=0.5824565;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 3380 ];\r\nexp=10.7975318;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[296 71 ];\r\nexp=0.2275088;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[38 81 ];\r\nexp=16.6740056;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[24 1 ];\r\nexp=0.4874355;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[280 31 ];\r\nexp=0.1110109;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 8690 ];\r\nexp=35.5640799;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 4160 ];\r\nexp=13.4674481;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[252 61 ];\r\nexp=0.2696832;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[98 71 ];\r\nexp=2.0773304;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[209 81 ];\r\nexp=0.5206370;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 2710 ];\r\nexp=8.5814338;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[57 21 ];\r\nexp=1.8158465;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[102 51 ];\r\nexp=1.3767520;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 1770 ];\r\nexp=5.5561708;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 8160 ];\r\nexp=31.3447605;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[74 71 ];\r\nexp=3.6499694;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[51 41 ];\r\nexp=4.4432920;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[297 91 ];\r\nexp=0.2896374;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[48 71 ];\r\nexp=8.7887794;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[140 41 ];\r\nexp=0.5873229;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[284 61 ];\r\nexp=0.2123322;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[229 41 ];\r\nexp=0.2195007;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[294 81 ];\r\nexp=0.2630966;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[138 71 ];\r\nexp=1.0469250;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[84 11 ];\r\nexp=0.4376931;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[220 11 ];\r\nexp=0.0638067;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 650 ];\r\nexp=2.0293307;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[261 31 ];\r\nexp=0.1277617;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[259 11 ];\r\nexp=0.0460375;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[150 21 ];\r\nexp=0.2620364;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 3580 ];\r\nexp=11.4717190;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[295 71 ];\r\nexp=0.2290539;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 8330 ];\r\nexp=32.5500293;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[127 21 ];\r\nexp=0.3655463;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[196 91 ];\r\nexp=0.6651000;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 7230 ];\r\nexp=25.9654030;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[55 51 ];\r\nexp=4.7550987;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[118 61 ];\r\nexp=1.2303199;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[172 61 ];\r\nexp=0.5789235;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 3990 ];\r\nexp=12.8756810;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[49 41 ];\r\nexp=4.8168001;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 8400 ];\r\nexp=33.0792168;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[272 51 ];\r\nexp=0.1935327;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[246 51 ];\r\nexp=0.2366048;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[209 71 ];\r\nexp=0.4563550;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[113 51 ];\r\nexp=1.1216128;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[58 11 ];\r\nexp=0.9181841;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[90 21 ];\r\nexp=0.7279469;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 5580 ];\r\nexp=18.7080845;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[26 1 ];\r\nexp=0.4153242;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 6020 ];\r\nexp=20.4792082;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[153 71 ];\r\nexp=0.8516442;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[231 71 ];\r\nexp=0.3735643;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[296 41 ];\r\nexp=0.1313774;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[218 51 ];\r\nexp=0.3012894;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[156 71 ];\r\nexp=0.8191945;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[244 91 ];\r\nexp=0.4291377;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[97 61 ];\r\nexp=1.8213680;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[33 21 ];\r\nexp=5.4466530;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[48 21 ];\r\nexp=2.5623281;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 5180 ];\r\nexp=17.1679811;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 3630 ];\r\nexp=11.6413032;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[164 81 ];\r\nexp=0.8456275;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[180 3306 ];\r\nexp=44.7534375;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[49 61 ];\r\nexp=7.2085690;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[89 21 ];\r\nexp=0.7444009;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 2110 ];\r\nexp=6.6413404;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[199 4040 ];\r\nexp=44.3892211;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[297 31 ];\r\nexp=0.0986662;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 5920 ];\r\nexp=20.0686784;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 7180 ];\r\nexp=25.7138602;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 5210 ];\r\nexp=17.2814667;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[212 11 ];\r\nexp=0.0687132;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[246 1 ];\r\nexp=0.0046393;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[250 11 ];\r\nexp=0.0494119;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[47 1 ];\r\nexp=0.1270938;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[112 41 ];\r\nexp=0.9177847;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 5110 ];\r\nexp=16.9043649;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 6410 ];\r\nexp=22.1324926;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 7030 ];\r\nexp=24.9752527;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 7970 ];\r\nexp=30.1045540;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[255 1 ];\r\nexp=0.0043176;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[222 5028 ];\r\nexp=44.4345459;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[247 61 ];\r\nexp=0.2807124;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[40 163 ];\r\nexp=43.3665978;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[88 21 ];\r\nexp=0.7614192;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[91 51 ];\r\nexp=1.7300957;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[145 21 ];\r\nexp=0.2804200;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[170 61 ];\r\nexp=0.5926273;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[95 11 ];\r\nexp=0.3421957;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[137 1 ];\r\nexp=0.0149581;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[220 51 ];\r\nexp=0.2958362;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[132 51 ];\r\nexp=0.8218652;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 6850 ];\r\nexp=24.1177523;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[271 61 ];\r\nexp=0.2331926;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[184 31 ];\r\nexp=0.2570695;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 3250 ];\r\nexp=10.3626812;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[11 1 ];\r\nexp=2.3227865;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[148 81 ];\r\nexp=1.0384257;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 5400 ];\r\nexp=18.0076051;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[287 31 ];\r\nexp=0.1056617;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[183 11 ];\r\nexp=0.0922168;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[278 81 ];\r\nexp=0.2942536;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[291 1 ];\r\nexp=0.0033154;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[64 71 ];\r\nexp=4.8902189;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[290 61 ];\r\nexp=0.2036368;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[124 51 ];\r\nexp=0.9313695;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[230 21 ];\r\nexp=0.1114509;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[109 51 ];\r\nexp=1.2054913;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[84 91 ];\r\nexp=3.6304847;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[289 81 ];\r\nexp=0.2722793;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[138 1 ];\r\nexp=0.0147421;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[130 91 ];\r\nexp=1.5124296;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[182 21 ];\r\nexp=0.1779910;\r\ntheta=Cannon(vd(1),vd(2));\r\nassert(abs(theta-exp)\u003c2e-6)\r\n%%\r\nvd=[300 8780 ];\r\nexp=36.4745305","published":true,"deleted":false,"likes_count":3,"comments_count":3,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":20,"test_suite_updated_at":"2014-02-10T18:16:06.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2013-09-15T23:22:36.000Z","updated_at":"2014-02-10T18:22:50.000Z","published_at":"2013-09-15T23:34:41.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis Challenge is derived from\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://code.google.com/codejam/contest/2933486/dashboard#s=p1\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eGJam 2013 China Captain Hammer\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. The problem is modified to fit within Cody dimensions.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe Challenge is to return the lower angle of a cannon given a target distance and an initial cannonball velocity. Gravity is a constant at 9.8m/sec^2, A valid solution is assured. (Error tolerance 2e-6).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e [v d] Velocity and Distance in meters.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e theta in units of degrees with an accuracy of 2e-6\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCompetition Summary:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Best Time of 8 minutes, 755/1070 completed\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe winner completed all three GJam China Challenges in 26 minutes with second at 43 minutes.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":2083,"title":"Independent direction vectors of a plane","description":"Given the equation of a plan of the form ax+by+cz=d, return 2 independent direction vectors which could e.g. be used to determine a parametric equation.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 21px; transform-origin: 407px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 379px 8px; transform-origin: 379px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven the equation of a plan of the form ax+by+cz=d, return 2 independent direction vectors which could e.g. be used to determine a parametric equation.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [v1,v2] = directionvectors(a,b,c,d)\r\n  y = x;\r\nend","test_suite":"%%\r\na=1;\r\nb=1;\r\nc=1;\r\nd=1234;\r\n[v1,v2] = directionvectors(a,b,c,d);\r\n\r\nassert(abs(sum([a b c].*(v1+[0 0 d/c]))-d)\u003c1e-4);\r\nassert(abs(sum([a b c].*(v2+[0 0 d/c]))-d)\u003c1e-4);\r\nassert(dot(v1,v2)~=0);\r\n\r\n%%\r\na=0;\r\nb=5;\r\nc=7;\r\nd=1234;\r\n[v1,v2] = directionvectors(a,b,c,d);\r\n\r\nassert(abs(sum([a b c].*(v1+[0 0 d/c]))-d)\u003c1e-4);\r\nassert(abs(sum([a b c].*(v2+[0 0 d/c]))-d)\u003c1e-4);\r\nassert(dot(v1,v2)~=0);\r\n\r\n%%\r\na=0;\r\nb=randi(10);\r\nc=-randi(10);\r\nd=randi(100);\r\n[v1,v2] = directionvectors(a,b,c,d);\r\n\r\nassert(abs(sum([a b c].*(v1+[0 0 d/c]))-d)\u003c1e-4);\r\nassert(abs(sum([a b c].*(v2+[0 0 d/c]))-d)\u003c1e-4);\r\nassert(dot(v1,v2)~=0);\r\n\r\n%%\r\na=0;\r\nb=0;\r\nc=randi(100)-50;\r\nd=0;\r\n[v1,v2] = directionvectors(a,b,c,d);\r\n\r\nassert(abs(sum([a b c].*(v1+[0 0 d/c]))-d)\u003c1e-4);\r\nassert(abs(sum([a b c].*(v2+[0 0 d/c]))-d)\u003c1e-4);\r\nassert(dot(v1,v2)~=0);","published":true,"deleted":false,"likes_count":0,"comments_count":9,"created_by":20079,"edited_by":223089,"edited_at":"2023-02-26T20:11:42.000Z","deleted_by":null,"deleted_at":null,"solvers_count":19,"test_suite_updated_at":"2023-02-26T20:11:42.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2013-12-29T12:54:54.000Z","updated_at":"2024-11-11T02:43:11.000Z","published_at":"2013-12-29T13:08:35.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven the equation of a plan of the form ax+by+cz=d, return 2 independent direction vectors which could e.g. be used to determine a parametric equation.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":43025,"title":"Check if a directory is on the current MATLAB search path","description":"Given a directory name as a string, return true if the directory is on the current MATLAB search path, and false otherwise.","description_html":"\u003cp\u003eGiven a directory name as a string, return true if the directory is on the current MATLAB search path, and false otherwise.\u003c/p\u003e","function_template":"function tf = isonpath(str)\r\n    tf = 0;\r\nend","test_suite":"%%\r\nstr = '/opt/mlsedu/matlab/R2016b/toolbox/matlab/mss/mlt_rmt_tmw/scoring-engine';\r\nassert(isequal(isonpath(str),true))\r\n\r\n%%\r\nstr = '/opt/mlsedu/matlab/R2016b/toolbox/matlab/testframework/parallel';\r\nassert(isequal(isonpath(str),true))\r\n\r\n%%\r\nstr = '/opt/mlsedu/matlab/R2016b/toolbox/shared/imageslib';\r\nassert(isequal(isonpath(str),true))\r\n\r\n%%\r\nstr = '/opt/mlsedu/matlab/R2016b/help/toolbox/vision/examples';\r\nassert(isequal(isonpath(str),true))\r\n\r\n%%\r\nstr = '/opt/mlsedu/matlab/R2016b/toolbox/shared/bigdata';\r\nassert(isequal(isonpath(str),true))\r\n\r\n%%\r\nstr = '/opt/mlsedu/matlab/R2016b/toolbox/matlab/demos';\r\nassert(isequal(isonpath(str),true))\r\n\r\n%%\r\nstr = '/opt/mlsedu/matlab/R2016b/toolbox/matlab/funfun';\r\nassert(isequal(isonpath(str),true))\r\n\r\n%%\r\nstr = '/opt/mlsedu/matlab/R2016b/toolbox/matlab/system';\r\nassert(isequal(isonpath(str),true))\r\n\r\n%%\r\nstr = '/opt/mlsedu/matlab/R2016b/toolbox/shared/simulink';\r\nassert(isequal(isonpath(str),true))\r\n\r\n%%\r\nstr = '';\r\nassert(isequal(isonpath(str),false))\r\n\r\n%%\r\nstr = '/opt/';\r\nassert(isequal(isonpath(str),false))\r\n\r\n%%\r\nstr = 'matlab';\r\nassert(isequal(isonpath(str),false))\r\n\r\n%%\r\nstr = '/matlab/R2016b/toolbox';\r\nassert(isequal(isonpath(str),false))\r\n\r\n%%\r\nstr = 'not a directory';\r\nassert(isequal(isonpath(str),false))\r\n\r\n%%\r\nstr = '/opt/mlsedu/matlab/R2016b/toolbox/matlab/timefun/fakedirectory';\r\nassert(isequal(isonpath(str),false))\r\n\r\n%%\r\nstr = 'blah/blah/blah';\r\nassert(isequal(isonpath(str),false))\r\n\r\n%%\r\nstr = 'C:\\Program Files\\MATLAB\\R2016a\\toolbox\\matlab\\datafun';\r\nassert(isequal(isonpath(str),false))\r\n\r\n%%\r\nstr = [];\r\nassert(isequal(isonpath(str),false))\r\n\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":3,"created_by":4793,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":15,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2016-10-04T20:08:03.000Z","updated_at":"2024-11-13T11:24:47.000Z","published_at":"2016-10-04T20:08:03.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a directory name as a string, return true if the directory is on the current MATLAB search path, and false otherwise.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44074,"title":"GJam 2017 Kickstart: Parentheses (Small)","description":"This Challenge is derived from \u003chttp://code.google.com/codejam/contest/6304486/dashboard#s=p2 GJam 2017 Kickstart Parentheses\u003e. This is the first 100 small cases with max L+R\u003c=20.\r\n\r\n\u003chttp://code.google.com/codejam Google Code Jam 2017 Qualifier\u003e is March 7, 2017. Typically four challenges with small and large aspects with 27 hours to complete.\r\n\r\nThe GJam story is given L left and R right parentheses determine the maximum number of parentheses pairings.\r\n\r\n*Input:* [L,R], the quantity of parentheses types\r\n\r\n*Output:* [V], the maximum number of parentheses pairings\r\n\r\n*Examples:* [L,R] [V]; [3,2] [3]\r\n\r\nFor the case ()()(, for example, the three balanced groups are () from indexes 1 to 2, () from indexes 3 to 4, and ()() from indexes 1 to 4.\r\n\r\n*Theory:* Brute force permutations and counting will not succeed in a timely manner for L+R=20. Determining the inherent mathematical pattern is usually the best way to succeed in GJam.   \u003chttp://code.google.com/codejam/contest/6304486/scoreboard#vf=1 GJam Kickstart solutions(C++,Python)\u003e. ","description_html":"\u003cp\u003eThis Challenge is derived from \u003ca href = \"http://code.google.com/codejam/contest/6304486/dashboard#s=p2\"\u003eGJam 2017 Kickstart Parentheses\u003c/a\u003e. This is the first 100 small cases with max L+R\u0026lt;=20.\u003c/p\u003e\u003cp\u003e\u003ca href = \"http://code.google.com/codejam\"\u003eGoogle Code Jam 2017 Qualifier\u003c/a\u003e is March 7, 2017. Typically four challenges with small and large aspects with 27 hours to complete.\u003c/p\u003e\u003cp\u003eThe GJam story is given L left and R right parentheses determine the maximum number of parentheses pairings.\u003c/p\u003e\u003cp\u003e\u003cb\u003eInput:\u003c/b\u003e [L,R], the quantity of parentheses types\u003c/p\u003e\u003cp\u003e\u003cb\u003eOutput:\u003c/b\u003e [V], the maximum number of parentheses pairings\u003c/p\u003e\u003cp\u003e\u003cb\u003eExamples:\u003c/b\u003e [L,R] [V]; [3,2] [3]\u003c/p\u003e\u003cp\u003eFor the case ()()(, for example, the three balanced groups are () from indexes 1 to 2, () from indexes 3 to 4, and ()() from indexes 1 to 4.\u003c/p\u003e\u003cp\u003e\u003cb\u003eTheory:\u003c/b\u003e Brute force permutations and counting will not succeed in a timely manner for L+R=20. Determining the inherent mathematical pattern is usually the best way to succeed in GJam.   \u003ca href = \"http://code.google.com/codejam/contest/6304486/scoreboard#vf=1\"\u003eGJam Kickstart solutions(C++,Python)\u003c/a\u003e.\u003c/p\u003e","function_template":"function val=parenc(L,R)\r\n% L number of Left parentheses, R number of Right parentheses \r\n% Determine maxinum number of parenthese pairings\r\n% http://code.google.com/codejam/contest/6304486/dashboard#s=p2\r\n\r\nval=0;\r\n \r\nend","test_suite":"%%\r\nv=parenc(19,1);\r\nassert(~isempty(v))\r\nassert(v==1)\r\n%%\r\nv=parenc(14,4);\r\nassert(~isempty(v))\r\nassert(v==10)\r\n%%\r\nv=parenc(4,15);\r\nassert(~isempty(v))\r\nassert(v==10)\r\n%%\r\nv=parenc(8,6);\r\nassert(~isempty(v))\r\nassert(v==21)\r\n%%\r\nv=parenc(14,1);\r\nassert(~isempty(v))\r\nassert(v==1)\r\n%%\r\nv=parenc(10,2);\r\nassert(~isempty(v))\r\nassert(v==3)\r\n%%\r\nv=parenc(10,10);\r\nassert(~isempty(v))\r\nassert(v==55)\r\n%%\r\nv=parenc(3,7);\r\nassert(~isempty(v))\r\nassert(v==6)\r\n%%\r\nv=parenc(3,13);\r\nassert(~isempty(v))\r\nassert(v==6)\r\n%%\r\nv=parenc(4,12);\r\nassert(~isempty(v))\r\nassert(v==10)\r\n%%\r\nv=parenc(2,2);\r\nassert(~isempty(v))\r\nassert(v==3)\r\n%%\r\nv=parenc(6,11);\r\nassert(~isempty(v))\r\nassert(v==21)\r\n%%\r\nv=parenc(4,12);\r\nassert(~isempty(v))\r\nassert(v==10)\r\n%%\r\nv=parenc(15,5);\r\nassert(~isempty(v))\r\nassert(v==15)\r\n%%\r\nv=parenc(14,3);\r\nassert(~isempty(v))\r\nassert(v==6)\r\n%%\r\nv=parenc(20,0);\r\nassert(~isempty(v))\r\nassert(v==0)\r\n%%\r\nv=parenc(12,3);\r\nassert(~isempty(v))\r\nassert(v==6)\r\n%%\r\nv=parenc(0,10);\r\nassert(~isempty(v))\r\nassert(v==0)\r\n%%\r\nv=parenc(18,2);\r\nassert(~isempty(v))\r\nassert(v==3)\r\n%%\r\nv=parenc(16,4);\r\nassert(~isempty(v))\r\nassert(v==10)\r\n%%\r\nv=parenc(3,12);\r\nassert(~isempty(v))\r\nassert(v==6)\r\n%%\r\nv=parenc(8,12);\r\nassert(~isempty(v))\r\nassert(v==36)\r\n%%\r\nv=parenc(8,6);\r\nassert(~isempty(v))\r\nassert(v==21)\r\n%%\r\nv=parenc(1,8);\r\nassert(~isempty(v))\r\nassert(v==1)\r\n%%\r\nv=parenc(7,13);\r\nassert(~isempty(v))\r\nassert(v==28)\r\n%%\r\nv=parenc(7,6);\r\nassert(~isempty(v))\r\nassert(v==21)\r\n%%\r\nv=parenc(11,8);\r\nassert(~isempty(v))\r\nassert(v==36)\r\n%%\r\nv=parenc(17,1);\r\nassert(~isempty(v))\r\nassert(v==1)\r\n%%\r\nv=parenc(4,2);\r\nassert(~isempty(v))\r\nassert(v==3)\r\n%%\r\nv=parenc(1,6);\r\nassert(~isempty(v))\r\nassert(v==1)\r\n%%\r\nv=parenc(5,4);\r\nassert(~isempty(v))\r\nassert(v==10)\r\n%%\r\nv=parenc(1,1);\r\nassert(~isempty(v))\r\nassert(v==1)\r\n%%\r\nv=parenc(7,13);\r\nassert(~isempty(v))\r\nassert(v==28)\r\n%%\r\nv=parenc(6,12);\r\nassert(~isempty(v))\r\nassert(v==21)\r\n%%\r\nv=parenc(15,2);\r\nassert(~isempty(v))\r\nassert(v==3)\r\n%%\r\nv=parenc(14,2);\r\nassert(~isempty(v))\r\nassert(v==3)\r\n%%\r\nv=parenc(12,1);\r\nassert(~isempty(v))\r\nassert(v==1)\r\n%%\r\nv=parenc(4,15);\r\nassert(~isempty(v))\r\nassert(v==10)\r\n%%\r\nv=parenc(12,7);\r\nassert(~isempty(v))\r\nassert(v==28)\r\n%%\r\nv=parenc(5,1);\r\nassert(~isempty(v))\r\nassert(v==1)\r\n%%\r\nv=parenc(19,1);\r\nassert(~isempty(v))\r\nassert(v==1)\r\n%%\r\nv=parenc(6,5);\r\nassert(~isempty(v))\r\nassert(v==15)\r\n%%\r\nv=parenc(11,5);\r\nassert(~isempty(v))\r\nassert(v==15)\r\n%%\r\nv=parenc(8,12);\r\nassert(~isempty(v))\r\nassert(v==36)\r\n%%\r\nv=parenc(18,2);\r\nassert(~isempty(v))\r\nassert(v==3)\r\n%%\r\nv=parenc(18,1);\r\nassert(~isempty(v))\r\nassert(v==1)\r\n%%\r\nv=parenc(13,4);\r\nassert(~isempty(v))\r\nassert(v==10)\r\n%%\r\nv=parenc(3,6);\r\nassert(~isempty(v))\r\nassert(v==6)\r\n%%\r\nv=parenc(6,1);\r\nassert(~isempty(v))\r\nassert(v==1)\r\n%%\r\nv=parenc(3,3);\r\nassert(~isempty(v))\r\nassert(v==6)\r\n%%\r\nv=parenc(19,1);\r\nassert(~isempty(v))\r\nassert(v==1)\r\n%%\r\nv=parenc(9,11);\r\nassert(~isempty(v))\r\nassert(v==45)\r\n%%\r\nv=parenc(10,1);\r\nassert(~isempty(v))\r\nassert(v==1)\r\n%%\r\nv=parenc(0,11);\r\nassert(~isempty(v))\r\nassert(v==0)\r\n%%\r\nv=parenc(11,3);\r\nassert(~isempty(v))\r\nassert(v==6)\r\n%%\r\nv=parenc(3,2);\r\nassert(~isempty(v))\r\nassert(v==3)\r\n%%\r\nv=parenc(18,2);\r\nassert(~isempty(v))\r\nassert(v==3)\r\n%%\r\nv=parenc(1,0);\r\nassert(~isempty(v))\r\nassert(v==0)\r\n%%\r\nv=parenc(9,1);\r\nassert(~isempty(v))\r\nassert(v==1)\r\n%%\r\nv=parenc(1,19);\r\nassert(~isempty(v))\r\nassert(v==1)\r\n%%\r\nv=parenc(4,3);\r\nassert(~isempty(v))\r\nassert(v==6)\r\n%%\r\nv=parenc(13,7);\r\nassert(~isempty(v))\r\nassert(v==28)\r\n%%\r\nv=parenc(8,6);\r\nassert(~isempty(v))\r\nassert(v==21)\r\n%%\r\nv=parenc(7,1);\r\nassert(~isempty(v))\r\nassert(v==1)\r\n%%\r\nv=parenc(16,2);\r\nassert(~isempty(v))\r\nassert(v==3)\r\n%%\r\nv=parenc(16,4);\r\nassert(~isempty(v))\r\nassert(v==10)\r\n%%\r\nv=parenc(7,8);\r\nassert(~isempty(v))\r\nassert(v==28)\r\n%%\r\nv=parenc(13,3);\r\nassert(~isempty(v))\r\nassert(v==6)\r\n%%\r\nv=parenc(4,14);\r\nassert(~isempty(v))\r\nassert(v==10)\r\n%%\r\nv=parenc(7,8);\r\nassert(~isempty(v))\r\nassert(v==28)\r\n%%\r\nv=parenc(9,5);\r\nassert(~isempty(v))\r\nassert(v==15)\r\n%%\r\nv=parenc(4,7);\r\nassert(~isempty(v))\r\nassert(v==10)\r\n%%\r\nv=parenc(12,2);\r\nassert(~isempty(v))\r\nassert(v==3)\r\n%%\r\nv=parenc(10,1);\r\nassert(~isempty(v))\r\nassert(v==1)\r\n%%\r\nv=parenc(17,3);\r\nassert(~isempty(v))\r\nassert(v==6)\r\n%%\r\nv=parenc(4,13);\r\nassert(~isempty(v))\r\nassert(v==10)\r\n%%\r\nv=parenc(11,1);\r\nassert(~isempty(v))\r\nassert(v==1)\r\n%%\r\nv=parenc(10,5);\r\nassert(~isempty(v))\r\nassert(v==15)\r\n%%\r\nv=parenc(7,7);\r\nassert(~isempty(v))\r\nassert(v==28)\r\n%%\r\nv=parenc(6,4);\r\nassert(~isempty(v))\r\nassert(v==10)\r\n%%\r\nv=parenc(5,13);\r\nassert(~isempty(v))\r\nassert(v==15)\r\n%%\r\nv=parenc(10,10);\r\nassert(~isempty(v))\r\nassert(v==55)\r\n%%\r\nv=parenc(14,3);\r\nassert(~isempty(v))\r\nassert(v==6)\r\n%%\r\nv=parenc(8,4);\r\nassert(~isempty(v))\r\nassert(v==10)\r\n%%\r\nv=parenc(14,5);\r\nassert(~isempty(v))\r\nassert(v==15)\r\n%%\r\nv=parenc(0,20);\r\nassert(~isempty(v))\r\nassert(v==0)\r\n%%\r\nv=parenc(0,1);\r\nassert(~isempty(v))\r\nassert(v==0)\r\n%%\r\nv=parenc(1,10);\r\nassert(~isempty(v))\r\nassert(v==1)\r\n%%\r\nv=parenc(13,3);\r\nassert(~isempty(v))\r\nassert(v==6)\r\n%%\r\nv=parenc(0,9);\r\nassert(~isempty(v))\r\nassert(v==0)\r\n%%\r\nv=parenc(1,17);\r\nassert(~isempty(v))\r\nassert(v==1)\r\n%%\r\nv=parenc(0,2);\r\nassert(~isempty(v))\r\nassert(v==0)\r\n%%\r\nv=parenc(2,0);\r\nassert(~isempty(v))\r\nassert(v==0)\r\n%%\r\nv=parenc(4,12);\r\nassert(~isempty(v))\r\nassert(v==10)\r\n%%\r\nv=parenc(11,9);\r\nassert(~isempty(v))\r\nassert(v==45)\r\n%%\r\nv=parenc(18,2);\r\nassert(~isempty(v))\r\nassert(v==3)\r\n%%\r\nv=parenc(15,3);\r\nassert(~isempty(v))\r\nassert(v==6)\r\n%%\r\nv=parenc(16,2);\r\nassert(~isempty(v))\r\nassert(v==3)\r\n%%\r\nv=parenc(17,2);\r\nassert(~isempty(v))\r\nassert(v==3)\r\n%%\r\nv=parenc(14,5);\r\nassert(~isempty(v))\r\nassert(v==15)\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":3,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":18,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2017-02-25T21:52:46.000Z","updated_at":"2017-02-25T22:07:38.000Z","published_at":"2017-02-25T22:07:38.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis Challenge is derived from\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://code.google.com/codejam/contest/6304486/dashboard#s=p2\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eGJam 2017 Kickstart Parentheses\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. This is the first 100 small cases with max L+R\u0026lt;=20.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"http://code.google.com/codejam\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eGoogle Code Jam 2017 Qualifier\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e is March 7, 2017. Typically four challenges with small and large aspects with 27 hours to complete.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe GJam story is given L left and R right parentheses determine the maximum number of parentheses pairings.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e [L,R], the quantity of parentheses types\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e [V], the maximum number of parentheses pairings\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExamples:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e [L,R] [V]; [3,2] [3]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor the case ()()(, for example, the three balanced groups are () from indexes 1 to 2, () from indexes 3 to 4, and ()() from indexes 1 to 4.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eTheory:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Brute force permutations and counting will not succeed in a timely manner for L+R=20. Determining the inherent mathematical pattern is usually the best way to succeed in GJam. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://code.google.com/codejam/contest/6304486/scoreboard#vf=1\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eGJam Kickstart solutions(C++,Python)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44075,"title":"GJam 2017 Kickstart: Parentheses (Large)","description":"This Challenge is derived from \u003chttp://code.google.com/codejam/contest/6304486/dashboard#s=p2 GJam 2017 Kickstart Parentheses\u003e. This is the first 100 large cases with  1\u003c=L+R\u003c=10^5.\r\n\r\n\u003chttp://code.google.com/codejam Google Code Jam 2017 Qualifier\u003e is March 7, 2017. Typically four challenges with small and large aspects with 27 hours to complete.\r\n\r\nThe GJam story is given L left and R right parentheses determine the maximum number of parentheses pairings.\r\n\r\n*Input:* [L,R], the quantity of parentheses types\r\n\r\n*Output:* [V], the maximum number of parentheses pairings\r\n\r\n*Examples:* [L,R] [V]; [3,2] [3]\r\n\r\nFor the case ()()(, for example, the three balanced groups are () from indexes 1 to 2, () from indexes 3 to 4, and ()() from indexes 1 to 4.\r\n\r\n*Theory:* Brute force permutations and counting will not succeed in a timely manner for L+R=10^5. Determining the inherent mathematical pattern is usually the best way to succeed in GJam.   \u003chttp://code.google.com/codejam/contest/6304486/scoreboard#vf=1 GJam Kickstart solutions(C++,Python)\u003e. ","description_html":"\u003cp\u003eThis Challenge is derived from \u003ca href = \"http://code.google.com/codejam/contest/6304486/dashboard#s=p2\"\u003eGJam 2017 Kickstart Parentheses\u003c/a\u003e. This is the first 100 large cases with  1\u0026lt;=L+R\u0026lt;=10^5.\u003c/p\u003e\u003cp\u003e\u003ca href = \"http://code.google.com/codejam\"\u003eGoogle Code Jam 2017 Qualifier\u003c/a\u003e is March 7, 2017. Typically four challenges with small and large aspects with 27 hours to complete.\u003c/p\u003e\u003cp\u003eThe GJam story is given L left and R right parentheses determine the maximum number of parentheses pairings.\u003c/p\u003e\u003cp\u003e\u003cb\u003eInput:\u003c/b\u003e [L,R], the quantity of parentheses types\u003c/p\u003e\u003cp\u003e\u003cb\u003eOutput:\u003c/b\u003e [V], the maximum number of parentheses pairings\u003c/p\u003e\u003cp\u003e\u003cb\u003eExamples:\u003c/b\u003e [L,R] [V]; [3,2] [3]\u003c/p\u003e\u003cp\u003eFor the case ()()(, for example, the three balanced groups are () from indexes 1 to 2, () from indexes 3 to 4, and ()() from indexes 1 to 4.\u003c/p\u003e\u003cp\u003e\u003cb\u003eTheory:\u003c/b\u003e Brute force permutations and counting will not succeed in a timely manner for L+R=10^5. Determining the inherent mathematical pattern is usually the best way to succeed in GJam.   \u003ca href = \"http://code.google.com/codejam/contest/6304486/scoreboard#vf=1\"\u003eGJam Kickstart solutions(C++,Python)\u003c/a\u003e.\u003c/p\u003e","function_template":"function val=parenc(L,R)\r\n% L number of Left parentheses, R number of Right parentheses \r\n% Determine maxinum number of parenthese pairings\r\n% http://code.google.com/codejam/contest/6304486/dashboard#s=p2\r\n\r\nval=0;\r\n \r\nend","test_suite":"%%\r\nv=parenc(36499,40104);\r\nassert(~isempty(v))\r\nassert(v==666106750)\r\n%%\r\nv=parenc(75814,21934);\r\nassert(~isempty(v))\r\nassert(v==240561145)\r\n%%\r\nv=parenc(88684,2943);\r\nassert(~isempty(v))\r\nassert(v==4332096)\r\n%%\r\nv=parenc(63688,19182);\r\nassert(~isempty(v))\r\nassert(v==183984153)\r\n%%\r\nv=parenc(71034,19757);\r\nassert(~isempty(v))\r\nassert(v==195179403)\r\n%%\r\nv=parenc(95210,572);\r\nassert(~isempty(v))\r\nassert(v==163878)\r\n%%\r\nv=parenc(50000,50000);\r\nassert(~isempty(v))\r\nassert(v==1250025000)\r\n%%\r\nv=parenc(37583,54023);\r\nassert(~isempty(v))\r\nassert(v==706259736)\r\n%%\r\nv=parenc(13403,50583);\r\nassert(~isempty(v))\r\nassert(v==89826906)\r\n%%\r\nv=parenc(74324,16176);\r\nassert(~isempty(v))\r\nassert(v==130839576)\r\n%%\r\nv=parenc(95662,20);\r\nassert(~isempty(v))\r\nassert(v==210)\r\n%%\r\nv=parenc(84426,8859);\r\nassert(~isempty(v))\r\nassert(v==39245370)\r\n%%\r\nv=parenc(1764,75732);\r\nassert(~isempty(v))\r\nassert(v==1556730)\r\n%%\r\nv=parenc(75135,17355);\r\nassert(~isempty(v))\r\nassert(v==150606690)\r\n%%\r\nv=parenc(16014,48995);\r\nassert(~isempty(v))\r\nassert(v==128232105)\r\n%%\r\nv=parenc(100000,0);\r\nassert(~isempty(v))\r\nassert(v==0)\r\n%%\r\nv=parenc(90812,5679);\r\nassert(~isempty(v))\r\nassert(v==16128360)\r\n%%\r\nv=parenc(55860,34690);\r\nassert(~isempty(v))\r\nassert(v==601715395)\r\n%%\r\nv=parenc(82678,16936);\r\nassert(~isempty(v))\r\nassert(v==143422516)\r\n%%\r\nv=parenc(50696,22228);\r\nassert(~isempty(v))\r\nassert(v==247053106)\r\n%%\r\nv=parenc(60183,19425);\r\nassert(~isempty(v))\r\nassert(v==188675025)\r\n%%\r\nv=parenc(88288,3180);\r\nassert(~isempty(v))\r\nassert(v==5057790)\r\n%%\r\nv=parenc(18628,32214);\r\nassert(~isempty(v))\r\nassert(v==173510506)\r\n%%\r\nv=parenc(99681,195);\r\nassert(~isempty(v))\r\nassert(v==19110)\r\n%%\r\nv=parenc(7,13);\r\nassert(~isempty(v))\r\nassert(v==28)\r\n%%\r\nv=parenc(62367,35577);\r\nassert(~isempty(v))\r\nassert(v==632879253)\r\n%%\r\nv=parenc(54171,29950);\r\nassert(~isempty(v))\r\nassert(v==448516225)\r\n%%\r\nv=parenc(22417,8626);\r\nassert(~isempty(v))\r\nassert(v==37208251)\r\n%%\r\nv=parenc(37824,9490);\r\nassert(~isempty(v))\r\nassert(v==45034795)\r\n%%\r\nv=parenc(95981,624);\r\nassert(~isempty(v))\r\nassert(v==195000)\r\n%%\r\nv=parenc(57025,7699);\r\nassert(~isempty(v))\r\nassert(v==29641150)\r\n%%\r\nv=parenc(1,1);\r\nassert(~isempty(v))\r\nassert(v==1)\r\n%%\r\nv=parenc(16007,35971);\r\nassert(~isempty(v))\r\nassert(v==128120028)\r\n%%\r\nv=parenc(2306,52078);\r\nassert(~isempty(v))\r\nassert(v==2659971)\r\n%%\r\nv=parenc(70555,4927);\r\nassert(~isempty(v))\r\nassert(v==12140128)\r\n%%\r\nv=parenc(19454,63092);\r\nassert(~isempty(v))\r\nassert(v==189238785)\r\n%%\r\nv=parenc(73352,18081);\r\nassert(~isempty(v))\r\nassert(v==163470321)\r\n%%\r\nv=parenc(71344,18591);\r\nassert(~isempty(v))\r\nassert(v==172821936)\r\n%%\r\nv=parenc(76452,13351);\r\nassert(~isempty(v))\r\nassert(v==89131276)\r\n%%\r\nv=parenc(88885,3106);\r\nassert(~isempty(v))\r\nassert(v==4825171)\r\n%%\r\nv=parenc(53619,9977);\r\nassert(~isempty(v))\r\nassert(v==49775253)\r\n%%\r\nv=parenc(39466,15681);\r\nassert(~isempty(v))\r\nassert(v==122954721)\r\n%%\r\nv=parenc(33791,51813);\r\nassert(~isempty(v))\r\nassert(v==570932736)\r\n%%\r\nv=parenc(40408,42624);\r\nassert(~isempty(v))\r\nassert(v==816423436)\r\n%%\r\nv=parenc(998,12);\r\nassert(~isempty(v))\r\nassert(v==78)\r\n%%\r\nv=parenc(58818,23613);\r\nassert(~isempty(v))\r\nassert(v==278798691)\r\n%%\r\nv=parenc(82533,6389);\r\nassert(~isempty(v))\r\nassert(v==20412855)\r\n%%\r\nv=parenc(73823,18704);\r\nassert(~isempty(v))\r\nassert(v==174929160)\r\n%%\r\nv=parenc(24046,69819);\r\nassert(~isempty(v))\r\nassert(v==289117081)\r\n%%\r\nv=parenc(83603,2337);\r\nassert(~isempty(v))\r\nassert(v==2731953)\r\n%%\r\nv=parenc(95719,1658);\r\nassert(~isempty(v))\r\nassert(v==1375311)\r\n%%\r\nv=parenc(9,11);\r\nassert(~isempty(v))\r\nassert(v==45)\r\n%%\r\nv=parenc(29910,7601);\r\nassert(~isempty(v))\r\nassert(v==28891401)\r\n%%\r\nv=parenc(59540,36291);\r\nassert(~isempty(v))\r\nassert(v==658536486)\r\n%%\r\nv=parenc(45871,53970);\r\nassert(~isempty(v))\r\nassert(v==1052097256)\r\n%%\r\nv=parenc(92763,325);\r\nassert(~isempty(v))\r\nassert(v==52975)\r\n%%\r\nv=parenc(9038,44798);\r\nassert(~isempty(v))\r\nassert(v==40847241)\r\n%%\r\nv=parenc(1,0);\r\nassert(~isempty(v))\r\nassert(v==0)\r\n%%\r\nv=parenc(86549,6287);\r\nassert(~isempty(v))\r\nassert(v==19766328)\r\n%%\r\nv=parenc(14401,46864);\r\nassert(~isempty(v))\r\nassert(v==103701601)\r\n%%\r\nv=parenc(93424,6259);\r\nassert(~isempty(v))\r\nassert(v==19590670)\r\n%%\r\nv=parenc(52933,31692);\r\nassert(~isempty(v))\r\nassert(v==502207278)\r\n%%\r\nv=parenc(91388,2050);\r\nassert(~isempty(v))\r\nassert(v==2102275)\r\n%%\r\nv=parenc(83487,14454);\r\nassert(~isempty(v))\r\nassert(v==104466285)\r\n%%\r\nv=parenc(26996,20778);\r\nassert(~isempty(v))\r\nassert(v==215873031)\r\n%%\r\nv=parenc(88436,1856);\r\nassert(~isempty(v))\r\nassert(v==1723296)\r\n%%\r\nv=parenc(52967,22634);\r\nassert(~isempty(v))\r\nassert(v==256160295)\r\n%%\r\nv=parenc(24373,71635);\r\nassert(~isempty(v))\r\nassert(v==297033751)\r\n%%\r\nv=parenc(25964,41310);\r\nassert(~isempty(v))\r\nassert(v==337077630)\r\n%%\r\nv=parenc(89807,7750);\r\nassert(~isempty(v))\r\nassert(v==30035125)\r\n%%\r\nv=parenc(84029,12987);\r\nassert(~isempty(v))\r\nassert(v==84337578)\r\n%%\r\nv=parenc(23884,41559);\r\nassert(~isempty(v))\r\nassert(v==285234670)\r\n%%\r\nv=parenc(96652,1790);\r\nassert(~isempty(v))\r\nassert(v==1602945)\r\n%%\r\nv=parenc(72470,2981);\r\nassert(~isempty(v))\r\nassert(v==4444671)\r\n%%\r\nv=parenc(51157,44196);\r\nassert(~isempty(v))\r\nassert(v==976665306)\r\n%%\r\nv=parenc(5964,125);\r\nassert(~isempty(v))\r\nassert(v==7875)\r\n%%\r\nv=parenc(5011,79606);\r\nassert(~isempty(v))\r\nassert(v==12557566)\r\n%%\r\nv=parenc(54850,32315);\r\nassert(~isempty(v))\r\nassert(v==522145770)\r\n%%\r\nv=parenc(94427,666);\r\nassert(~isempty(v))\r\nassert(v==222111)\r\n%%\r\nv=parenc(61766,28774);\r\nassert(~isempty(v))\r\nassert(v==413985925)\r\n%%\r\nv=parenc(90805,8083);\r\nassert(~isempty(v))\r\nassert(v==32671486)\r\n%%\r\nv=parenc(50250,34260);\r\nassert(~isempty(v))\r\nassert(v==586890930)\r\n%%\r\nv=parenc(59514,16501);\r\nassert(~isempty(v))\r\nassert(v==136149751)\r\n%%\r\nv=parenc(21448,21340);\r\nassert(~isempty(v))\r\nassert(v==227708470)\r\n%%\r\nv=parenc(48294,20183);\r\nassert(~isempty(v))\r\nassert(v==203686836)\r\n%%\r\nv=parenc(0,100000);\r\nassert(~isempty(v))\r\nassert(v==0)\r\n%%\r\nv=parenc(0,1);\r\nassert(~isempty(v))\r\nassert(v==0)\r\n%%\r\nv=parenc(9321,9795);\r\nassert(~isempty(v))\r\nassert(v==43445181)\r\n%%\r\nv=parenc(33373,207);\r\nassert(~isempty(v))\r\nassert(v==21528)\r\n%%\r\nv=parenc(78080,18989);\r\nassert(~isempty(v))\r\nassert(v==180300555)\r\n%%\r\nv=parenc(89341,7009);\r\nassert(~isempty(v))\r\nassert(v==24566545)\r\n%%\r\nv=parenc(0,2);\r\nassert(~isempty(v))\r\nassert(v==0)\r\n%%\r\nv=parenc(2,0);\r\nassert(~isempty(v))\r\nassert(v==0)\r\n%%\r\nv=parenc(90124,7716);\r\nassert(~isempty(v))\r\nassert(v==29772186)\r\n%%\r\nv=parenc(36611,12311);\r\nassert(~isempty(v))\r\nassert(v==75786516)\r\n%%\r\nv=parenc(45498,3564);\r\nassert(~isempty(v))\r\nassert(v==6352830)\r\n%%\r\nv=parenc(28355,23958);\r\nassert(~isempty(v))\r\nassert(v==287004861)\r\n%%\r\nv=parenc(58516,24422);\r\nassert(~isempty(v))\r\nassert(v==298229253)\r\n%%\r\nv=parenc(42157,56858);\r\nassert(~isempty(v))\r\nassert(v==888627403)\r\n%%\r\nv=parenc(32854,55517);\r\nassert(~isempty(v))\r\nassert(v==539709085)\r\n\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":17,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2017-02-25T22:17:05.000Z","updated_at":"2017-02-25T22:18:40.000Z","published_at":"2017-02-25T22:18:40.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis Challenge is derived from\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://code.google.com/codejam/contest/6304486/dashboard#s=p2\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eGJam 2017 Kickstart Parentheses\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. This is the first 100 large cases with 1\u0026lt;=L+R\u0026lt;=10^5.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"http://code.google.com/codejam\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eGoogle Code Jam 2017 Qualifier\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e is March 7, 2017. Typically four challenges with small and large aspects with 27 hours to complete.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe GJam story is given L left and R right parentheses determine the maximum number of parentheses pairings.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e [L,R], the quantity of parentheses types\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e [V], the maximum number of parentheses pairings\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExamples:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e [L,R] [V]; [3,2] [3]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor the case ()()(, for example, the three balanced groups are () from indexes 1 to 2, () from indexes 3 to 4, and ()() from indexes 1 to 4.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eTheory:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Brute force permutations and counting will not succeed in a timely manner for L+R=10^5. Determining the inherent mathematical pattern is usually the best way to succeed in GJam. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://code.google.com/codejam/contest/6304486/scoreboard#vf=1\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eGJam Kickstart solutions(C++,Python)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":739,"title":"Battleship_000 : (TM)  Classic Game - Easy computer bot","description":"The Classic Battleship(TM) game implemented between a computer bot and a player's bot.\r\n\r\n\u003chttp://en.wikipedia.org/wiki/Battleship_%28game%29 Battleship\u003e\r\n\r\nYou and your opponent have 9 ships of various sizes.\r\n\r\nThese Ships/Sizes/Qty are Carrier-5, Battleship-4, Submarine-3(qty 2), Cruiser-3(qty 2), Destroyer-2(qty 3).\r\n\r\nThe board is 10x10. (index 1-100)\r\nUnknown=0, Miss=1, Hit=2\r\n\r\n*The Play:*\r\n\r\nPlayer places his ships on the board. Ships may not overlap but may touch.\r\n\r\nShips array is [9,2] where 1 is the Carrier and 9 is a Destroyer. \r\n\r\n[start_idx, orientation; start_idx, orientation...]. An orientation of 0 is Down and a 1 is Right. \r\n\r\nShips[1 1;...] places the Carrier in cells [1 11 22 33 44]\r\n\r\nPlayer takes a shot on the board - idx 1:100.\r\n\r\nThe computer bot will take a shot if he has any ships remaining.\r\n\r\nThe player will see an updated board for his next shot if he has any ships remaining.\r\n\r\n*Pass: Win*\r\n\r\nBattleship_bot_000 randomly fires. \r\n\r\nThere is a Bernoulli probability question if this strategy could ever win against anything but another random bot.\r\n\r\n","description_html":"\u003cp\u003eThe Classic Battleship™ game implemented between a computer bot and a player's bot.\u003c/p\u003e\u003cp\u003e\u003ca href=\"http://en.wikipedia.org/wiki/Battleship_%28game%29\"\u003eBattleship\u003c/a\u003e\u003c/p\u003e\u003cp\u003eYou and your opponent have 9 ships of various sizes.\u003c/p\u003e\u003cp\u003eThese Ships/Sizes/Qty are Carrier-5, Battleship-4, Submarine-3(qty 2), Cruiser-3(qty 2), Destroyer-2(qty 3).\u003c/p\u003e\u003cp\u003eThe board is 10x10. (index 1-100)\r\nUnknown=0, Miss=1, Hit=2\u003c/p\u003e\u003cp\u003e\u003cb\u003eThe Play:\u003c/b\u003e\u003c/p\u003e\u003cp\u003ePlayer places his ships on the board. Ships may not overlap but may touch.\u003c/p\u003e\u003cp\u003eShips array is [9,2] where 1 is the Carrier and 9 is a Destroyer.\u003c/p\u003e\u003cp\u003e[start_idx, orientation; start_idx, orientation...]. An orientation of 0 is Down and a 1 is Right.\u003c/p\u003e\u003cp\u003eShips[1 1;...] places the Carrier in cells [1 11 22 33 44]\u003c/p\u003e\u003cp\u003ePlayer takes a shot on the board - idx 1:100.\u003c/p\u003e\u003cp\u003eThe computer bot will take a shot if he has any ships remaining.\u003c/p\u003e\u003cp\u003eThe player will see an updated board for his next shot if he has any ships remaining.\u003c/p\u003e\u003cp\u003e\u003cb\u003ePass: Win\u003c/b\u003e\u003c/p\u003e\u003cp\u003eBattleship_bot_000 randomly fires.\u003c/p\u003e\u003cp\u003eThere is a Bernoulli probability question if this strategy could ever win against anything but another random bot.\u003c/p\u003e","function_template":"function [mv,ships] = Battleship(b)\r\n % b is 10x10; idx 1:100\r\n % output mv is idx 1 thru 100\r\n % b: 0-open ocean; 1-miss shot, 2-Hit\r\n % ships: Placement of player ships\r\n % ships are initialized on first turn sum(b(:))==0\r\n % Place 9 ships [idx1 0/1;idx2 0/1;...idx9 0/1]\r\n % Ship lengths : 5/4/3/3/3/3/2/2/2\r\n % Ship orientation : 0-Vert Down; 1-Horiz Right \r\n % ships=[1 1;2 1;...8 1;99 0] \r\n % Places 8 ships on Left edge, one down in bottom rt corner\r\n % ships may not overlap - Loss\r\n \r\n% Need ships each call or will Lose; Ships placed only on first move\r\n  ships=[1 1;2 1;3 1;4 1;5 1;6 1;7 1;8 1;99 0]; \r\n \r\n % randomly pick an open spot (same as Battleship_bot_000)\r\n mv=randi(100);\r\n \r\nend % Battleship","test_suite":"%%\r\n%Test Suite\r\n%Battleship_000\r\n% Carrier/Battleship/Sub/Cruiser/Destroyer\r\n% 5/4/3/3/2  Qty 1/1/2/2/3\r\n% b 0- Unknown 1-Miss 2-Hit\r\nseed=clock;\r\nseed=1000*seed(6);\r\nrng(seed);\r\ngame_over=false;\r\nwins=0; % player wins\r\nbp=zeros(10);\r\nbc=zeros(10);\r\nships_p=ones(10);\r\nships_c=ones(10);\r\nship_vec=[5 4 3 3 3 3 2 2 2]; % Length of ships\r\n\r\ntic\r\n% initialize Computer Ships\r\nfor ship=1:9\r\n placed=false;\r\n while~placed\r\n  idx=randi(100);\r\n  [r c]=ind2sub([10 10],idx);\r\n  dwn_rt=randi(2)-1; % 0-down, 1-right\r\n  try % may go beyond board size\r\n   if dwn_rt==0 % down\r\n    blocked=any(ships_c(r:r+ship_vec(ship)-1,c)==2);\r\n   else % right\r\n    blocked=any(ships_c(r,c:c+ship_vec(ship)-1)==2);\r\n   end\r\n  catch\r\n   blocked=true; % invalid placement\r\n  end\r\n  if ~blocked % No ship conflict\r\n   if dwn_rt==0 % down\r\n    ships_c(r:r+ship_vec(ship)-1,c)=2;\r\n   else % right\r\n    ships_c(r,c:c+ship_vec(ship)-1)=2;\r\n   end\r\n   placed=true;\r\n  end \r\n end % placed\r\nend % ship\r\n \r\n% Initialize Player's ships and first move\r\n  try % for invalid mvP values\r\n   [mvP,ships]=Battleship(bp); % \r\n   bp(mvP(1))=ships_c(mvP(1));\r\n   \r\n    for ship=1:9\r\n      [r c]=ind2sub([10 10],ships(ship,1));\r\n      dwn_rt=ships(ship,2); \r\n      try % may go beyond board size\r\n       if dwn_rt==0 % down\r\n        blocked=any(ships_p(r:r+ship_vec(ship)-1,c)==2);\r\n       else % right\r\n        blocked=any(ships_p(r,c:c+ship_vec(ship)-1)==2);\r\n       end\r\n      catch\r\n       blocked=true; % invalid placement\r\n      end\r\n      if ~blocked % No ship conflict\r\n       if dwn_rt==0 % down\r\n        ships_p(r:r+ship_vec(ship)-1,c)=2;\r\n       else % right\r\n        ships_p(r,c:c+ship_vec(ship)-1)=2;\r\n       end\r\n      end \r\n    end % ship\r\n   \r\n   if sum(ships_p(:))~=127 % Expect 127 board if all placed\r\n    fprintf('Invalid Ship placement - Game over\\n');\r\n    ships\r\n    ships_p\r\n    game_over=true;\r\n   end\r\n   \r\n  catch\r\n   fprintf('Invalid first respone - Game over\\n');\r\n   mvP\r\n   ships\r\n   game_over=true;\r\n  end\r\n\r\n% Main Game Loop\r\n\r\n while ~game_over \r\n  % Computer move\r\n  % Author: Richard Z\r\n  % Battleship_000 bot: Random\r\n  mvC=randi(100);\r\n  % End Battleship_000 bot: Random\r\n  \r\n  bc(mvC)=ships_p(mvC); % Hit=2, Miss=1\r\n\r\n %figure(1);imagesc(bc,[-2 2]);axis equal;pause(0.1)  \r\n  if length(find(bc==2))\u003e=27 % Computer Wins\r\n   break;\r\n  end\r\n  \r\n  % Player's Second move and thereafter\r\n  try % for invalid mvP values\r\n   [mvP,ships]=Battleship(bp); % \r\n   bp(mvP(1))=ships_c(mvP(1)); % Hit=2, Miss=1\r\n  catch\r\n   fprintf('Ignoring Illegal move %i \\n',mvP(1));\r\n  end\r\n  \r\n %figure(2);imagesc(bp,[-2 2]);axis equal\r\n  if length(find(bp==2))\u003e=27 % All ships sunk\r\n   wins=1;\r\n   break;\r\n  end\r\n  \r\n end % While ~game_over\r\n\r\ntoc\r\n \r\n % Player must win to Pass\r\n assert(isequal(wins,1))\r\n%Pass=1;\r\n%assert(isequal(Pass,1));\r\n\r\n bc\r\n bp\r\n wins","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":16,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2012-06-04T03:25:36.000Z","updated_at":"2024-10-24T20:11:18.000Z","published_at":"2012-06-04T03:50:52.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe Classic Battleship™ game implemented between a computer bot and a player's bot.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/Battleship_%28game%29\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eBattleship\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou and your opponent have 9 ships of various sizes.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThese Ships/Sizes/Qty are Carrier-5, Battleship-4, Submarine-3(qty 2), Cruiser-3(qty 2), Destroyer-2(qty 3).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe board is 10x10. (index 1-100) Unknown=0, Miss=1, Hit=2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eThe Play:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePlayer places his ships on the board. Ships may not overlap but may touch.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eShips array is [9,2] where 1 is the Carrier and 9 is a Destroyer.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e[start_idx, orientation; start_idx, orientation...]. An orientation of 0 is Down and a 1 is Right.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eShips[1 1;...] places the Carrier in cells [1 11 22 33 44]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePlayer takes a shot on the board - idx 1:100.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe computer bot will take a shot if he has any ships remaining.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe player will see an updated board for his next shot if he has any ships remaining.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ePass: Win\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBattleship_bot_000 randomly fires.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThere is a Bernoulli probability question if this strategy could ever win against anything but another random bot.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":843,"title":"Hyperspectral Processing: Determine Material Components given a Hyperspectral vector","description":"Given a hyperspectral data set and Reflectance Spectral Signature Library determine a pixel's component percentages. \r\n\r\n\u003chttp://aviris.jpl.nasa.gov/aviris/index.html NASA AVIRIS\u003e\r\n\r\nA Ground Square is imaged by hundreds of pixels, each at a different wavelength.\r\nThe signal on pixel 1(500nm to 505nm) is a sum of the components (Concrete/Tree/Grass...) by percentage of area covered times the material reflectance.\r\nPixel 2 (510-515nm) is different by the Reflectance deltas between Concrete and a Tree.\r\n\r\nLet S(i,j) be the response of Material i for band j\r\n\r\ng( j )= %(Concrete)*S(1,j)+%(Tree)*S(2,j)+...%(Grass)*S(end,j);\r\n\r\nA 300-Band 9-Material Spectral file is loaded. Comparison between foliage and rocks is quite significant. The materials are Bush, Calcite, Concrete, Conifer, Grass (not that type), Fir tree, Gypsum, Maple, Sage\r\n\r\n*g=S*f*  where f is the percentage of the imaged pixel covered by the\r\nmaterial.\r\n\r\n*Input:* \r\ng spectral sum [301,1]; \r\nS spectral material response [301,9]  Nine materials\r\n\r\n*Output:*\r\nSolve for f  ....( eg f=[0 .5 0 .25 .25 0 0 0 0]' )\r\n\r\n( f should sum to 1, max(f) is 1 and min(f) is 0 )\r\n\r\nThe test Suite will round to 2 decimal places.\r\nCases of \"other materials\" which will induce negative values are not\r\ntested.\r\n\r\nThis is introductory and ignores atmospheric absorption.\r\n\r\nThere is a matrix operation hint in the test suite for a method to solve for f.\r\n\r\n\r\n\u003chttp://aviris.jpl.nasa.gov/data/free_data.html AVARIS Free Data\u003e\r\nThese data files are large with 224 bands x 750 channels x 2000 samples\r\n\r\nTo expand these files may require a tar converter\r\n\u003chttp://aviris.jpl.nasa.gov/alt_locator/111013_AV_Download.readme NASA readme\u003e\r\n...and... \r\n\u003chttp://aviris.jpl.nasa.gov/alt_gulf/ NASA Tools bottom Left\u003e\r\nThere are some possible issues with the NASA tar tool. Two non-standard files can be found at \u003chttp://dll-files.org/7968/index.html libiconv-2.dll\u003e and \u003chttp://dll-files.org/7975/libintl-2.dll.html libintl-2.dll\u003e\r\n\r\nSee the Test Suite for details on opening the AVIRIS Moffett Field file.","description_html":"\u003cp\u003eGiven a hyperspectral data set and Reflectance Spectral Signature Library determine a pixel's component percentages.\u003c/p\u003e\u003cp\u003e\u003ca href=\"http://aviris.jpl.nasa.gov/aviris/index.html\"\u003eNASA AVIRIS\u003c/a\u003e\u003c/p\u003e\u003cp\u003eA Ground Square is imaged by hundreds of pixels, each at a different wavelength.\r\nThe signal on pixel 1(500nm to 505nm) is a sum of the components (Concrete/Tree/Grass...) by percentage of area covered times the material reflectance.\r\nPixel 2 (510-515nm) is different by the Reflectance deltas between Concrete and a Tree.\u003c/p\u003e\u003cp\u003eLet S(i,j) be the response of Material i for band j\u003c/p\u003e\u003cp\u003eg( j )= %(Concrete)*S(1,j)+%(Tree)*S(2,j)+...%(Grass)*S(end,j);\u003c/p\u003e\u003cp\u003eA 300-Band 9-Material Spectral file is loaded. Comparison between foliage and rocks is quite significant. The materials are Bush, Calcite, Concrete, Conifer, Grass (not that type), Fir tree, Gypsum, Maple, Sage\u003c/p\u003e\u003cp\u003e\u003cb\u003eg=S*f\u003c/b\u003e  where f is the percentage of the imaged pixel covered by the\r\nmaterial.\u003c/p\u003e\u003cp\u003e\u003cb\u003eInput:\u003c/b\u003e \r\ng spectral sum [301,1]; \r\nS spectral material response [301,9]  Nine materials\u003c/p\u003e\u003cp\u003e\u003cb\u003eOutput:\u003c/b\u003e\r\nSolve for f  ....( eg f=[0 .5 0 .25 .25 0 0 0 0]' )\u003c/p\u003e\u003cp\u003e( f should sum to 1, max(f) is 1 and min(f) is 0 )\u003c/p\u003e\u003cp\u003eThe test Suite will round to 2 decimal places.\r\nCases of \"other materials\" which will induce negative values are not\r\ntested.\u003c/p\u003e\u003cp\u003eThis is introductory and ignores atmospheric absorption.\u003c/p\u003e\u003cp\u003eThere is a matrix operation hint in the test suite for a method to solve for f.\u003c/p\u003e\u003cp\u003e\u003ca href=\"http://aviris.jpl.nasa.gov/data/free_data.html\"\u003eAVARIS Free Data\u003c/a\u003e\r\nThese data files are large with 224 bands x 750 channels x 2000 samples\u003c/p\u003e\u003cp\u003eTo expand these files may require a tar converter \u003ca href=\"http://aviris.jpl.nasa.gov/alt_locator/111013_AV_Download.readme\"\u003eNASA readme\u003c/a\u003e\r\n...and...  \u003ca href=\"http://aviris.jpl.nasa.gov/alt_gulf/\"\u003eNASA Tools bottom Left\u003c/a\u003e\r\nThere are some possible issues with the NASA tar tool. Two non-standard files can be found at \u003ca href=\"http://dll-files.org/7968/index.html\"\u003elibiconv-2.dll\u003c/a\u003e and \u003ca href=\"http://dll-files.org/7975/libintl-2.dll.html\"\u003elibintl-2.dll\u003c/a\u003e\u003c/p\u003e\u003cp\u003eSee the Test Suite for details on opening the AVIRIS Moffett Field file.\u003c/p\u003e","function_template":"function f = hyperspectral(g,S)\r\n% g is [301,1]\r\n% S is [301,9]\r\n  f = zeros(size(S,2),1);\r\nend","test_suite":"%%\r\n% The AVIRIS fileread info is at the bottom\r\n% Solution Hint:\r\n% The Matrix hint is inv(S'S)(S'S)=I\r\n% With g=Sf multiply both sides by h'\r\n% S'g=S'Sf, now multiply both sides by inv(S'S)\r\n% inv(S'S)(S'g)=inv(S'S)(S'S)f which is I*f\r\n% Now simplify the right side and there is a solution\r\n% Solution Bigger/Better Hint: Search on mldivide\r\n%%\r\nglobal S\r\n%http://tinyurl.com/matlab-hyper-spectra\r\n%http://rmatlabtest.appspot.com/Spectra.mat\r\nurlwrite('http://rmatlabtest.appspot.com/Spectra.mat','Spectra.mat') ;\r\nload('Spectra.mat'); % S is the variable in Spectra.mat\r\nf_exp=[.5 .5 0 0 0 0 0 0 0 ]';\r\ng=S*f_exp;\r\n\r\nf = hyperspectral(g,S);\r\nassert(isequal(round(100*f)/100,f_exp),sprintf('%f\\n',f))\r\n%%\r\nglobal S\r\nf_exp=[0 .5 0.25 0 0 0 0.25 0 0 ]';\r\ng=S*f_exp;\r\nf = hyperspectral(g,S);\r\nassert(isequal(round(100*f)/100,f_exp),sprintf('%f\\n',f))\r\n%%\r\nglobal S\r\nf_exp=[0 .25 0.6 0 0 0 0 0.15 0 ]';\r\ng=S*f_exp;\r\nf = hyperspectral(g,S);\r\nassert(isequal(round(100*f)/100,f_exp),sprintf('%f\\n',f))\r\n%%\r\n%\r\n%Reading of the full Moffett Field file: (8GB RAM recommended)\r\n% The file is 600MB\r\n%cd 'C:\\Users\\???' % Your file location\r\n%fn='f080611t01p00r07rdn_c_sc01_ort_img'\r\n%fid = fopen (fn,'r');\r\n%A = int16(fread(fid, 'int16', 'ieee-be'));\r\n%A2 = reshape (A, 224,753,1924); % Specifics found in text files\r\n%A3 = permute (A2,[3 2 1]); % X Y Band\r\n%figure;imagesc(squeeze(A3(:,:,1))); % To view top layer\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":2,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":"2013-02-02T19:05:40.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-07-19T02:49:02.000Z","updated_at":"2013-02-02T19:05:40.000Z","published_at":"2012-07-19T03:34:29.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a hyperspectral data set and Reflectance Spectral Signature Library determine a pixel's component percentages.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"http://aviris.jpl.nasa.gov/aviris/index.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eNASA AVIRIS\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA Ground Square is imaged by hundreds of pixels, each at a different wavelength. The signal on pixel 1(500nm to 505nm) is a sum of the components (Concrete/Tree/Grass...) by percentage of area covered times the material reflectance. Pixel 2 (510-515nm) is different by the Reflectance deltas between Concrete and a Tree.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLet S(i,j) be the response of Material i for band j\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eg( j )= %(Concrete)*S(1,j)+%(Tree)*S(2,j)+...%(Grass)*S(end,j);\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA 300-Band 9-Material Spectral file is loaded. Comparison between foliage and rocks is quite significant. The materials are Bush, Calcite, Concrete, Conifer, Grass (not that type), Fir tree, Gypsum, Maple, Sage\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eg=S*f\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e where f is the percentage of the imaged pixel covered by the material.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e g spectral sum [301,1]; S spectral material response [301,9] Nine materials\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Solve for f ....( eg f=[0 .5 0 .25 .25 0 0 0 0]' )\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e( f should sum to 1, max(f) is 1 and min(f) is 0 )\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe test Suite will round to 2 decimal places. Cases of \\\"other materials\\\" which will induce negative values are not tested.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis is introductory and ignores atmospheric absorption.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThere is a matrix operation hint in the test suite for a method to solve for f.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"http://aviris.jpl.nasa.gov/data/free_data.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eAVARIS Free Data\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e These data files are large with 224 bands x 750 channels x 2000 samples\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTo expand these files may require a tar converter\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://aviris.jpl.nasa.gov/alt_locator/111013_AV_Download.readme\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eNASA readme\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e ...and... \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://aviris.jpl.nasa.gov/alt_gulf/\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eNASA Tools bottom Left\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e There are some possible issues with the NASA tar tool. Two non-standard files can be found at\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://dll-files.org/7968/index.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003elibiconv-2.dll\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://dll-files.org/7975/libintl-2.dll.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003elibintl-2.dll\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSee the Test Suite for details on opening the AVIRIS Moffett Field file.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":973,"title":"Partial pivoting for Gauss Elimination","description":"Write a function to implement partial pivoting for Gauss elimination, given the pivot element.","description_html":"\u003cp\u003eWrite a function to implement partial pivoting for Gauss elimination, given the pivot element.\u003c/p\u003e","function_template":"function Ab = PartialPivot(A,b,pivot)\r\n% A = m-by-n coefficient matrix\r\n% b = m-by-1 right-hand-side vector\r\n% pivot = pivot row and column\r\n% Ab = m-by-(n+1) Augmented matrix after pivot step\r\n  Ab = \r\nend","test_suite":"%%\r\nA = [0 2; 1 3];\r\nb = [4; 2];\r\nAb = [1 3 2; 0 2 4];\r\nassert(isequal(PartialPivot(A,b,1),Ab))\r\n%%\r\nA = [0 2 3; 4 6 7; 2, -3, 6];\r\nb = [8; -3; 5];\r\nAb = [A([2 1 3],:), b([2 1 3])];\r\nassert(isequal(PartialPivot(A,b,1),Ab))\r\n%%\r\nA = [4 6 7; 0 2 3; 0, -6, 5/2];\r\nb = [-3; 8; 13/2];\r\nAb = [A([1 3 2],:), b([1 3 2])];\r\nassert(isequal(PartialPivot(A,b,2),Ab))\r\n%%\r\nA = [0 2 5; 2 1 1; 3 1 0];\r\nb = [1; 1; 2];\r\nAb = [A([3 2 1],:), b([3 2 1])];\r\nassert(isequal(PartialPivot(A,b,1),Ab))\r\n%%\r\nA = eye(4);\r\nb = ones(4,1);\r\nassert(isequal(PartialPivot(A,b,3),[A,b]))","published":true,"deleted":false,"likes_count":2,"comments_count":4,"created_by":279,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":11,"test_suite_updated_at":"2012-10-10T03:30:19.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-10-08T00:42:34.000Z","updated_at":"2024-10-27T09:13:34.000Z","published_at":"2012-10-08T01:51:50.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to implement partial pivoting for Gauss elimination, given the pivot element.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":52839,"title":"Easy Sequences 33: Web Trapped Ant","description":"An ant is trapped on a spider web inside a can with open top. The can has a radius  and height . A spider sitting on the outside face of the can, sensed the trapped ant and started crawling towards it. The relative positions of the ant and spider are shown in the figure below.\r\n                         \r\n is the initial distance of the spider from the from the bottom of the can,  is the distance of the ant from the top of the can, and  and , are the y-offsets of the spider and ant, respectively, from the center of the circular top.\r\nIf the spider moves at a constant crawling speed, calculate the total length of the path to reach the ant at the quickest possible time. Please round-off your answer to the nearest four decimal places.\r\nCLARIFICATIONS: \r\nIt is understood there can be 2 possible positions, given a single y-offset. In this exercise please consider only the position as drawn above. That means at the top view, the ant and the spidert shall only be within the first and third quadrant, respectively.\r\nThe dotted lines is not the spider's path. They are used only to project the heights to the side.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440000534057617px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 609px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eAn \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003eant is\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e trapped on a spider web \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003einside\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e a can with open top. The can has a radius \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);\"\u003eR\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e and height \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);\"\u003eH\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e. A \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003espider sitting\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e on the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003eoutside\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e face of the can, sensed the trapped ant and started crawling towards it. The relative positions of the ant and spider are shown in the figure below.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 315px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e                         \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"551\" height=\"309\" style=\"vertical-align: baseline;width: 551px;height: 309px\" 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src=\"data:image/png;base64,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\" width=\"18\" height=\"18\" style=\"width: 18px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e is the distance of the ant from the top of the can, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"16.5\" height=\"18\" style=\"width: 16.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"18\" height=\"18\" style=\"width: 18px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e, are the y-offsets of the spider and ant, respectively, from the center of the circular top.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eIf the spider moves at a constant crawling speed, calculate the total length of the path to reach the ant at the quickest possible time. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003ePlease round-off your answer to the nearest four decimal places.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eCLARIFICATIONS: \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 80px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 60px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; text-align: left; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; \"\u003e\u003cspan style=\"\"\u003eIt is understood there can be 2 possible positions, given a single y-offset. In this exercise please consider only the position as drawn above. That means at the top view, the ant and the spidert shall only be within the first and third quadrant, respectively.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; text-align: left; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; \"\u003e\u003cspan style=\"\"\u003eThe dotted lines is not the spider's path. They are used only to project the heights to the side.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function s = spiderPath(H,R,hs,ha,xs,xa)\r\n    y = x;\r\nend","test_suite":"%%\r\nH = 10; R = 5; hs = 1; ha = 1; xs = 1; xa = 1;\r\ns_correct = 18.6210;\r\nassert(isequal(spiderPath(H,R,hs,ha,xs,xa),s_correct))\r\n%%\r\nH = 5; R = 2; hs = 0.3; ha = 0.4; xs = 0.5; xa = 0.6;\r\ns_correct = 8.0120;\r\nassert(isequal(spiderPath(H,R,hs,ha,xs,xa),s_correct))\r\n%%\r\nH = 15.5; R = 5.5; hs = 3; ha = 2.5; xs = 1.5; xa = 1;\r\ns_correct = 22.4960;\r\nassert(isequal(spiderPath(H,R,hs,ha,xs,xa),s_correct))\r\n%%\r\nH = 123; R = 123; hs = 12; ha = 25; xs = 30; xa = 40;\r\ns_correct = 399.8218;\r\nassert(isequal(spiderPath(H,R,hs,ha,xs,xa),s_correct))\r\n%%\r\nH = linspace(5,150,50); R = linspace(5,120,50); \r\nhs = linspace(0.5,10,50); ha = linspace(0.5,20,100); \r\nxs = linspace(0.4,12,50); xa = linspace(0.4,10,50);\r\ns = sum(arrayfun(@(i) spiderPath(H(i),R(i),hs(i),ha(i),xs(i),xa(i)),1:50));\r\ns_correct = 10509.4142;\r\nassert(isequal(s,s_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":8,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":"2021-10-02T18:43:11.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2021-09-30T07:18:49.000Z","updated_at":"2024-11-20T12:40:50.000Z","published_at":"2021-09-30T08:12:11.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAn \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eant is\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e trapped on a spider web \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einside\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e a can with open top. The can has a radius \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and height \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eH\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. A \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003espider sitting\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e on the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eoutside\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e face of the can, sensed the trapped ant and started crawling towards it. The relative positions of the ant and spider are shown in the figure below.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                         \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"309\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"551\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ehs\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the initial distance of the spider from the from the bottom of the can, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eha\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the distance of the ant from the top of the can, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003exs\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003exa\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, are the y-offsets of the spider and ant, respectively, from the center of the circular top.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eIf the spider moves at a constant crawling speed, calculate the total length of the path to reach the ant at the quickest possible time. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ePlease round-off your answer to the nearest four decimal places.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCLARIFICATIONS: \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIt is understood there can be 2 possible positions, given a single y-offset. In this exercise please consider only the position as drawn above. That means at the top view, the ant and the spidert shall only be within the first and third quadrant, respectively.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe dotted lines is not the spider's path. They are used only to project the heights to the 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drawpolygon or patch","description":"Recently, I tried to plot a polygon in matlab, and I found there is a lot of embedded function that can be used. However, some functions will plot points at vertexes, it is really disgusting. Try to use different embedded functions given in the title and find their difference!\r\nvertexes coordinates is given as follow:\r\nx = [0 1 1 0];\r\ny = [0 0 1 1];\r\nTips: patch is the answer!","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 183px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 91.5px; transform-origin: 407px 91.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eRecently, I tried to plot a polygon in matlab, and I found there is a lot of embedded function that can be used. However, some functions will plot points at vertexes, it is really disgusting. Try to use different embedded functions given in the title and find their difference!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003evertexes coordinates is given as follow:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ex = [0 1 1 0];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ey = [0 0 1 1];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTips: patch is the answer!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function Output = Plot_polygon(x,y)\r\nbw = poly2mask(x,y,256,256);\r\nimshow(bw)\r\n\r\nmy_vertices = [x;y];\r\nh = drawpolygon('Position',my_vertices,'LineWidth',1,'Color','cyan');\r\n\r\npatch(x,y,'cyan')\r\n\r\nOutput = 'poly2mask';\r\nend","test_suite":"%%\r\nx = [0 1 1 0];\r\ny = [0 0 1 1];\r\nassert(isequal(Plot_polygon(x,y),'patch'));\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":1133393,"edited_by":427930,"edited_at":"2024-07-08T18:22:03.000Z","deleted_by":null,"deleted_at":null,"solvers_count":14,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-10-03T05:53:41.000Z","updated_at":"2024-11-20T12:34:09.000Z","published_at":"2021-10-03T05:53:41.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRecently, I tried to plot a polygon in matlab, and I found there is a lot of embedded function that can be used. However, some functions will plot points at vertexes, it is really disgusting. Try to use different embedded functions given in the title and find their difference!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003evertexes coordinates is given as follow:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex = [0 1 1 0];\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey = [0 0 1 1];\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTips: patch is the answer!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":490,"title":"Fastest shortest-path-finder in the west","description":"Given connectivity information about a graph, your job is to find the \u003chttp://en.wikipedia.org/wiki/Shortest_path_problem *shortest-path distance*\u003e between every pair of vertices in this graph. \r\n\r\nNote: Valid solutions will be scored based on their *speed*, not their *size* (hence the _fastest in the west_...).\r\n\r\n*Format:* D = mindist(from,to)\r\n\r\n*Inputs:* two vectors, _from_ and _to_, listing the vertex labels for each edge in the graph (note: vertex labels are positive integers, connectivity is unidirectional, meaning that a connection between vertex _a_ and _b_ does not imply a connection between vertex _b_ and _a_; in other words this is a directed graph)\r\n\r\n*Output:* _D_ is a square matrix where _D(a,b)_ is the number of edges in the shortest-path starting from vertex _a_ and ending in vertex _b_ (or _inf_ if there is no path connecting them). Note: Your algorithm is not required to output the actual optimal paths between each pair of vertices, just their distance. \r\n\r\n*Example:* \r\n\r\n    D=mindist([1,2,3],[2,3,4])\r\n    D =\r\n\r\n     0     1     2     3\r\n   Inf     0     1     2\r\n   Inf   Inf     0     1\r\n   Inf   Inf   Inf     0\r\n\r\n     \r\n*Important note \u0026 disclaimer:* Your algorithm will be scored based on its *speed*, not based on its cody *size*. The reported 'size' measure for any valid entry will instead reflect the time (in milliseconds) your algorithm takes to solve various test suite problems (see the test suite for details). There has been some discussion (e.g. \u003chttp://blogs.mathworks.com/desktop/2012/02/06/scoring-in-cody/#comments\u003e) regarding the cody scoring method. This problem is just a little experiment on _tweaking_ cody to use a different scoring method other than the default node-length measure. Of course scoring based on running time has its own issues (e.g. lack of appropriate repeatability), please feel free to comment on ways you would improve how this problem is scored. ","description_html":"\u003cp\u003eGiven connectivity information about a graph, your job is to find the \u003ca href=\"http://en.wikipedia.org/wiki/Shortest_path_problem\"\u003e\u003cb\u003eshortest-path distance\u003c/b\u003e\u003c/a\u003e between every pair of vertices in this graph.\u003c/p\u003e\u003cp\u003eNote: Valid solutions will be scored based on their \u003cb\u003espeed\u003c/b\u003e, not their \u003cb\u003esize\u003c/b\u003e (hence the \u003ci\u003efastest in the west\u003c/i\u003e...).\u003c/p\u003e\u003cp\u003e\u003cb\u003eFormat:\u003c/b\u003e D = mindist(from,to)\u003c/p\u003e\u003cp\u003e\u003cb\u003eInputs:\u003c/b\u003e two vectors, \u003ci\u003efrom\u003c/i\u003e and \u003ci\u003eto\u003c/i\u003e, listing the vertex labels for each edge in the graph (note: vertex labels are positive integers, connectivity is unidirectional, meaning that a connection between vertex \u003ci\u003ea\u003c/i\u003e and \u003ci\u003eb\u003c/i\u003e does not imply a connection between vertex \u003ci\u003eb\u003c/i\u003e and \u003ci\u003ea\u003c/i\u003e; in other words this is a directed graph)\u003c/p\u003e\u003cp\u003e\u003cb\u003eOutput:\u003c/b\u003e \u003ci\u003eD\u003c/i\u003e is a square matrix where \u003ci\u003eD(a,b)\u003c/i\u003e is the number of edges in the shortest-path starting from vertex \u003ci\u003ea\u003c/i\u003e and ending in vertex \u003ci\u003eb\u003c/i\u003e (or \u003ci\u003einf\u003c/i\u003e if there is no path connecting them). Note: Your algorithm is not required to output the actual optimal paths between each pair of vertices, just their distance.\u003c/p\u003e\u003cp\u003e\u003cb\u003eExample:\u003c/b\u003e\u003c/p\u003e\u003cpre\u003e    D=mindist([1,2,3],[2,3,4])\r\n    D =\u003c/pre\u003e\u003cpre\u003e     0     1     2     3\r\n   Inf     0     1     2\r\n   Inf   Inf     0     1\r\n   Inf   Inf   Inf     0\u003c/pre\u003e\u003cp\u003e\u003cb\u003eImportant note \u0026 disclaimer:\u003c/b\u003e Your algorithm will be scored based on its \u003cb\u003espeed\u003c/b\u003e, not based on its cody \u003cb\u003esize\u003c/b\u003e. The reported 'size' measure for any valid entry will instead reflect the time (in milliseconds) your algorithm takes to solve various test suite problems (see the test suite for details). There has been some discussion (e.g. \u003ca href=\"http://blogs.mathworks.com/desktop/2012/02/06/scoring-in-cody/#comments\"\u003ehttp://blogs.mathworks.com/desktop/2012/02/06/scoring-in-cody/#comments\u003c/a\u003e) regarding the cody scoring method. This problem is just a little experiment on \u003ci\u003etweaking\u003c/i\u003e cody to use a different scoring method other than the default node-length measure. Of course scoring based on running time has its own issues (e.g. lack of appropriate repeatability), please feel free to comment on ways you would improve how this problem is scored.\u003c/p\u003e","function_template":"function D = mindist(from,to)\r\n  D=zeros(max([from,to]));\r\nend","test_suite":"%%\r\n% test small connectivity matrix (3x3)\r\nassert(isequal(mindist([1,3,2,3],[2,2,1,2]),[0 1 Inf;1 0 Inf;2 1 0]))\r\nt0=clock;\r\nD=mindist([1,3,2,3],[2,2,1,2]);\r\nt1=etime(clock,t0)*1e3;\r\ndisp('Time (ms)'); \r\ndisp(t1)\r\n\r\n%%\r\n% test small connectivity matrix (10 vertices, 15 edges)\r\nassert(isequal(mindist([10 5 5 7 7 3 3 4 6 6 1 8 7 1 10],[7 4 10 6 8 4 1 7 9 4 6 9 6 10 9]),[0 Inf Inf 2 Inf 1 2 3 2 1;Inf 0 Inf Inf Inf Inf Inf Inf Inf Inf;1 Inf 0 1 Inf 2 2 3 3 2;Inf Inf Inf 0 Inf 2 1 2 3 Inf;Inf Inf Inf 1 0 3 2 3 2 1;Inf Inf Inf 1 Inf 0 2 3 1 Inf;Inf Inf Inf 2 Inf 1 0 1 2 Inf;Inf Inf Inf Inf Inf Inf Inf 0 1 Inf;Inf Inf Inf Inf Inf Inf Inf Inf 0 Inf;Inf Inf Inf 3 Inf 2 1 2 1 0]))\r\nt0=clock;\r\nD=mindist([10 5 5 7 7 3 3 4 6 6 1 8 7 1 10],[7 4 10 6 8 4 1 7 9 4 6 9 6 10 9]);\r\nt1=etime(clock,t0)*1e3;\r\ndisp('Time (ms)');\r\ndisp(t1)\r\n\r\n%%\r\n% test small connectivity matrix (10 vertices, 30 edges)\r\nassert(isequal(mindist([4 10 2 9 8 2 7 10 3 7 5 9 2 6 9 3 2 9 8 7 9 9 10 8 2 7 3 2 1 8],[2 6 9 4 3 1 4 8 10 5 4 6 5 5 7 4 7 1 4 4 3 8 5 7 5 4 7 3 4 1]),[0 2 3 1 3 4 3 4 3 4;1 0 1 2 1 2 1 2 1 2;3 2 0 1 2 2 1 2 3 1;2 1 2 0 2 3 2 3 2 3;3 2 3 1 0 4 3 4 3 4;4 3 4 2 1 0 4 5 4 5;3 2 3 1 1 4 0 4 3 4;1 2 1 1 2 3 1 0 3 2;1 2 1 1 2 1 1 1 0 2;2 3 2 2 1 1 2 1 4 0]))\r\nt0=clock;\r\nD=mindist([4 10 2 9 8 2 7 10 3 7 5 9 2 6 9 3 2 9 8 7 9 9 10 8 2 7 3 2 1 8],[2 6 9 4 3 1 4 8 10 5 4 6 5 5 7 4 7 1 4 4 3 8 5 7 5 4 7 3 4 1]);\r\nt1=etime(clock,t0)*1e3;\r\ndisp('Time (ms)');\r\ndisp(t1)\r\n\r\n%%\r\n% test medium connectivity matrix (100 vertices, 200 edges)\r\ni=[17 21 97 93 63 87 68 14 40 12 30 60 45 63 55 43 71 74 32 66 48 27 10 80 1 50 36 40 100 35 84 75 93 94 79 49 6 6 60 24 80 43 60 41 64 87 1 17 44 63 6 89 15 70 74 48 69 68 63 24 77 82 48 69 33 50 100 90 37 29 10 62 61 87 69 6 45 27 77 8 100 94 77 26 8 72 59 4 4 36 59 47 9 60 95 88 15 27 32 50 51 42 40 76 22 32 68 39 46 82 32 27 15 39 75 63 33 63 63 91 64 43 13 10 2 56 10 62 45 24 44 58 80 2 44 98 80 92 31 97 76 82 48 68 5 100 91 65 65 90 77 96 95 44 84 4 29 85 25 99 26 75 47 2 47 64 63 4 83 73 63 26 56 99 9 98 47 7 82 53 86 84 66 40 83 76 69 86 74 60 18 99 69 3 10 35 85];\r\nj=[6 27 87 92 2 77 23 12 86 60 81 18 14 69 98 84 91 76 12 81 22 81 4 26 25 27 56 39 52 20 56 92 21 37 61 100 24 67 34 76 77 90 46 25 76 69 44 94 65 9 80 28 56 39 65 68 37 51 12 1 64 21 98 50 46 99 86 21 46 99 99 81 16 60 80 20 88 74 68 15 72 55 28 67 11 31 24 39 85 35 64 42 65 87 45 95 78 59 49 13 61 30 28 31 28 35 13 74 13 7 94 60 2 40 74 93 38 18 91 84 25 29 72 36 98 12 41 28 31 54 73 71 49 29 43 82 10 46 8 91 30 80 54 26 83 46 84 51 17 20 78 7 50 30 58 58 27 30 36 15 42 54 32 13 80 89 4 50 56 88 16 98 49 24 91 72 55 77 65 83 79 12 82 70 93 19 95 35 62 98 51 70 48 68 56 28 6];\r\n\r\nassert(isequal(interp2(mindist(i,j),[2 55 45 33 34 87 53 43 99 50],[90 66 53 41 94 68 94 38 23 76],'nearest'),[8,5,8,Inf,7,7,Inf,Inf,Inf,9]))\r\nt0=clock;\r\nD=mindist(i,j);\r\nt1=etime(clock,t0)*1e3;\r\ndisp('Time (ms)');\r\ndisp(t1)\r\n\r\n%%\r\n% Time-score evaluation\r\n% test medium connectivity matrix (100 vertices, 200 edges)\r\nrand('state',2); \r\nn=100;m=200; \r\ni=ceil(n*rand(1,m));\r\nj=ceil(n*rand(1,m));\r\nk=i==j;i(k)=[];j(k)=[];\r\nI=ceil(n*rand(1,10));J=ceil(n*rand(1,10));\r\n\r\n% first run for initialization\r\nassert(isequal(interp2(mindist(i,j),I,J,'nearest'),[6 6 Inf 0 5 Inf 4 8 6 3]))\r\n\r\n% second run for time evaluation\r\nt0=clock;\r\nD=mindist(i,j);\r\nt1(1)=etime(clock,t0)*1e3;\r\n\r\n% test large connectivity matrix (1000 vertices, 2000 edges)\r\nrand('state',0); \r\nn=1000;m=2000; \r\ni=ceil(n*rand(1,m));\r\nj=ceil(n*rand(1,m));\r\nk=i==j;i(k)=[];j(k)=[];\r\nI=ceil(n*rand(1,10));J=ceil(n*rand(1,10));\r\n\r\n% first run for initialization\r\nassert(isequal(interp2(mindist(i,j),I,J,'nearest'),[8 8 9 8 11 7 Inf 5 8 Inf]))\r\n\r\n% second run for time evaluation\r\nt0=clock;\r\nD=mindist(i,j);\r\nt1(2)=etime(clock,t0)*1e3;\r\n\r\n% test large connectivity matrix (1000 vertices, 10000 edges)\r\nrand('state',1); \r\nn=1000;m=10000; \r\ni=ceil(n*rand(1,m));\r\nj=ceil(n*rand(1,m));\r\nk=i==j;i(k)=[];j(k)=[];\r\nI=ceil(n*rand(1,10));J=ceil(n*rand(1,10));\r\n\r\n% second run for time evaluation\r\nt0=clock;\r\nD=mindist(i,j);\r\nt1(3)=etime(clock,t0)*1e3;\r\nassert(isequal(interp2(D,I,J,'nearest'),[3 4 3 4 4 3 3 2 3 3]))\r\n\r\n% convert time to score\r\ndisp('Time (ms)');\r\ndisp(t1);\r\n\r\nurlwrite('https://sites.google.com/a/alfnie.com/alfnie/software/SetSolutionScore.p?attredirects=0\u0026amp;d=1','SetSolutionScore.p');\r\nrehash path; \r\nSetSolutionScore(round(sum(t1)));\r\n%feval(@evalin,'caller',sprintf('score=%d',round(sum(t1))));\r\n%%fh=fopen('mindist.m','wt');\r\n%%fprintf(fh,'%s\\n',repmat('1;',[1,ceil(sum(t1)/2)]));\r\n%%fclose(fh);","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":43,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":15,"test_suite_updated_at":"2015-06-23T04:22:41.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-03-13T04:35:04.000Z","updated_at":"2024-11-12T08:57:02.000Z","published_at":"2012-03-15T18:12:51.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven connectivity information about a graph, your job is to find the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/Shortest_path_problem\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eshortest-path distance\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e between every pair of vertices in this graph.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNote: Valid solutions will be scored based on their\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003espeed\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, not their\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003esize\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (hence the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003efastest in the west\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e...).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eFormat:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e D = mindist(from,to)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInputs:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e two vectors,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003efrom\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eto\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, listing the vertex labels for each edge in the graph (note: vertex labels are positive integers, connectivity is unidirectional, meaning that a connection between vertex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e does not imply a connection between vertex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e; in other words this is a directed graph)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eD\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is a square matrix where\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eD(a,b)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the number of edges in the shortest-path starting from vertex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and ending in vertex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (or\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einf\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if there is no path connecting them). Note: Your algorithm is not required to output the actual optimal paths between each pair of vertices, just their distance.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[    D=mindist([1,2,3],[2,3,4])\\n    D =\\n\\n     0     1     2     3\\n   Inf     0     1     2\\n   Inf   Inf     0     1\\n   Inf   Inf   Inf     0]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eImportant note \u0026amp; disclaimer:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Your algorithm will be scored based on its\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003espeed\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, not based on its cody\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003esize\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. The reported 'size' measure for any valid entry will instead reflect the time (in milliseconds) your algorithm takes to solve various test suite problems (see the test suite for details). There has been some discussion (e.g.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://blogs.mathworks.com/desktop/2012/02/06/scoring-in-cody/#comments\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ehttp://blogs.mathworks.com/desktop/2012/02/06/scoring-in-cody/#comments\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e) regarding the cody scoring method. This problem is just a little experiment on\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003etweaking\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e cody to use a different scoring method other than the default node-length measure. Of course scoring based on running time has its own issues (e.g. lack of appropriate repeatability), please feel free to comment on ways you would improve how this problem is scored.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":58144,"title":"Given the mass and stiffness of an undamped SDOF system, find the natural frequency and the natural period of vibration","description":"Problem Statement\r\nGiven the mass  and stiffness  of an undamped SDOF system, find the system's natural frequency in both Hz and radians per second as well as the natural period of vibration. \r\nBackground\r\nAn undamped, linear single degree-of-freedom (SDOF) system can be visualized as a spring with stiffness , fixed at one end and having a mass  attached to the other:\r\n\r\nOnce set into motion, the system will oscillate at its natural frequency, or fundamental frequency: \r\n\r\nwhere the natural frequency  is in radians per second. \r\nThe time required for the undamped system to complete one cycle of free vibration is the natural period of vibration of the system, , which has units of seconds:\r\n\r\nA system executes  cycles in 1 second. This is the natural cyclic frequency of vibration:\r\n\r\nwhich has units of Hertz (Hz) or cycles per second. The term natural frequency of vibration applies to both  and . They have the relationship:\r\n\r\nExample\r\nm = 10;\r\nk = 2;\r\n[wn,fn,Tn] = udSDOF(m,k)\r\nwn = 5\r\nfn = 0.7958\r\nTn = 1.2566\r\n\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 878.625px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 439.312px; transform-origin: 407px 439.312px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20px; border-block-end-color: rgb(60, 60, 60); border-block-start-color: rgb(60, 60, 60); border-bottom-color: rgb(60, 60, 60); border-inline-end-color: rgb(60, 60, 60); border-inline-start-color: rgb(60, 60, 60); border-left-color: rgb(60, 60, 60); border-right-color: rgb(60, 60, 60); border-top-color: rgb(60, 60, 60); caret-color: rgb(60, 60, 60); color: rgb(60, 60, 60); column-rule-color: rgb(60, 60, 60); font-family: Helvetica, Arial, sans-serif; font-size: 20px; font-weight: 700; line-height: 20px; margin-block-end: 5px; margin-block-start: 3px; margin-bottom: 5px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 3px; outline-color: rgb(60, 60, 60); perspective-origin: 384px 10px; text-align: left; text-decoration: none; text-decoration-color: rgb(60, 60, 60); text-emphasis-color: rgb(60, 60, 60); transform-origin: 384px 10px; white-space: pre-wrap; margin-left: 4px; margin-top: 3px; margin-bottom: 5px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eProblem Statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGiven the mass \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003em\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and stiffness \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ek\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e of an undamped SDOF system, find the system's natural frequency in both Hz and radians per second as well as the natural period of vibration. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20px; border-block-end-color: rgb(60, 60, 60); border-block-start-color: rgb(60, 60, 60); border-bottom-color: rgb(60, 60, 60); border-inline-end-color: rgb(60, 60, 60); border-inline-start-color: rgb(60, 60, 60); border-left-color: rgb(60, 60, 60); border-right-color: rgb(60, 60, 60); border-top-color: rgb(60, 60, 60); caret-color: rgb(60, 60, 60); color: rgb(60, 60, 60); column-rule-color: rgb(60, 60, 60); font-family: Helvetica, Arial, sans-serif; font-size: 20px; font-weight: 700; line-height: 20px; margin-block-end: 5px; margin-block-start: 20px; margin-bottom: 5px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 20px; outline-color: rgb(60, 60, 60); perspective-origin: 384px 10px; text-align: left; text-decoration: none; text-decoration-color: rgb(60, 60, 60); text-emphasis-color: rgb(60, 60, 60); transform-origin: 384px 10px; white-space: pre-wrap; margin-left: 4px; margin-top: 20px; margin-bottom: 5px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eBackground\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eAn undamped, linear single degree-of-freedom (SDOF) system can be visualized as a spring with stiffness \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ek\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, fixed at one end and having a mass \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003em\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e attached to the other:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 99px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 49.5px; text-align: left; transform-origin: 384px 49.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"90\" height=\"93\" style=\"vertical-align: baseline;width: 90px;height: 93px\" src=\"data:image/jpeg;base64,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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eOnce set into motion, the system will oscillate at its \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003enatural frequency\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, or fundamental frequency: \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 41px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 20.5px; text-align: left; transform-origin: 384px 20.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-16px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"62.5\" height=\"41\" style=\"width: 62.5px; height: 41px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.75px; text-align: left; transform-origin: 384px 10.75px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhere the natural frequency \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"18.5\" height=\"20\" style=\"width: 18.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e is in radians per second. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.25px; text-align: left; transform-origin: 384px 21.25px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThe time required for the undamped system to complete one cycle of free vibration is the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003enatural period\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e of vibration of the system, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"16.5\" height=\"20\" style=\"width: 16.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, which has units of seconds:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 37px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 18.5px; text-align: left; transform-origin: 384px 18.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"51.5\" height=\"37\" style=\"width: 51.5px; height: 37px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.75px; text-align: left; transform-origin: 384px 10.75px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eA system executes \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"31.5\" height=\"20\" style=\"width: 31.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e cycles in 1 second. This is the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003enatural cyclic frequency\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e of vibration:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 37px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 18.5px; text-align: left; transform-origin: 384px 18.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"44\" height=\"37\" style=\"width: 44px; height: 37px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.25px; text-align: left; transform-origin: 384px 21.25px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhich has units of Hertz (Hz) or cycles per second. The term natural frequency of vibration applies to both \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"18.5\" height=\"20\" style=\"width: 18.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"12\" height=\"20\" style=\"width: 12px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. They have the relationship:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 38px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 19px; text-align: left; transform-origin: 384px 19px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"47.5\" height=\"38\" style=\"width: 47.5px; height: 38px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20px; border-block-end-color: rgb(60, 60, 60); border-block-start-color: rgb(60, 60, 60); border-bottom-color: rgb(60, 60, 60); border-inline-end-color: rgb(60, 60, 60); border-inline-start-color: rgb(60, 60, 60); border-left-color: rgb(60, 60, 60); border-right-color: rgb(60, 60, 60); border-top-color: rgb(60, 60, 60); caret-color: rgb(60, 60, 60); color: rgb(60, 60, 60); column-rule-color: rgb(60, 60, 60); font-family: Helvetica, Arial, sans-serif; font-size: 20px; font-weight: 700; line-height: 20px; margin-block-end: 5px; margin-block-start: 20px; margin-bottom: 5px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 20px; outline-color: rgb(60, 60, 60); perspective-origin: 384px 10px; text-align: left; text-decoration: none; text-decoration-color: rgb(60, 60, 60); text-emphasis-color: rgb(60, 60, 60); transform-origin: 384px 10px; white-space: pre-wrap; margin-left: 4px; margin-top: 20px; margin-bottom: 5px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eExample\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 122.625px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 61.3125px; transform-origin: 404px 61.3125px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2188px; transform-origin: 404px 10.2188px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003em = 10;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2188px; transform-origin: 404px 10.2188px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003ek = 2;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2188px; transform-origin: 404px 10.2188px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e[wn,fn,Tn] = udSDOF(m,k)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2188px; transform-origin: 404px 10.2188px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003ewn = 5\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2188px; transform-origin: 404px 10.2188px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003efn = 0.7958\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2188px; transform-origin: 404px 10.2188px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eTn = 1.2566\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [wn,fn,Tn] = udSDOF(m,k)\r\n  % put yo answer here ^(o.O)^\r\nend","test_suite":"%%\r\nm = 2;\r\nk = 50;\r\ny_correct = [5 0.7958 1.2566];\r\n[wn,fn,Tn] = udSDOF(m,k);\r\nassert(sum(round([wn,fn,Tn]./y_correct,2))==3)\r\n\r\n%%\r\nm = 0.2;\r\nk = 2000;\r\ny_correct = [100 15.9 0.0628];\r\n[wn,fn,Tn] = udSDOF(m,k);\r\nassert(sum(round([wn,fn,Tn]./y_correct,2))==3)\r\n\r\n%%\r\nm = 0.2533; \r\nk = 10; \r\ny_correct = [6.2832 1 1];\r\n[wn,fn,Tn] = udSDOF(m,k);\r\nassert(sum(round([wn,fn,Tn]./y_correct,2))==3)\r\n\r\n%%\r\nfiletext = fileread('udSDOF.m');\r\nnot_allowed = contains(filetext, 'regex');\r\nassert(~not_allowed)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":91130,"edited_by":91130,"edited_at":"2023-04-28T00:16:14.000Z","deleted_by":null,"deleted_at":null,"solvers_count":31,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-04-27T23:21:12.000Z","updated_at":"2024-11-12T05:54:32.000Z","published_at":"2023-04-28T00:16:14.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"heading\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eProblem Statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven the mass \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003em\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and stiffness \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of an undamped SDOF system, find the system's natural frequency in both Hz and radians per second as well as the natural period of vibration. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"heading\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBackground\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAn undamped, linear single degree-of-freedom (SDOF) system can be visualized as a spring with stiffness \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, fixed at one end and having a mass \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003em\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e attached to the other:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"93\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"90\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOnce set into motion, the system will oscillate at its \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003enatural frequency\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, or fundamental frequency: \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e$\\\\omega_n =\\\\sqrt{\\\\frac{k}{m}}$\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere the natural frequency \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e$\\\\omega_n$\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is in radians per second. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe time required for the undamped system to complete one cycle of free vibration is the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003enatural period\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e of vibration of the system, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eT_n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, which has units of seconds:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e$T_n =\\\\frac{2\\\\pi }{\\\\omega_n }$\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA system executes \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e1/T_n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e cycles in 1 second. This is the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003enatural cyclic frequency\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e of vibration:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e$f_n =\\\\frac{1}{T_n }$\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhich has units of Hertz (Hz) or cycles per second. The term natural frequency of vibration applies to both \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e$\\\\omega_n$\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef_n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. They have the relationship:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e$f_n =\\\\frac{\\\\omega_n }{2\\\\pi }$\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"heading\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[m = 10;\\nk = 2;\\n[wn,fn,Tn] = udSDOF(m,k)\\nwn = 5\\nfn = 0.7958\\nTn = 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the Voltage Through a Step-Up Transformer","description":"Given a step-up transformer has a primary coil with A number loops, a secondary coil with B number loops, and a primary voltage of 12 volts. What is the secondary voltage in each transformer?","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407.5px 21px; transform-origin: 407.5px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 21px; text-align: left; transform-origin: 384.5px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGiven a step-up transformer has a primary coil with A number loops, a secondary coil with B number loops, and a primary voltage of 12 volts. What is the secondary voltage in each transformer?\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function V_s = SecVolt(A,B)\r\n  V_s = ;\r\nend","test_suite":"%%\r\nA = 30;\r\nB = 75;\r\nassert(isequal(SecVolt(A,B),30))\r\n%%\r\nA = 20;\r\nB = 40;\r\nassert(isequal(SecVolt(A,B),24))\r\n%%\r\nA = 40;\r\nB = 90;\r\nassert(isequal(SecVolt(A,B),27))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":3227359,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":41,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-05-17T17:08:40.000Z","updated_at":"2024-11-19T12:00:46.000Z","published_at":"2023-05-17T17:08:40.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a step-up transformer has a primary coil with A number loops, a secondary coil with B number loops, and a primary voltage of 12 volts. What is the secondary voltage in each transformer?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":55920,"title":"Juros Simples","description":"Faça uma função que calcule o montagem de um investimento com juros simples que receba como argumentos o capital inicial C, a taxa de juros i em %, e o tempo de aplicação t.\r\nO valor deve ser arrendondado em 2 casas.\r\nJurosSimples(2490, 2.5, 8) = 2988;","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 102.438px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 51.2188px; transform-origin: 407px 51.2188px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFaça uma função que calcule o montagem de um investimento com juros simples que receba como argumentos o capital inicial \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eC\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, a taxa de juros \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ei \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eem %\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e e o tempo de aplicação \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003et\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eO valor deve ser arrendondado em 2 casas.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20.4375px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 10.2188px; transform-origin: 404px 10.2188px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; 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\"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eJurosSimples(2490, 2.5, 8) = 2988;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function m = JurosSimples(c, i, t)\r\n  %faça a sua função aqui\r\nend","test_suite":"%%\r\nc = 2490;\r\ni = 2.5;\r\nt = 8;\r\ny_correct = 2988;\r\nassert(isequal(JurosSimples(c, i, t),y_correct))\r\n\r\n%%\r\nc = 400;\r\ni = 4;\r\nt = 5;\r\ny_correct = 480;\r\nassert(isequal(JurosSimples(c, i, t),y_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2564100,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":42,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-17T19:18:46.000Z","updated_at":"2024-11-17T23:57:56.000Z","published_at":"2022-09-17T19:18:46.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFaça uma função que calcule o montagem de um investimento com juros simples que receba como argumentos o capital inicial \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eC\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, a taxa de juros \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ei \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eem %\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e e o tempo de aplicação \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eO valor deve ser arrendondado em 2 casas.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[JurosSimples(2490, 2.5, 8) = 2988;]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":58653,"title":"Alternate Arrangement","description":"Determine the ways of arranging 'm' men and 'w' women alternatively in a row of 's' seats.\r\nAssumptions :\r\ns\u003cm and s\u003cw","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 81px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 40.5px; transform-origin: 407px 40.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eDetermine the ways of arranging 'm' men and 'w' women alternatively in a row of 's' seats.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eAssumptions :\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003es\u0026lt;m and s\u0026lt;w\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = arrangement(m,w,s)\r\n  y = x;\r\nend","test_suite":"%%\r\nm = 2\r\nw = 3\r\ns = 3\r\nx = 1;\r\ny_correct = 9;\r\nassert(isequal(arrangement(m,w,s),y_correct))\r\n","published":true,"deleted":false,"likes_count":13,"comments_count":3,"created_by":3495088,"edited_by":3495088,"edited_at":"2023-07-18T15:12:10.000Z","deleted_by":null,"deleted_at":null,"solvers_count":17,"test_suite_updated_at":"2023-07-18T15:12:10.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2023-07-18T15:00:55.000Z","updated_at":"2024-11-12T13:44:57.000Z","published_at":"2023-07-18T15:12:10.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDetermine the ways of arranging 'm' men and 'w' women alternatively in a row of 's' seats.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAssumptions :\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003es\u0026lt;m and s\u0026lt;w\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":56035,"title":"sinus de pulsation a","description":"Ecrire une fonction sinat qui prend en entrée un vecteur t  (de valeurs croissantes)  et renvoie un vecteur y de de même dimension que t qui contient les valeurs de sin(at) où la pulsation a est choisie de façon à ce qu'il y ait excatement une période de sin(at) sur l'intervalle [min(t), max(t)] ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 63px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 31.5px; transform-origin: 407px 31.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 380px 8px; transform-origin: 380px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eEcrire une fonction sinat qui prend en entrée un vecteur t  (de valeurs croissantes)  et renvoie un vecteur y de de même dimension que t qui contient les valeurs de sin(at) où la pulsation a est choisie de façon à ce qu'il y ait excatement une période de sin(at) sur l'intervalle [min(t), max(t)] \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [y] = sinat(t)\r\n  %à vous de jouer\r\nend","test_suite":"%%\r\na=rand\r\nt=linspace(-pi/a,pi/a)\r\ny_correct = sin(a*t);\r\nassert(max(abs(sinat(t)-y_correct))\u003c=1e-10)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":63915,"edited_by":223089,"edited_at":"2022-10-22T13:06:29.000Z","deleted_by":null,"deleted_at":null,"solvers_count":28,"test_suite_updated_at":"2022-10-22T13:06:29.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-23T12:46:39.000Z","updated_at":"2024-11-18T00:12:54.000Z","published_at":"2022-09-23T12:46:39.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eEcrire une fonction sinat qui prend en entrée un vecteur t  (de valeurs croissantes)  et renvoie un vecteur y de de même dimension que t qui contient les valeurs de sin(at) où la pulsation a est choisie de façon à ce qu'il y ait excatement une période de sin(at) sur l'intervalle [min(t), max(t)] \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":58797,"title":"Array Width (no usage of size)","description":"Find the array width. \r\nSize may not be used.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 51px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 25.5px; transform-origin: 407px 25.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 66.5px 8px; transform-origin: 66.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFind the array width. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 69.5px 8px; transform-origin: 69.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSize may not be used.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function w = find_width(m)\r\n%Size is not allowed\r\n  w=0;\r\nend","test_suite":"%%\r\nw=randi(10);\r\nh=randi(10);\r\nm=ones(h,w);\r\nassert(isequal(find_width(m),w))\r\n%%\r\nfiletext = fileread('find_width.m');\r\nassert(~contains(filetext,'size'));\r\n\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":3097,"edited_by":3097,"edited_at":"2023-08-04T14:35:36.000Z","deleted_by":null,"deleted_at":null,"solvers_count":41,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-08-04T14:29:25.000Z","updated_at":"2024-11-18T00:47:52.000Z","published_at":"2023-08-04T14:35:36.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the array width. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSize may not be used.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":58877,"title":"Neural Net Image Convolution: Return only Valid portion of conv2","description":"This challenge is to return only the Valid portion of a 2-D convolution. Valid is deemed to be where all elements of the kernel are applied against the image. The (1,1) point with a ones(3) kernel would be invalid while point (2,2) would return a Valid convolution value. The images will be even-square,m, and the kernels will be odd-square,K.The m=ones(6) and K=ones(3) would return a 4x4 matrix of 9s.\r\nmValidConv2=create_ValidConv2(m,K)\r\nIn neural net processing of the Mnist database of digits(0-9) one Convolutional Neural Network method uses 9x9 kernels on the 28x28 images to return the Valid 20x20 central core for the next processing step. The third image includes a black border of four around Valid to maintain scale.\r\n  \r\nThe entire Matlab code from Convolutional Neural Networks in Matlab by Nuruzzaman Faruqui , a Matlab Neural Net Tutorial for Mnist processing, is included in the function template. Loading the Mnist Train/Test Images/Labels from posted MAT files or THE MNIST DATABASE of handwritten digits are provided. The Neural Net tutorial explains Neural Net processing for Digit Recognition. The neural net training method uses 784 input nodes,  20 convolutions(9x9), ReLU, Pooling, batch sampling, single hidden layer of 100 nodes, updating parameters via backwards propagation, and updating convolution kernels. The digit prediction accuracy is \u003e94% after 50s of training. The final feature kernels are very amorphous and unexpected.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 545.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 272.75px; transform-origin: 407px 272.75px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 369.5px 8px; transform-origin: 369.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis challenge is to return only the Valid portion of a 2-D convolution. Valid is deemed to be where all elements of the kernel are applied against the image. The (1,1) point with a ones(3) kernel would be invalid while point (2,2) would return a Valid convolution value. The images will be even-square,m, and the kernels will be odd-square,K.The m=ones(6) and K=ones(3) would return a 4x4 matrix of 9s.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 121.5px 8px; transform-origin: 121.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003emValidConv2=create_ValidConv2(m,K)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 379px 8px; transform-origin: 379px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn neural net processing of the Mnist database of digits(0-9) one Convolutional Neural Network method uses 9x9 kernels on the 28x28 images to return the Valid 20x20 central core for the next processing step. The third image includes a black border of four around Valid to maintain scale.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 194.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 97.25px; text-align: left; transform-origin: 384px 97.25px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline;width: 252px;height: 189px\" 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\" data-image-state=\"image-loaded\" width=\"252\" height=\"189\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 147px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 73.5px; text-align: left; transform-origin: 384px 73.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 91px 8px; transform-origin: 91px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe entire Matlab code from \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.youtube.com/watch?v=ZOXOwYUVCqw\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eConvolutional Neural Networks in Matlab by Nuruzzaman Faruqui\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 70px 8px; transform-origin: 70px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e , a Matlab Neural Net Tutorial for Mnist processing, is included in the function template. Loading the Mnist Train/Test Images/Labels from posted MAT files or \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"/#null\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eTHE MNIST DATABASE of handwritten digits\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 181.5px 8px; transform-origin: 181.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are provided. The Neural Net tutorial explains Neural Net processing for Digit Recognition. The neural net training method uses 784 input nodes,  20 convolutions(9x9), ReLU, Pooling, batch sampling, single hidden layer of 100 nodes, updating parameters via backwards propagation, and updating convolution kernels. The digit prediction accuracy is \u0026gt;94% after 50s of training. The final feature kernels are very amorphous and unexpected.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function mValidConv2=create_ValidConv2(m,K)\r\n  mValidConv2=conv2(m,K,'same');\r\nend\r\n\r\n% Code from Convolutional Neural Network in Matlab by Nuruzzaman Faruqui\r\n% Youtube:  https://www.youtube.com/watch?v=ZOXOwYUVCqw\r\n% I have made comments noted by raz and a couple speed enhancements\r\n% I also provide alternate direct source for MNIST files as .mat files\r\n%{\r\nfunction MNIST_Process\r\n%Based upon https://www.youtube.com/watch?v=ZOXOwYUVCqw\r\n%784 input nodes;20 conv 9x9 filters,ReLU;2x2 submatrix Pooling layer,single hidden layer 100 nodes\r\n\r\n%Matlab Convolutional Neural Network in Matlab\r\n%Processing MNIST digits using conv, contents, \r\n%MNIST files  http://yann.lecun.com/exdb/mnist/\r\n%Create filters\r\n%File Exchange NN https://www.mathworks.com/matlabcentral/fileexchange/59223-convolution-neural-network-simple-code-simple-to-use?s_tid=ta_fx_results\r\n%\r\n%use Test_images.mat if avail, use MNIST ubyte files if avail, load Test_images.mat\r\ndir_struct=dir;\r\nfilenames={dir_struct.name};\r\nfn='Test_images.mat';\r\nptr=find(ismember(filenames,fn));\r\nif ~isempty(ptr) % Test images/labels mat files exist\r\n tic;\r\n load('Test_images'); % images [28,28,10000] uint8\r\n load('Test_labels'); % labels [10000,1] uint8 values 0:9\r\n fprintf('Images:%i  Time:%.2f\\n',size(images,3),toc);\r\n Images=double(images)/255; %raz values must be 0:1 or bad things happen\r\n Labels=double(labels);\r\n Labels(Labels==0)=10; % 0 remapped to 10\r\n\r\nelse % Check for Mnist file\r\n %MNIST files source  http://yann.lecun.com/exdb/mnist/\r\n fn='t10k-images.idx3-ubyte'; %NMIST gzip expanded file for Test Images 10K\r\n filenames={dir_struct.name};\r\n ptr=find(ismember(filenames,fn));\r\n if ~isempty(ptr)\r\n  tic\r\n  Images=loadMNISTImages(fn);\r\n  fprintf('MNIST Images Process Time: %.2f\\n',toc); %raz\r\n  Images=reshape(Images,28,28,[]); % Un-vectorize the images\r\n  %Images already scaled by 1/255 in loadMNISTImages\r\n \r\n  Labels=loadMNISTLabels('t10k-labels.idx1-ubyte');\r\n  Labels(Labels==0)=10; % 0 to 10\r\nelse % download Test_images.mat, Test_labels.mat and load\r\n fnameTestI='Test_images.mat'; %load('Test_images.mat') creates images(28,28,10000) 1.6MB\r\n fnameTrainI='Train_images.mat'; %load('Train_images.mat') creates images(28,28,60000)  9.9MB\r\n fnameTestL='Test_labels.mat'; %load('Test_images.mat') creates labels(10000,1) 5KB\r\n fnameTrainL='Train_labels.mat'; %load('Train_images.mat') creates labels(60000,1) 30KB\r\n \r\n %Google Drive Dowloads need to come from shared files\r\n% Tweak link: file/d/ to uc?export=download\u0026id=   while removing /view?usp=sharing\r\n% https://drive.google.com/file/d/1v3GsGgP3p905wzdvUqypL_-djYmxiyzK/view?usp=sharing\r\n% https://drive.google.com/uc?export=download\u0026id=1v3GsGgP3p905wzdvUqypL_-djYmxiyzK\r\n \r\n\r\n  urlTeI='https://drive.google.com/uc?export=download\u0026id=10ReGWlfSvr9p6uq6FQlqw6vw3UXgWo57';\r\n  urlTeL='https://drive.google.com/uc?export=download\u0026id=105zTcVgItZ2JjFiUkJulU33R7lXNl29-';\r\n  urlTrI='https://drive.google.com/uc?export=download\u0026id=1HJZssH6_9OcQ8mXwS_DtvsS_Kk86BDFY';\r\n  urlTrL='https://drive.google.com/uc?export=download\u0026id=1KNTn2eNXbQkQJNe6xhO1LMmvkDRP-XLq';\r\n \r\n  tic\r\n  urlwrite(urlTeI,fnameTestI); %Writing GoogleDrive MNIST_Test_images.pdf  Test_images.mat \r\n  fprintf('Download 1.6MB Time: %.1f  sec\\n\\n',toc); %1.6MB download Time, about 1.1 sec\r\n \r\n  tic\r\n  urlwrite(urlTeL,fnameTestL); %Writing GoogleDrive MNIST_Test_labels.pdf  Test_labels.mat\r\n  fprintf('Download 5KB Time: %.1f  sec\\n\\n',toc); %5KB download Time, about 0.5 sec\r\n \r\n  tic\r\n  urlwrite(urlTrI,fnameTrainI); %Writing GoogleDrive MNIST_Train_images.pdf  Train_images.mat\r\n  fprintf('Download 9.9MB Time: %.1f  sec\\n\\n',toc); %9.9MB download Time, about 4.1 sec\r\n \r\n  tic\r\n  urlwrite(urlTrL,fnameTrainL); %Writing GoogleDrive MNIST_Train_labels.pdf  Train_labels.mat\r\n  fprintf('Download 30KB Time: %.1f  sec\\n\\n',toc); %30KB download Time, about 0.6 sec\r\n\r\n  tic\r\n  load('Test_images'); % images [28,28,10000] uint8\r\n  load('Test_labels'); % labels [10000,1] uint8 values 0:9\r\n  fprintf('Images:%i  Time:%.2f\\n',size(images,3),toc); %.05s\r\n  Images=double(images)/255; %raz values must be 0:1 or bad things happen\r\n  Labels=double(labels);\r\n  Labels(Labels==0)=10; % 0 to 10\r\n end % if MNIST ubyte files\r\n\r\nend % if Test_images.mat\r\n\r\n\r\nrng(1); %raz not liked by curretn matlab\r\n\r\nW1=.01*randn([9 9 20]); %Conv Kernels   base .01\r\nW5=(2*rand(100,2000)-1)*sqrt(6)/sqrt(360+2000); %Hidden layer coeff of 100 pooled\r\nWo=(2*rand(10, 100)-1)*sqrt(6)/sqrt( 10+ 100); %Output coeff to find 0:9 best match\r\n\r\nX=Images(:,:,1:8000);\r\nD=Labels(1:8000);\r\nztic=tic;\r\nfor epoch=1:3  %Repeat cycles of all Training data\r\n fprintf('epoch:%i  Time:%.2f\\n',epoch,toc(ztic));\r\n [W1, W5, Wo]=MnistConv(W1,W5,Wo,X,D);\r\nend %epoch\r\n\r\n%save('MnistConv.mat'); % Used for Post analysis, see video\r\n\r\nX=Images(:,:,8001:10000);\r\nD=Labels(8001:10000);\r\nacc=0;\r\nN=length(D);\r\n\r\nfor k=1:N\r\n x=X(:,:,k);\r\n y1=Conv(x,W1); %Neural Net Processing  W1 kernels on image-x\r\n y2=ReLU(y1);   %Rectification process\r\n y3=Pool(y2);   %Take 20x20 conv images into 100 values\r\n y4=reshape(y3,[],1);\r\n v5=W5*y4;      %Hidden layer weights\r\n y5=ReLU(v5);   %Rectification process\r\n v=Wo*y5;       %Wo Output weight processing\r\n y=Softmax(v);  %create vector length 10 of expected probability, uses exp(x) smoothing\r\n                %Needed in training but not sure why in evaluation\r\n \r\n [~,i]=max(y);\r\n if i==D(k)\r\n  acc=acc+1;\r\n end\r\nend %k\r\n\r\n acc=acc/N;\r\n fprintf('Accuracy is %.2f%%  Time:%.2f\\n',100*acc,toc(ztic));  %raz output/time\r\n\r\nend% MNIST_Process\r\n\r\nfunction [W1, W5,Wo]=MnistConv(W1, W5,Wo,X,D)\r\n alpha=.01;\r\n beta=0.95;\r\n z=reshape(1:100,10,10); % raz\r\n kmap=kron(z,ones(2)); % raz\r\n \r\n momentum1=zeros(size(W1));\r\n momentum5=zeros(size(W5));\r\n momentumo=zeros(size(Wo));\r\n \r\n N=length(D);\r\n \r\n bsize=100;\r\n blist=1:bsize:(N-bsize+1);\r\n \r\n for batch=1:length(blist) % Batch/Updates, each Batch creates updates to Params\r\n  dW1=zeros(size(W1));\r\n  dW5=zeros(size(W5));\r\n  dWo=zeros(size(Wo));\r\n  \r\n  begin=blist(batch);\r\n  for k=begin:begin+bsize-1  %Subset Group of Training samples for param adjust\r\n   x=X(:,:,k);\r\n   y1=Conv(x,W1); %8K/5.8s  3.5s\r\n   y2=ReLU(y1);\r\n   y3=Pool(y2);\r\n   y4=reshape(y3,[],1);\r\n   v5=W5*y4;\r\n   y5=ReLU(v5);\r\n   v=Wo*y5;\r\n   y=Softmax(v); %10 Probability Bins for [1-9 0] \r\n   \r\n   d=zeros(10,1);\r\n   d(sub2ind(size(d),D(k),1))=1;\r\n   \r\n    e=d-y; % raz should this be (e-y)^2*sign(e-y)?\r\n    delta=e;\r\n    e5=Wo'*delta;\r\n    delta5=(y5\u003e0).*e5;\r\n    e4=W5'*delta5;\r\n    e3=reshape(e4,size(y3));\r\n    e2=zeros(size(y2));\r\n    W3=ones(size(y2))/(2*2);\r\n    \r\n    for c=1:20\r\n     %e2(:,:,c)=kron(e3(:,:,c),ones([2 2])).*W3(:,:,c); %160K/4.5s\r\n     e3c=e3(:,:,c); %160K/.27 raz\r\n     e2(:,:,c)=e3c(kmap).*W3(:,:,c);  %160K/.8s  raz\r\n    end %c\r\n    \r\n    delta2=(y2\u003e0).*e2;\r\n    delta1_x=zeros(size(W1)); \r\n    \r\n    for c=1:20\r\n     delta1_x(:,:,c)=conv2(x(:,:),rot90(delta2(:,:,c),2),'valid'); %160K/5.3s\r\n    end %c\r\n    \r\n    dW1=dW1+delta1_x; %error per kernel plane\r\n    dW5=dW5+delta5*y4'; %8K/4.2s  100x2000\r\n    dWo=dWo+delta*y5';\r\n  end %k\r\n  dW1=dW1/bsize;\r\n  dW5=dW5/bsize;\r\n  dWo=dWo/bsize;\r\n  \r\n  momentum1=alpha*dW1+beta*momentum1;\r\n  W1       = W1+momentum1;\r\n  \r\n  momentum5=alpha*dW5+beta*momentum5;\r\n  W5       = W5+momentum5;\r\n  \r\n  momentumo=alpha*dWo+beta*momentumo;\r\n  Wo       = Wo+momentumo;\r\n  \r\n end % batch\r\n \r\nend %MnistConv\r\n\r\nfunction rng(x)\r\n randn('seed',x);\r\n rand('seed',x);\r\nend % rng\r\n\r\nfunction y=Pool(x)\r\n [xrow,xcol,numFilters]=size(x);\r\n y=zeros(xrow/2,xcol/2,numFilters);\r\n for k=1:numFilters\r\n  filter=ones(2)/(2*2);\r\n  image=conv2(x(:,:,k),filter,'valid');\r\n  y(:,:,k)=image(1:2:end,1:2:end);\r\n end\r\n\r\nend %Pool\r\n\r\nfunction y=Conv(x,W)\r\n [wrow,wcol,numFilters]=size(W);\r\n [xrow,xcol,~         ]=size(x);\r\n \r\n yrow=xrow-wrow+1;\r\n ycol=xcol-wcol+1;\r\n \r\n y=zeros(yrow,ycol,numFilters);\r\n \r\n for k=1:numFilters\r\n  filter=W(:,:,k);\r\n  filter=rot90(squeeze(filter),2); %200K/2.5s  raz remove test/92.15%\r\n  y(:,:,k)=conv2(x,filter,'valid'); %200K/3.7s  3.5s\r\n end\r\nend %Conv\r\n\r\nfunction y=Softmax(x)\r\n ex=exp(x);\r\n y=ex/sum(ex);\r\nend %Softmax\r\n\r\nfunction y=ReLU(x)\r\n y=max(0,x);\r\nend %ReLU\r\n\r\n\r\n\r\nfunction images=loadMNISTImages(filename)\r\n%\r\nfp=fopen(filename,'rb');\r\nassert(fp~=-1,['Could not open', filename,'']);\r\nmagic=fread(fp,1,'int32',0,'ieee-be');\r\nassert(magic==2051,['Bad magic number in', filename, '']); %2051 Images\r\nnumImages=fread(fp,1,'int32',0,'ieee-be');\r\nnumRows=fread(fp,1,'int32',0,'ieee-be');\r\nnumCols=fread(fp,1,'int32',0,'ieee-be');\r\nimages=fread(fp,inf,'unsigned char=\u003eunsigned char');\r\nfclose(fp);\r\nfprintf('Images:%i  rows:%i  cols:%i\\n',numImages,numRows,numCols); %raz\r\n\r\nimages=reshape(images,numCols,numRows,numImages);\r\nimages=permute(images,[2 1 3]); \r\n\r\nimages=reshape(images,size(images,1)*size(images,2),size(images,3)); %raz Will be reverted\r\nimages=double(images)/255;\r\n \r\nend %loadMNISTImages\r\n\r\nfunction labels=loadMNISTLabels(filename)\r\n%\r\nfp=fopen(filename,'rb');\r\nassert(fp~=-1,['Could not open', filename,'']);\r\nmagic=fread(fp,1,'int32',0,'ieee-be');\r\nassert(magic==2049,['Bad magic number in ', filename,'']);\r\nnumLabels=fread(fp,1,'int32',0,'ieee-be');\r\nlabels=fread(fp,inf,'unsigned char');\r\nassert(size(labels,1)==numLabels,'Mismatch in label count');\r\nfclose(fp);\r\nfprintf('Labels:%i\\n',numLabels); %raz\r\n\r\n\r\nend %loadMNISTLabels\r\n%}","test_suite":"%%\r\n%Google Drive Dowloads need to come from shared files\r\n% Tweak link: file/d/ to uc?export=download\u0026id=   while removing /view?usp=sharing\r\n% https://drive.google.com/file/d/1v3GsGgP3p905wzdvUqypL_-djYmxiyzK/view?usp=sharing\r\n% https://drive.google.com/uc?export=download\u0026id=1v3GsGgP3p905wzdvUqypL_-djYmxiyzK\r\n fnameTestI='Test_images.mat'; %load('Test_images.mat') creates images(28,28,10000) 1.6MB\r\n fnameTrainI='Train_images.mat'; %load('Train_images.mat') creates images(28,28,60000)  9.9MB\r\n fnameTestL='Test_labels.mat'; %load('Test_images.mat') creates labels(10000,1) 5KB\r\n fnameTrainL='Train_labels.mat'; %load('Train_images.mat') creates labels(60000,1) 30KB\r\n \r\n urlTeI='https://drive.google.com/uc?export=download\u0026id=10ReGWlfSvr9p6uq6FQlqw6vw3UXgWo57';\r\n urlTeL='https://drive.google.com/uc?export=download\u0026id=105zTcVgItZ2JjFiUkJulU33R7lXNl29-';\r\n urlTrI='https://drive.google.com/uc?export=download\u0026id=1HJZssH6_9OcQ8mXwS_DtvsS_Kk86BDFY';\r\n urlTrL='https://drive.google.com/uc?export=download\u0026id=1KNTn2eNXbQkQJNe6xhO1LMmvkDRP-XLq';\r\n \r\n % fn.mat  https://drive.google.com/file/d/10GsOZTIjzMIuO7xAYIqLT1zIq9Cyubl-/view?usp=drive_link\r\n % Google Gives warning thus aborts urlwrite\r\n %\r\n %fname='Mnist_Test_images.pdf'\r\n %Fake name of .pdf on GoogleDrive,  write as a mat\r\n \r\n %url='https://drive.google.com/file/d/1mgxzsmVQNXgqHEdd61QR2r0STm3N9lgG/view?usp=drive_link';\r\n %ptr=strfind(url,'/view'); % Tweaking the url\r\n %url(ptr:end)=[];\r\n %url=strrep(url,'file/d/','uc?export=download\u0026id=');\r\n \r\n tic\r\n urlwrite(urlTeI,fnameTestI); %Writing GoogleDrive MNIST_Test_images.pdf  Test_images.mat\r\n fprintf('Download 1.6MB Time: %.1f  sec\\n',toc); %1.6MB download Time, about 1.5 sec\r\n \r\n tic\r\n urlwrite(urlTeL,fnameTestL); %Writing GoogleDrive MNIST_Test_labels.pdf  Test_labels.mat\r\n fprintf('Download 5KB Time: %.1f  sec\\n',toc); %5KB download Time, about .5 sec\r\n \r\n global labels images \r\n \r\n load('Test_images'); % images [28,28,10000] uint8\r\n load('Test_labels'); % labels [10000,1] uint8 values 0:9\r\n \r\n %Showing a Label and an image from Mnist\r\n ptr=randi(10000);\r\n fprintf('Label:%i\\n',labels(ptr));\r\n figure(1);imagesc(images(:,:,ptr)); colormap gray;\r\n \r\n \r\nvalid=1;\r\nassert(valid)\r\n%%\r\n%Showing a Label and an image from Mnist\r\n global labels images\r\n valid=1;\r\n ptr=randi(10000);\r\n fprintf('Label:%i\\n',labels(ptr));\r\n m=double(images(:,:,ptr))/255;\r\n figure(2);imagesc(m); colormap gray;\r\n \r\n K=repmat([0 0 .5 1 1 1 .5 0 0],9,1); % Vert Bar\r\n mValidConv2=create_ValidConv2(m,K);\r\n figure(3);imagesc(mValidConv2); colormap gray;\r\n mc=conv2(m,K,'same');\r\n if ~isequal(mc(5:end-4,5:end-4),mValidConv2)\r\n  valid=0;\r\n end\r\n \r\nassert(valid)\r\n\r\n%%\r\n%Showing a Label and an image from Mnist\r\n global labels images\r\n valid=1;\r\n ptr=randi(10000);\r\n fprintf('Label:%i\\n',labels(ptr));\r\n m=double(images(:,:,ptr))/255;\r\n figure(2);imagesc(m); colormap gray;\r\n \r\n K=repmat([0 0 .5 1 1 1 .5 0 0]',1,9); %Horiz Bar\r\n mValidConv2=create_ValidConv2(m,K);\r\n figure(3);imagesc(mValidConv2); colormap gray;\r\n mc=conv2(m,K,'same');\r\n if ~isequal(mc(5:end-4,5:end-4),mValidConv2)\r\n  valid=0;\r\n end\r\n \r\nassert(valid)\r\n\r\n%%\r\n%Showing a Label and an image from Mnist\r\n global labels images\r\n valid=1;\r\n m=rand(24);\r\n K=repmat([0 .5 1 1 1 .5 0]',1,7); %Horiz Bar\r\n mValidConv2=create_ValidConv2(m,K)\r\n mc=conv2(m,K,'same');\r\n if ~isequal(mc(4:end-3,4:end-3),mValidConv2)\r\n  valid=0;\r\n end\r\n \r\nassert(valid)\r\n\r\n%%\r\n%Showing a Label and an image from Mnist\r\n global labels images\r\n valid=1;\r\n m=rand(8);\r\n K=ones(3)/9;\r\n mValidConv2=create_ValidConv2(m,K)\r\n mc=conv2(m,K,'same');\r\n if ~isequal(mc(2:end-1,2:end-1),mValidConv2)\r\n  valid=0;\r\n end\r\n \r\nassert(valid)\r\n\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":3097,"edited_by":3097,"edited_at":"2023-08-17T19:33:19.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-08-17T14:03:38.000Z","updated_at":"2024-11-12T13:42:48.000Z","published_at":"2023-08-17T19:33:20.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis challenge is to return only the Valid portion of a 2-D convolution. Valid is deemed to be where all elements of the kernel are applied against the image. The (1,1) point with a ones(3) kernel would be invalid while point (2,2) would return a Valid convolution value. The images will be even-square,m, and the kernels will be odd-square,K.The m=ones(6) and K=ones(3) would return a 4x4 matrix of 9s.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003emValidConv2=create_ValidConv2(m,K)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn neural net processing of the Mnist database of digits(0-9) one Convolutional Neural Network method uses 9x9 kernels on the 28x28 images to return the Valid 20x20 central core for the next processing step. The third image includes a black border of four around Valid to maintain scale.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"189\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"252\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"189\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"252\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"189\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"252\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId3\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe entire Matlab code from \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.youtube.com/watch?v=ZOXOwYUVCqw\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eConvolutional Neural Networks in Matlab by Nuruzzaman Faruqui\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e , a Matlab Neural Net Tutorial for Mnist processing, is included in the function template. Loading the Mnist Train/Test Images/Labels from posted MAT files or \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eTHE MNIST DATABASE of handwritten digits\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e are provided. The Neural Net tutorial explains Neural Net processing for Digit Recognition. The neural net training method uses 784 input nodes,  20 convolutions(9x9), ReLU, Pooling, batch sampling, single hidden layer of 100 nodes, updating parameters via backwards propagation, and updating convolution kernels. The digit prediction accuracy is \u0026gt;94% after 50s of training. The final feature kernels are very amorphous and 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Nets: Activation functions","description":"Return values of selected Activation function type for value,vector, and matrices.\r\ny=Activation(x,id); where id is 1:4 for ReLU, sigmoid, hyperbolic_tan, Softmax\r\nReLU: Rectified Linear Unit, clips negatives  max(0,x)   Trains faster than sigmoid\r\nSigmoid: Exponential normalization [0:1]      \r\nHyperTan: Normalization[-1:1]   tanh(x)\r\nSoftmax: Normalizes output sum to 1, individual values [0:1]      Used on Output node\r\n\r\nWorking though a series of Neural Net challenges from Perceptron, Hidden Layers, Back Propogation, ..., to the Convolutional Neural Net/Training for Handwritten Digits from Mnist. \r\nMight take a day or two  to completely cover Neural Nets in a Matlab centric fashion. \r\nEssentially Out=Softmax(ReLU(X*W)*WP)","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: 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0px; perspective-origin: 252.5px 8px; transform-origin: 252.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eReturn values of selected Activation function type for value,vector, and matrices.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 240.5px 8px; transform-origin: 240.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ey=Activation(x,id); where id is 1:4 for ReLU, sigmoid, hyperbolic_tan, Softmax\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 253.5px 8px; transform-origin: 253.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eReLU: Rectified Linear Unit, clips negatives  max(0,x)   Trains faster than sigmoid\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 137px 8px; transform-origin: 137px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSigmoid: Exponential normalization [0:1]      \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 72.5px; height: 19.5px;\" width=\"72.5\" height=\"19.5\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 120.5px 8px; transform-origin: 120.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHyperTan: Normalization[-1:1]   tanh(x)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 192px 8px; transform-origin: 192px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSoftmax: Normalizes output sum to 1, individual values [0:1]   \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 43px; height: 19.5px;\" width=\"43\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 73.5px 8px; transform-origin: 73.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e   Used on Output node\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 352.5px 8px; transform-origin: 352.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWorking though a series of Neural Net challenges from Perceptron, Hidden Layers, Back Propogation, ..., to the Convolutional Neural Net/Training for Handwritten Digits from Mnist. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 265px 8px; transform-origin: 265px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eMight take a day or two  to completely cover Neural Nets in a Matlab centric fashion. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 130px 8px; transform-origin: 130px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eEssentially Out=Softmax(ReLU(X*W)*WP)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = Activation(x,id)\r\n%id/function 1/ReLU 2/Sigmoid 3/Hyperbolictan 4/Softmax\r\n%x may be a point, vector or matrix\r\n  y = x;\r\nend","test_suite":"%%\r\nvalid=1;\r\nx = 2;\r\ny = Activation(x,1);\r\nif y~=max(0,x),valid=0;end\r\ny = Activation(x,2);\r\nif y~=1./(1+exp(-x)),valid=0;end\r\ny = Activation(x,3);\r\nif y~=tanh(x),valid=0;end\r\ny = Activation(x,4);\r\nif y~=1,valid=0;end\r\nassert(valid)\r\n%%\r\nvalid=1;\r\nx = [-1 0 1 2];\r\ny = Activation(x,1);\r\nif y~=max(0,x),valid=0;end\r\ny = Activation(x,2);\r\nif y~=1./(1+exp(-x)),valid=0;end\r\ny = Activation(x,3);\r\nif y~=tanh(x),valid=0;end\r\ny = Activation(x,4);\r\nif y~=exp(x)./sum(exp(x)),valid=0;end\r\nassert(valid)\r\n%%\r\nvalid=1;\r\nx = [-1 0 1 2;.5 .25 -2 5];\r\ny = Activation(x,1);\r\nif y~=max(0,x),valid=0;end\r\ny = Activation(x,2);\r\nif y~=1./(1+exp(-x)),valid=0;end\r\ny = Activation(x,3);\r\nif y~=tanh(x),valid=0;end\r\ny = Activation(x,4);\r\nif y~=exp(x)./sum(sum(exp(x))),valid=0;end\r\nassert(valid)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":3097,"edited_by":3097,"edited_at":"2023-08-19T14:59:54.000Z","deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-08-19T14:02:05.000Z","updated_at":"2024-11-11T13:31:29.000Z","published_at":"2023-08-19T14:59:56.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eReturn values of selected Activation function type for value,vector, and matrices.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ey=Activation(x,id); where id is 1:4 for ReLU, sigmoid, hyperbolic_tan, Softmax\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eReLU: Rectified Linear Unit, clips negatives  max(0,x)   Trains faster than sigmoid\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSigmoid: Exponential normalization [0:1]      \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e1/(1+e^{-x})\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHyperTan: Normalization[-1:1]   tanh(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSoftmax: Normalizes output sum to 1, individual values [0:1]   \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ee^x/\\\\Sigma e^x\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e   Used on Output node\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWorking though a series of Neural Net challenges from Perceptron, Hidden Layers, Back Propogation, ..., to the Convolutional Neural Net/Training for Handwritten Digits from Mnist. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMight take a day or two  to completely cover Neural Nets in a Matlab centric fashion. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eEssentially Out=Softmax(ReLU(X*W)*WP)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":58887,"title":"Neural Net: Best Index of Prediction array","description":"The final ouput of a neural net application is a Prediction matrix/vector,P, that gives the probability of the input being of a set of N classes represented by the columns.\r\nFor the XOR function the input matrix is [0 0;0 1;1 0;1 1] with an expected output vector of [0;1;1;0]. Ouput of Zero would be represented by a higher likelihood in column 1 than column 2 of the Prediction matrix.\r\nGiven a P matrix [m,n] where there are m cases and n possible outcomes return peak value for each case and the index of the most likely outcome.\r\n[case_peak,case_idx]=Prediction(P)\r\nif P was [0.1 0.5 0.9;0.2 0.8 0.4] (2 cases with 3 possible outcomes 1:3) return case_peak=[0.9;0.8] and case_idx=[3;2]\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 234px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 117px; transform-origin: 407px 117px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 379px 8px; transform-origin: 379px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe final ouput of a neural net application is a Prediction matrix/vector,P, that gives the probability of the input being of a set of N classes represented by the columns.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 379.5px 8px; transform-origin: 379.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor the XOR function the input matrix is [0 0;0 1;1 0;1 1] with an expected output vector of [0;1;1;0]. Ouput of Zero would be represented by a higher likelihood in column 1 than column 2 of the Prediction matrix.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 378.5px 8px; transform-origin: 378.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven a P matrix [m,n] where there are m cases and n possible outcomes return peak value for each case and the index of the most likely outcome.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 113px 8px; transform-origin: 113px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e[case_peak,case_idx]=Prediction(P)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 373px 8px; transform-origin: 373px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eif P was [0.1 0.5 0.9;0.2 0.8 0.4] (2 cases with 3 possible outcomes 1:3) return case_peak=[0.9;0.8] and case_idx=[3;2]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [case_peak,case_idx]=Prediction(P)\r\n%P provides probability that an input is probably type n\r\n%P may represent [Prob_dog Prob_cat Prob_cow Prob_sheep] when trained on four anaimals\r\n%P may be a [1,n] prediction vector for a single case or\r\n%P may be an [m,n] prediction matrix of m cases\r\n case_peak=max(P);\r\n case_idx=find(P==max(P));\r\nend","test_suite":"%%\r\nvalid=1;\r\n%Binary functions AND/OR/XOR\r\n%input [0 0;0 1;1 0;1 1] cases\r\nPor=[.75 .25;.1 .9;.2 .8;.05 .95]; % [Prob-0 Prob-1] Notional values\r\n[case_peak,case_idx]=Prediction(Por);\r\nif ~isequal(case_peak,max(Por,[],2))\r\n valid=0;\r\nend\r\nfor i=1:size(Por,1)\r\n    if case_idx(i)~=find(Por(i,:)==max(Por(i,:)))\r\n     valid=0;\r\n    end\r\nend\r\n\r\n%input [0 0;0 1;1 0;1 1] cases\r\nPand=[1 0;.8 0;.9 .1;.1 .9]; %[Prob-0 Prob-1] Notional values\r\n[case_peak,case_idx]=Prediction(Pand);\r\nif ~isequal(case_peak,max(Pand,[],2))\r\n valid=0;\r\nend\r\nfor i=1:size(Pand,1)\r\n    if case_idx(i)~=find(Pand(i,:)==max(Pand(i,:)))\r\n     valid=0;\r\n    end\r\nend\r\n\r\nPxor=[.9 .2;.1 .8;.3 .8;.8 .1]; % [Prob-0 Prob-1] Notional values\r\n[case_peak,case_idx]=Prediction(Pxor);\r\nif ~isequal(case_peak,max(Pxor,[],2))\r\n valid=0;\r\nend\r\nfor i=1:size(Pxor,1)\r\n    if case_idx(i)~=find(Pxor(i,:)==max(Pxor(i,:)))\r\n     valid=0;\r\n    end\r\nend\r\n\r\n\r\n\r\nassert(valid)\r\n%%\r\nvalid=1;\r\n%input [dog;cat;cow;sheep] cases\r\n%[Prob-dog Prob-cat Prob-cow Prob-sheep] Notional values\r\nP=[.8 .3 .2 .1;.3 .9 .2 .1;.1 .1 .7 .2;.25 .3 .1 .6]; \r\n[case_peak,case_idx]=Prediction(P);\r\nif ~isequal(case_peak,max(P,[],2))\r\n valid=0;\r\nend\r\nfor i=1:size(P,1)\r\n    if case_idx(i)~=find(P(i,:)==max(P(i,:)))\r\n     valid=0;\r\n    end\r\nend\r\n\r\nassert(valid)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":3097,"edited_by":3097,"edited_at":"2023-08-19T23:47:40.000Z","deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-08-19T22:24:20.000Z","updated_at":"2024-11-18T00:32:01.000Z","published_at":"2023-08-19T23:47:40.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe final ouput of a neural net application is a Prediction matrix/vector,P, that gives the probability of the input being of a set of N classes represented by the columns.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor the XOR function the input matrix is [0 0;0 1;1 0;1 1] with an expected output vector of [0;1;1;0]. Ouput of Zero would be represented by a higher likelihood in column 1 than column 2 of the Prediction matrix.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a P matrix [m,n] where there are m cases and n possible outcomes return peak value for each case and the index of the most likely outcome.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e[case_peak,case_idx]=Prediction(P)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eif P was [0.1 0.5 0.9;0.2 0.8 0.4] (2 cases with 3 possible outcomes 1:3) return case_peak=[0.9;0.8] and case_idx=[3;2]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":58892,"title":"Neural Net: Calculate Perceptron","description":"This challenge is to calculate the Neural Net Perceptron value,P, given X, WH, and WP using ReLU on the hidden layer. This example is for two inputs, two hidden nodes, and a single output. No offset terms are applied.\r\n \r\nThe function template includes the code to create this figure using Matlab Latex","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 626.85px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 313.425px; transform-origin: 407px 313.425px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 375.5px 8px; transform-origin: 375.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis challenge is to calculate the Neural Net Perceptron value,P, given X, WH, and WP using ReLU on the hidden layer. This example is for two inputs, two hidden nodes, and a single output. No offset terms are applied.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 545.85px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 272.925px; text-align: left; transform-origin: 384px 272.925px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline\" 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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 250px 8px; transform-origin: 250px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe function template includes the code to create this figure using Matlab Latex\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function P=Calc_Perceptron(X,WH,WP)\r\n%The P value in this case is a single value\r\n%No ReLU,Softmax, or Sigmoid applied to the output P\r\n  P=0;\r\nend\r\n\r\n%The figure was generated using Matlab and Latex\r\n%{\r\nfunction perceptron\r\n% put figure code into cody\r\nfigure(1);clf;\r\nplot([0;140;140;0;0],[-5;-5;100;100;-5],'k','linewidth',2);hold on\r\nxticks([]);yticks([]); %Tciks/Labels off\r\n\r\naxis equal;\r\naxis tight\r\n\r\n\r\nr = 10;\r\nphi = 0:0.01:2*pi;\r\ncxA = r*cos(phi);\r\ncyA = r*sin(phi);\r\n\r\nrxA=[0 2*r 2*r   0 0]';\r\nryA=[0   0 2*r 2*r 0]';\r\n\r\npatch(cxA+10,cyA+80,'y');text(10-2,80,'X_{1}','Fontsize',20);\r\npatch(cxA+10,cyA+20,'y');text(10-2,20,'X_{2}','Fontsize',20);\r\n\r\npatch(cxA+80,cyA+80,'y');text(80-6,94,'H_{1}','Fontsize',20);text(80-8,80,'\\Sigma','Fontsize',30);\r\npatch(cxA+80,cyA+20,'y');text(80-6,34,'H_{2}','Fontsize',20);text(80-8,20,'\\Sigma','Fontsize',30);\r\n\r\npatch(cxA+130,cyA+50,'y');text(130-2,50,'P','Fontsize',20);\r\n\r\npatch(rxA+80,ryA+70,'y');text(85,80,'ReLU','Fontsize',20);text(102,88,'Y_{1}','Fontsize',20);\r\npatch(rxA+80,ryA+10,'y');text(85,20,'ReLU','Fontsize',20);text(102,32,'Y_{2}','Fontsize',20);\r\n\r\nquiver(20,20,55,0,'k','LineWidth',3.5); % line arrowhead x,y,dx,dy,  VectorLine draw\r\nquiver(20,80,55,0,'k','LineWidth',3.5); % line arrowhead x,y,dx,dy,  VectorLine draw\r\nquiver(20,20,58.5,58.5,'k','LineWidth',3.5); % line arrowhead x,y,dx,dy,  VectorLine draw\r\nquiver(20,80,58.5,-58.5,'k','LineWidth',3.5); % line arrowhead x,y,dx,dy,  VectorLine draw\r\n\r\nquiver(100,20,25,25,'k','LineWidth',3.5,'MaxHeadSize',.5); % line arrowhead x,y,dx,dy,  VectorLine draw\r\nquiver(100,80,25,-25,'k','LineWidth',3.5,'MaxHeadSize',.5); % line arrowhead x,y,dx,dy,  VectorLine draw\r\n\r\ntext(40,85,'WH_{11}','Fontsize',20);\r\ntext(20,65,'WH_{12}','Fontsize',20);\r\ntext(40,25,'WH_{22}','Fontsize',20);\r\ntext(20,38,'WH_{21}','Fontsize',20);\r\n\r\ntext(115,68,'WP_{11}','Fontsize',20);\r\ntext(115,28,'WP_{21}','Fontsize',20);\r\n\r\nstr='$$ X=\\left[\\matrix{ X_{1} \u0026 X_{2}} \\right]  $$'; %valid\r\ntext(1,50,str,'Interpreter','latex','Fontsize',20);\r\n\r\nstr='$$ WH=\\left[\\matrix{ WH_{11} \u0026 WH_{12}\\cr WH_{21} \u0026 WH_{22} } \\right]  $$'; %valid\r\ntext(1,5,str,'Interpreter','latex','Fontsize',20);\r\n\r\nstr='$$ H=\\left[\\matrix{ H_{1} \u0026 H_{2}} \\right]  $$'; %valid\r\ntext(75,65,str,'Interpreter','latex','Fontsize',20);\r\n\r\nstr='$$ ReLU(H)=Y  $$'; %valid\r\ntext(75,58,str,'Interpreter','latex','Fontsize',20);\r\n\r\nstr='$$ Y=\\left[\\matrix{ Y_{1} \u0026 Y_{2}} \\right]  $$'; %valid\r\ntext(75,51,str,'Interpreter','latex','Fontsize',20);\r\n\r\nstr='$$ X*WH=H  $$'; %valid\r\ntext(60,5,str,'Interpreter','latex','Fontsize',20);\r\n\r\nstr='$$ Y*WP=P  $$'; %valid\r\ntext(60,0,str,'Interpreter','latex','Fontsize',20);\r\n\r\nstr='$$ WP=\\left[\\matrix{ WP_{11}\\cr WP_{21} } \\right]  $$'; %valid\r\ntext(100,5,str,'Interpreter','latex','Fontsize',20);\r\n\r\n\r\n\r\nend % Perceptron \r\n%}\r\n","test_suite":"%%\r\nX=[1 2]; WH=[1 2;3 4];WP=[.5; -1];\r\nP=Calc_Perceptron(X,WH,WP);\r\nPexp=-6.5;\r\nvalid=isequal(P,Pexp);\r\nassert(valid)\r\n%%\r\nX=[3 1.5]; WH=[1 -3;3 4];WP=[1; 2];\r\nP=Calc_Perceptron(X,WH,WP);\r\nPexp=7.5;\r\nvalid=isequal(P,Pexp);\r\nassert(valid)\r\n%%\r\nX=[-.5 .5]; WH=[4 2;1 4];WP=[.1; .4];\r\nP=Calc_Perceptron(X,WH,WP);\r\nPexp=0.4;\r\nvalid=isequal(P,Pexp);\r\nassert(valid)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":3097,"edited_by":3097,"edited_at":"2023-08-20T22:48:06.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-08-20T22:16:25.000Z","updated_at":"2023-08-20T22:48:07.000Z","published_at":"2023-08-20T22:48:07.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis challenge is to calculate the Neural Net Perceptron value,P, given X, WH, and WP using ReLU on the hidden layer. This example is for two inputs, two hidden nodes, and a single output. No offset terms are applied.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"864\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"1228\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe function template includes the code to create this figure using Matlab 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"rela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Net: Calculate Bias Single Perceptron (AND/NAND/OR/NOR/XOR)","description":"This challenge is to calculate the Neural Net Bias Perceptron vector,P, given X, WH, and WP using ReLU on the hidden layer. Test Cases will be all two input conditions for functions  XOR, AND, NAND, OR, and NOR.\r\nSince X wll be a 4x3 matrix the output P will be a 4x1 vector with values 0 or 1.\r\n \r\nThe function template includes the code to create this figure using Matlab Latex","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 664.65px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 332.325px; transform-origin: 407px 332.325px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 374px 8px; transform-origin: 374px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis challenge is to calculate the Neural Net Bias Perceptron vector,P, given X, WH, and WP using ReLU on the hidden layer. Test Cases will be all two input conditions for functions  XOR, AND, NAND, OR, and NOR.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 243.5px 8px; transform-origin: 243.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSince X wll be a 4x3 matrix the output P will be a 4x1 vector with values 0 or 1.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 553.65px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 276.825px; text-align: left; transform-origin: 384px 276.825px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline\" 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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 250px 8px; transform-origin: 250px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe function template includes the code to create this figure using Matlab Latex\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function P=Calc_Single_Bias_Perceptron(X,WH,WP)\r\n%The P value in this case is a single value for each case\r\n%X will be four rows and three columns\r\n%No ReLU,Softmax, or Sigmoid applied to the output P\r\n  P=[0 0 0 0]';\r\nend\r\n\r\n%The figure was generated using Matlab and Latex\r\n%{\r\nfunction perceptron_bias\r\nfigure(1);clf;\r\nplot([0;140;140;0;0],[-5;-5;100;100;-5],'k','linewidth',2);hold on\r\nxticks([]);yticks([]); %Ticks/Labels off\r\n\r\naxis equal;\r\naxis tight\r\n\r\nr = 10;\r\nphi = 0:0.01:2*pi;\r\ncxA = r*cos(phi);\r\ncyA = r*sin(phi);\r\n\r\nrxA=[0 2*r 2*r   0 0]';\r\nryA=[0   0 2*r 2*r 0]';\r\n\r\ntext(1,95,'Single Bias Perceptron','Fontsize',20);\r\n\r\npatch(cxA+10,cyA+80,'y');text(10-2,80,'X_{1}','Fontsize',20);\r\npatch(cxA+10,cyA+20,'y');text(10-2,20,'X_{2}','Fontsize',20);\r\n\r\npatch(cxA+80,cyA+80,'y');text(80-6,94,'H_{1}','Fontsize',20);text(80-8,80,'\\Sigma','Fontsize',30);\r\npatch(cxA+80,cyA+20,'y');text(80-6,34,'H_{2}','Fontsize',20);text(80-8,20,'\\Sigma','Fontsize',30);\r\n\r\npatch(cxA+130,cyA+50,'y');text(130-2,50,'P','Fontsize',20);\r\n\r\npatch(rxA+80,ryA+70,'y');text(85,80,'ReLU','Fontsize',20);text(100,92,'Y_{1}','Fontsize',20);\r\npatch(rxA+80,ryA+10,'y');text(85,20,'ReLU','Fontsize',20);text(100,32,'Y_{2}','Fontsize',20);\r\n\r\nquiver(20,20,55,0,'k','LineWidth',3.5); % line arrowhead x,y,dx,dy,  VectorLine draw\r\nquiver(20,80,55,0,'k','LineWidth',3.5); % line arrowhead x,y,dx,dy,  VectorLine draw\r\nquiver(20,20,58.5,58.5,'k','LineWidth',3.5); % line arrowhead x,y,dx,dy,  VectorLine draw\r\nquiver(20,80,58.5,-58.5,'k','LineWidth',3.5); % line arrowhead x,y,dx,dy,  VectorLine draw\r\n\r\nquiver(100,20,25,25,'k','LineWidth',3.5,'MaxHeadSize',.5); % line arrowhead x,y,dx,dy,  VectorLine draw\r\nquiver(100,80,25,-25,'k','LineWidth',3.5,'MaxHeadSize',.5); % line arrowhead x,y,dx,dy,  VectorLine draw\r\n%quiver(100,80,25,-25,'k','LineWidth',3.5,'Color','r'); % line arrowhead x,y,dx,dy,  VectorLine draw\r\nquiver(53,93,20,-10,'k','LineWidth',3.5,'MaxHeadSize',.6); text(53-8,92,'bH_{31}','Fontsize',20);\r\nquiver(60,5,13,10,'k','LineWidth',3.5,'MaxHeadSize',.7); text(60-6,4,'bH_{32}','Fontsize',20);\r\nquiver(130,26,0,15,'k','LineWidth',3.5,'MaxHeadSize',.8); text(130-6,25,'bP_{31}','Fontsize',20);\r\n\r\n\r\ntext(30,85,'WH_{11}','Fontsize',20);\r\ntext(20,65,'WH_{12}','Fontsize',20);\r\ntext(40,25,'WH_{22}','Fontsize',20);\r\ntext(20,38,'WH_{21}','Fontsize',20);\r\n\r\ntext(110,73,'WP_{11}','Fontsize',20);\r\ntext(107,23,'WP_{21}','Fontsize',20);\r\n\r\nstr='$$ X=\\left[\\matrix{ X_{1} \u0026 X_{2} \u0026 1} \\right]  $$'; %valid\r\ntext(1,50,str,'Interpreter','latex','Fontsize',20);\r\n\r\nstr='$$ WH=\\left[\\matrix{ WH_{11} \u0026 WH_{12} \u0026 0 \\cr WH_{21} \u0026 WH_{22} \u0026 0 \\cr bH_{31} \u0026 bH_{32} \u0026 1 } \\right]  $$'; %valid\r\ntext(1,3,str,'Interpreter','latex','Fontsize',20);\r\n\r\nstr='$$ H=\\left[\\matrix{ H_{1} \u0026 H_{2} \u0026 1} \\right]  $$'; %valid\r\ntext(75,65,str,'Interpreter','latex','Fontsize',20);\r\n\r\nstr='$$ ReLU(H)=Y  $$'; %valid\r\ntext(75,58,str,'Interpreter','latex','Fontsize',20);\r\n\r\nstr='$$ Y=\\left[\\matrix{ Y_{1} \u0026 Y_{2} \u0026 1} \\right]  $$'; %valid\r\ntext(75,51,str,'Interpreter','latex','Fontsize',20);\r\n\r\nstr='$$ X*WH=H  $$'; %valid\r\ntext(80,5,str,'Interpreter','latex','Fontsize',20);\r\n\r\nstr='$$ Y*WP=P  $$'; %valid\r\ntext(80,0,str,'Interpreter','latex','Fontsize',20);\r\n\r\nstr='$$ WP=\\left[\\matrix{ WP_{11}\\cr WP_{21} \\cr bP_{31} } \\right]  $$'; %valid\r\ntext(110,5,str,'Interpreter','latex','Fontsize',20);\r\n\r\nend %perceptron_bias\r\n\r\n%}","test_suite":"%%\r\n%XOR\r\nX=[0 0 1;0 1 1;1 0 1;1 1 1]; %All four cases  P will have results from all four input sets\r\nWH=[1 1 0;1 1 0;0 -1 1];\r\nWP=[1;-2;0];\r\n\r\nP=Calc_Single_Bias_Perceptron(X,WH,WP)\r\nvalid=isequal(P,[0 1 1 0]')\r\nassert(valid)\r\n%%\r\n%AND\r\nX=[0 0 1;0 1 1;1 0 1;1 1 1]; %All four cases  P will have results from all four input sets\r\nWH=[1 1 0;1 1 0;-1 -1 1];\r\nWP=[.5;.5;0];\r\n\r\nP=Calc_Single_Bias_Perceptron(X,WH,WP)\r\nvalid=isequal(P,[0 0 0 1]')\r\nassert(valid)\r\n%%\r\n%NAND\r\nX=[0 0 1;0 1 1;1 0 1;1 1 1]; %All four cases  P will have results from all four input sets\r\nWH=[1 1 0;1 1 0;-1 -1 1];\r\nWP=[-.5;-.5;1];\r\n\r\nP=Calc_Single_Bias_Perceptron(X,WH,WP)\r\nvalid=isequal(P,[1 1 1 0]')\r\nassert(valid)\r\n%%\r\n%OR\r\nX=[0 0 1;0 1 1;1 0 1;1 1 1]; %All four cases  P will have results from all four input sets\r\nWH=[1 -.5 0;-.5 1 0;0 0 1];\r\nWP=[1;1;0];\r\n\r\nP=Calc_Single_Bias_Perceptron(X,WH,WP)\r\nvalid=isequal(P,[0 1 1 1]')\r\nassert(valid)\r\n%%\r\n%NOR\r\nX=[0 0 1;0 1 1;1 0 1;1 1 1]; %All four cases  P will have results from all four input sets\r\nWH=[-1 -1 0;-1 -1 0;0.5 .5 1];\r\nWP=[1;1;0];\r\n\r\nP=Calc_Single_Bias_Perceptron(X,WH,WP)\r\nvalid=isequal(P,[1 0 0 0]')\r\nassert(valid)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":3097,"edited_by":3097,"edited_at":"2023-08-21T05:50:47.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-08-21T04:23:55.000Z","updated_at":"2023-08-21T05:50:47.000Z","published_at":"2023-08-21T05:50:47.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis challenge is to calculate the Neural Net Bias Perceptron vector,P, given X, WH, and WP using ReLU on the hidden layer. Test Cases will be all two input conditions for functions  XOR, AND, NAND, OR, and NOR.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSince X wll be a 4x3 matrix the output P will be a 4x1 vector with values 0 or 1.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"930\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"1303\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe function template includes the code to create this figure using Matlab 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.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Net: Back Propagation of Quad Output with Bias, ReLU","description":"This challenge is to return the WH_delta and WP_delta, given X, WH, WP, EPY using ReLU on the hidden layer and Softmax on the output layer. Test Cases will accumulate dWP and dWH to solve neural nets for Counter, Subtractor,Mux. Test Cases will have four output cases. ReLU performs well on multiple output cases.\r\n[dWP,dWH]=Neural_Back_Propagation_ReLU(X,WH,WP,EPY)\r\n \r\n \r\nThe matlab Latex code for making the Back Propagation chart included in template.\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 1230px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 615px; transform-origin: 407px 615px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 364px 8px; transform-origin: 364px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis challenge is to return the WH_delta and WP_delta, given X, WH, WP, EPY using ReLU on the hidden layer and Softmax on the output layer. Test Cases will accumulate dWP and dWH to solve neural nets for Counter, Subtractor,Mux. Test Cases will have four output cases. ReLU performs well on multiple output cases.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 192.5px 8px; transform-origin: 192.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e[dWP,dWH]=Neural_Back_Propagation_ReLU(X,WH,WP,EPY)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 529.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 264.75px; text-align: left; transform-origin: 384px 264.75px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline;width: 875px;height: 524px\" 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\" data-image-state=\"image-loaded\" width=\"875\" height=\"524\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 262px 8px; transform-origin: 262px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe matlab Latex code for making the Back Propagation chart included in template.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [dWP,dWH]=Neural_Back_Propagation_ReLU(X,WH,WP,EPY)\r\n%Comments/structure credit Christian Schröder\r\n% X will be single case [x1 x2 1]\r\n\r\n%Removing the comments below should make a working function\r\n\r\n  % Learning rate\r\n  %LR=1;\r\n  \r\n  % Forward pass\r\n  %H=X*WH; \r\n  % %HY=1./(1+exp(-H)); %[HY1 HY2 1]  Sigmoid\r\n  % %HY(:,end)=1; %Sigmoid\r\n  %HY=max(0,H); \r\n  \r\n  % Output layer, softmax activation function\r\n  %P=HY*WP;  %\r\n  %PY=exp(P)./sum(exp(P),2); %Softmax [PY1 PY2]\r\n  \r\n  % Backward pass\r\n  % Error\r\n  %ErrPY=EPY-PY; \r\n  \r\n  % Approx. changes for output layer\r\n  %dPY=PY.*(1-PY).*ErrPY;\r\n  %dWP=LR*HY'.*dPY;\r\n  \r\n  % Approx. changes for hidden layer\r\n  %dHY=HY.*(1-HY).*sum(WP.*dPY,2)';\r\n  %dWH=LR*X'.*dHY;\r\n  \r\nend % Neural_Back_Propagation_ReLU\r\n\r\n%Code to make the Back Prop chart\r\n%{\r\nfunction Back_Propagation_ReLU_Soft\r\n%Quad output classifier\r\n%Softmax y=exp(x)./sum(exp(x),2)\r\n\r\n% Back Propagation ReLU\r\n% https://www.youtube.com/watch?v=tUoUdOdTkRw\r\n% #1 Solved Example Back Propagation Algorithm Multi-Layer Perceptron Network by Dr. Mahesh Huddar\r\n% \r\n%                                                 Input     Expected Output\r\n%                                                 Cases         0 1 Logic Values/Classes\r\n% WH [0.2 -0.9 0  WP [ 9.5 -1.9 6.0 0.5  X [0 0 1  EPY [0 1 0 0  Case 1\r\n%     0.8 -0.1 0      -0.5  8.0 7.2 0.2     0 1 1       0 0 1 0  C2\r\n%     0.3  1.4 1]      3.5  6.4 3.6 9.6]    1 0 1       0 0 1 0  C3\r\n%                                           1 1 1]      1 0 0 0] C4\r\n% WH [WH11 WH12 0   WP [WP11 WP12 WP13 WP14\r\n%     WH21 WH22 0       WP21 WP22 WP23 WP24\r\n%     bH31 bH32 1]      bP31 bP32 bP33 bP34]\r\n% All four cases. Rows represent case(C)\r\n% HY =ReLU(X*WH)      PY = Softmax(HY*WP)                     ErrPY = EPY-PY \r\n% [0.3 1.4 1       [0.0000    0.8243    0.1750    0.0008    [-0.0000    0.1757   -0.1750   -0.0008\r\n%  1.1 1.3 1        0.0019    0.0078    0.9903    0.0001     -0.0019   -0.0078    0.0097   -0.0001\r\n%  0.5 0.5 1        0.0469    0.2000    0.4234    0.3297     -0.0469   -0.2000   -0.4234    0.6703\r\n%  1.3 0.4 1]       0.7942    0.0002    0.2018    0.0039]     0.2058   -0.0002   -0.2018   -0.0039]\r\n% \r\n% \r\n% d_j=o_j(1-o_j)(Truth_j-o_j) if j is an output layer\r\n% dPY=PY.*(1-PY).*ErrPY  thus dPY =[dPY_1 dPY_2]; C=case (rows 1 thru 4)\r\n% dPY=PY(1-PY)*ErrPY  [PY_C1*(1-PY_C1)*ErrPY_C1 PY_C2*(1-PY_C2)*ErrPY_C2]\r\n% dPY=PY.*(1-PY).*ErrPY   %Matlab per case [dPY1 dPY2]\r\n% -0.0000    0.0255   -0.0253   -0.0000  % All four cases \r\n% -0.0358   -0.5963    0.9413   -0.0001  1e-4 \r\n% -0.0021   -0.0320   -0.1034    0.1481\r\n%  0.0336   -0.0000   -0.0325   -0.0000\r\n%\r\n% gtw_ij=n*o_i*d_j, gtWP where o_i is Output(HY) and d_j is a delta(dPY)  \r\n% dWP=n*HY'.*dPY  %Matlab for a single case, n is learning rate set to 1 \r\n% n*[HY1;HY2;1].*[dPY1 dPY2]=n*[dPY1*HY1 dPY2*HY1  =gtWP \r\n%                               dPY1*HY2 dPY2*HY2  \r\n%                               dPY1*1   dPY2*1  ] \r\n% The WP values affecting P1/PY1 adjusted by dPY1. gtw=dWP\r\n% Cycle over all four cases\r\n% dWP=dWP+n*HY'.*dPY;  %Matlab combining single cases\r\n% [0 .0076 -.0076 0  [0 0 0 0   [-.0010 -.0160 -.0517 .0741  [.0437 0 -.0423 0\r\n%  0 .0356 -.0354 0   0 0 0 0    -.0010 -.0160 -.0517 .0741   .0135 0 -.0130 0\r\n%  0 .0255 -.0253 0]+ 0 0 0 0]+  -.0021 -.0320 -.1034 .1481]+ .0336 0 -.0325 0]\r\n% \r\n% d_j=o_j(1-o_j)Sigma_k(WP_jk*d_k) if j is a hidden layer, d_k is from next layer\r\n%   next layer WP and d terms combined and scaled by Hidden layer Output function\r\n%   Generate a dHY to apply against WH terms\r\n% dHY=HY.*(1-HY).*sum(WP.*dPY,2)'\r\n% dHY=HY(1-HY)*SumdW  \r\n% [HY_C1*(1-HY_C1)*SumdW_C1 HY_C2*(1-HY_C2)*SumdW_C2 HY_C3*(1-HY_C3)*SumdW_C3] where\r\n% SumdW_C1 = WP_11*dPY1+WP_12*dPY2   \r\n% SumdW_C2 = WP_21*dPY1+WP_22*dPY2   \r\n% SumdW_C3 = WP_31*dPY1+WP_32*dPY2 since HY_C3=1 this term is unused\r\n% dHY=HY.*(1-HY).*sum(WP.*dPY,2)'  % Matlab per case\r\n% dHY = [-.0420  -.0122 0  (9.5*0-1.9*.0255+6*-.0253+.5*0)=-.200 SumdW_11\r\n%                           (-.5*0+8*.0255+7.2*-.0253+.2*0)=.0218 SumdW_12\r\n%        -.0000 -0.0000 0\r\n%        -.1263 -0.2424 0\r\n%        -.0486  0.0602 0]\r\n%  -0.0420   -0.0122         0\r\n%  -0.7085   -0.7898         0  *1e-4\r\n%  -0.1263   -0.2424         0\r\n%  -0.0486   -0.0602         0\r\n% \r\n% \r\n% n*xc'.*dHy  % xc is a single row of x\r\n% dWH=n*XC'.*dHY   %Matlab single case\r\n% n*[XC1;XC2;1].*[dHY1 dHY2 dHY3]=\r\n% n*[dHY1*XC1 dHY2*XC1 dHY3*XC1  =gtWH \r\n%    dHY1*XC2 dHY2*XC2 dHY3*XC2\r\n%    dHY1*1   dHY2*1   dHY3*1 ]  since dHY3=0 end col is 0\r\n% dWH=dWH+n*XC'.*dHY; % matlab for accumulating cases\r\n% The WH values affecting H1/HY1 adjusted by dHY1. gtw=dWH\r\n% The WH values affecting H2/HY2 adjusted by dHY2\r\n% dWH=\r\n%  [ 0         0   0       [-.1263 -.2424 0  [-.0486   -.0602 0\r\n%    0         0   0           0       0  0   -.0486   -.0602 0\r\n%   -.042   -0.0122 0]+[0]+ -.1263 -.2424 0]+ -.0486   -.0602 0]\r\n\r\nf=figure(1);clf;\r\nf.Position=[1935 122 1459 873]; % Dual Monitor setting\r\n\r\nplot([0;160;160;0;0],[-5;-5;100;100;-5],'k','linewidth',2);hold on\r\nxticks([]);yticks([]); %Ticks/Labels off\r\n\r\naxis equal;\r\naxis tight\r\n\r\n% Back Propagation ReLU\r\n% https://www.youtube.com/watch?v=tUoUdOdTkRw\r\n% #1 Solved Example Back Propagation Algorithm Multi-Layer Perceptron Network by Dr. Mahesh Huddar\r\n\r\ntext(1,98,'Back Propagation ReLU','Fontsize',16);\r\ntext(37,98,'based upon #1 Solved Example Back Propagation Algorithm Multi-Layer Perceptron Network by Dr. Mahesh Huddar','Fontsize',12);\r\ntext(34,95,'https://www.youtube.com/watch?v=tUoUdOdTkRw ','Fontsize',12);\r\n\r\n% WH [0.2 -0.9 0  WP [ 9.5 -1.9 6.0 0.5  X [0 0 1  EPY [0 1 0 0  Case 1\r\n%     0.8 -0.1 0      -0.5  8.0 7.2 0.2     0 1 1       0 0 1 0  C2\r\n%     0.3  1.4 1]      3.5  6.4 3.6 9.6]    1 0 1       0 0 1 0  C3\r\n%                                           1 1 1]      1 0 0 0] C4\r\ntext(5,95,'WH','Fontsize',12);\r\nstr='$$ \\left[\\matrix{ .2 \u0026 -.9 \u0026 0 \\cr .8 \u0026 -.1 \u0026 0 \\cr .3 \u0026 1.4 \u0026 1 } \\right]  $$'; \r\ntext(1,89,str,'Interpreter','latex','Fontsize',11);\r\n\r\ntext(21,95,'WP','Fontsize',12);\r\nstr='$$ \\left[\\matrix{ 9.5 \u0026 -1.9 \u0026 6.0 \u0026 0.5 \\cr -.5 \u0026 8.0 \u0026 7.2 \u00260.2 \\cr 3.5 \u0026 6.4 \u0026 3.6 \u0026 9.6 } \\right]  $$'; \r\ntext(18,89,str,'Interpreter','latex','Fontsize',11);\r\n\r\nstr='$$ X=\\left[\\matrix{ 0 \u0026 0 \u0026 1 \\cr 0 \u0026 1 \u00261 \\cr 1 \u0026 0 \u0026 1 \\cr 1 \u0026 1 \u0026 1 } \\right]  $$'; \r\ntext(42,88,str,'Interpreter','latex','Fontsize',11);\r\n\r\nstr='$$ EPY=\\left[\\matrix{ 0\u00261\u00260\u00260 \\cr 0\u00260\u00261\u00260 \\cr 0\u00260\u00260\u00261 \\cr 1\u00260\u00260\u00260 } \\right]  $$'; \r\ntext(58,88,str,'Interpreter','latex','Fontsize',11);\r\n\r\n% WH [WH11 WH12 0   WP [WP11 WP12 WP13 WP14\r\n%     WH21 WH22 0       WP21 WP22 WP23 WP24\r\n%     bH31 bH32 1]      bP31 bP32 bP33 bP34]\r\n% str='$$ WH=\\left[\\matrix{ WH_{11} \u0026 WH_{12} \u0026 0 \\cr WH_{21} \u0026 WH_{22} \u0026 0 \\cr bH_{31} \u0026 bH_{32} \u0026 1 } \\right]  $$'; \r\n% text(1,80,str,'Interpreter','latex','Fontsize',12);\r\ntext(93,95,'WH','Fontsize',12);\r\nstr='$$ \\left[\\matrix{ WH_{11} \u0026 WH_{12} \u0026 0 \\cr WH_{21} \u0026 WH_{22} \u0026 0 \\cr bH_{31} \u0026 bH_{32} \u0026 1 } \\right]  $$'; \r\ntext(83,89,str,'Interpreter','latex','Fontsize',12);\r\n\r\nstr='$$ WP=\\left[\\matrix{ WP_{11} \u0026 WP_{12} \u0026 WP_{13} \u0026 WP_{14} \\cr WP_{21} \u0026 WP_{22} \u0026 WP_{23} \u0026 WP_{24} \\cr bP_{31} \u0026 bP_{32} \u0026 bP_{33} \u0026 bP_{34} } \\right]  $$'; \r\ntext(107,89,str,'Interpreter','latex','Fontsize',12);\r\n\r\n% All four cases. Rows represent case(C)\r\n% HY =ReLU(X*WH)      PY = Softmax(HY*WP)                     ErrPY = EPY-PY \r\n% [0.3 1.4 1       [0.0000    0.8243    0.1750    0.0008    [-0.0000    0.1757   -0.1750   -0.0008\r\n%  1.1 1.3 1        0.0019    0.0078    0.9903    0.0001     -0.0019   -0.0078    0.0097   -0.0001\r\n%  0.5 0.5 1        0.0469    0.2000    0.4234    0.3297     -0.0469   -0.2000   -0.4234    0.6703\r\n%  1.3 0.4 1]       0.7942    0.0002    0.2018    0.0039]     0.2058   -0.0002   -0.2018   -0.0039]\r\ntext(1,83,'All four cases. Rows represent case(C)','Fontsize',12);\r\ntext(0.5,80,'HY =ReLU(X*WH)        PY = Softmax(HY*WP)                ErrPY = EPY-PY','Fontsize',10);\r\nstr='$$ \\left[\\matrix{ 0.3 \u0026 1.4 \u0026 1 \\cr 1.1 \u0026 1.3 \u0026 1 \\cr 0.5 \u0026 0.5 \u0026 1 \\cr 1.3 \u0026 0.4 \u0026 1 } \\right]  $$'; \r\ntext(0,73,str,'Interpreter','latex','Fontsize',10);\r\nstr='$$ \\left[\\matrix{ .0000 \u0026 .8243 \u0026 .1750 \u0026 .0008 \\cr .0019 \u0026 .0078 \u0026 .9903 \u0026 .0001 \\cr .0469 \u0026 .2000 \u0026 .4234 \u0026 .3297 \\cr .7942 \u0026 .0002 \u0026 .2018 \u0026 .0039 } \\right]  $$'; \r\ntext(14,73,str,'Interpreter','latex','Fontsize',11);\r\nstr='$$ \\left[\\matrix{ -.0000 \u0026 .1757 \u0026 -.1750 \u0026 -.0008  \\cr -.0019  \u0026 -.0078 \u0026 .0097 \u0026 -.0001 \\cr -.0469 \u0026 -.2000 \u0026 -.4234 \u0026 0.6703 \\cr .2058 \u0026 -.0002 \u0026 -.2018 \u0026 -.0039 } \\right]  $$'; \r\ntext(43,73,str,'Interpreter','latex','Fontsize',11);\r\n\r\n% d_j=o_j(1-o_j)(Truth_j-o_j) if j is an output layer\r\n% dPY=PY.*(1-PY).*ErrPY  thus dPY =[dPY_1 dPY_2]; C=case (rows 1 thru 4)\r\n% dPY=PY(1-PY)*ErrPY  [PY_C1*(1-PY_C1)*ErrPY_C1 ...  PY_C4*(1-PY_C4)*ErrPY_C4]\r\n% dPY=PY.*(1-PY).*ErrPY   %Matlab per case [dPY1 dPY2]\r\n\r\n% -0.0000    0.0255   -0.0253   -0.0000  % All four cases \r\n% -0.0358   -0.5963    0.9413   -0.0001  1e-4 \r\n% -0.0021   -0.0320   -0.1034    0.1481\r\n%  0.0336   -0.0000   -0.0325   -0.0000\r\n\r\ntext(1,65,'\\delta_{j}=o_{j}(1-o_{j})(Truth_{j}-o_{j}) if j is an Output layer','Fontsize',14);\r\ntext(1,60,'\\deltaPY=PY*(1-PY)*ErrPY  thus \\deltaPY =[\\deltaPY_{1}   \\deltaPY_{2}   \\deltaPY_{3}   \\deltaPY_{4}]','Fontsize',14);\r\ntext(1,56,'\\deltaPY=[ PY_{C1}*(1-PY_{C1})*ErrPY_{C1} ... PY_{C4}*(1-PY_{C4})*ErrPY_{C4} ]','Fontsize',14);\r\ntext(1,52,'dPY=PY.*(1-PY).*ErrPY','Fontsize',14,'Color','b');\r\ntext(32,52,'%Matlab per case [dPY1 dPY2 dPY3 dPY4]','Fontsize',12,'Color','b');\r\ntext(43,49,'% All four cases','Fontsize',12);\r\ntext(43,45.7,' [-.0358 -.5963 .9413 -.0001]*1E-4','Fontsize',12);\r\nstr='$$ \\left[\\matrix{ -.0000 \u0026 0.0255 \u0026 -.0253 \u0026 -.0000 \\cr -.0000 \u0026 -.0000 \u0026 0.0000 \u0026 -.0000 \\cr -.0021 \u0026 -.0320 \u0026 -.1034 \u0026 0.1481 \\cr 0.0336 \u0026 -.0000 \u0026 -.0325 \u0026 -.0000 } \\right]  $$'; \r\ntext(3,44,str,'Interpreter','latex','Fontsize',12);\r\n\r\n% gtw_ij=n*o_i*d_j, gtWP where o_i is Output(HY) and d_j is a delta(dPY)  \r\n% dWP=n*HY'.*dPY  %Matlab for a single case, n is learning rate set to 1 \r\n% n*[HY1;HY2;1].*[dPY1 dPY2]=n*[dPY1*HY1 dPY2*HY1  =gtWP \r\n%                               dPY1*HY2 dPY2*HY2  \r\n%                               dPY1*1   dPY2*1  ] \r\n% The WP values affecting P1/PY1 adjusted by dPY1. gtw=dWP\r\n% Cycle over all four cases\r\n% dWP=dWP+n*HY'.*dPY;  %Matlab combining single cases\r\n\r\n% [0 .0076 -.0076 0  [0 0 0 0   [-.0010 -.0160 -.0517 .0741  [.0437 0 -.0423 0\r\n%  0 .0356 -.0354 0   0 0 0 0    -.0010 -.0160 -.0517 .0741   .0135 0 -.0130 0\r\n%  0 .0255 -.0253 0]+ 0 0 0 0]+  -.0021 -.0320 -.1034 .1481]+ .0336 0 -.0325 0]\r\n%case1\r\n%    -.0000    .0076   -.0076   -.0000\r\n%    -.0000    .0356   -.0354   -.0000\r\n%    -.0000    .0255   -.0253   -.0000\r\n%\r\n%case2    1.0e-03 *\r\n%    -0.0039   -0.0656    0.1035   -0.0000\r\n%    -0.0046   -0.0775    0.1224   -0.0000\r\n%    -0.0036   -0.0596    0.0941   -0.0000\r\n%case3\r\n%    -.0010 -.0160 -.0517 .0741\r\n%    -.0010 -.0160 -.0517 .0741\r\n%    -.0021 -.0320 -.1034 .1481\r\n%case4\r\n%     .0437 -.0 -.0423 -.0\r\n%     .0135 -.0 -.0130 -.0\r\n%     .0336 -.0 -.0325 -.0\r\n\r\ntext(1,36,'\\DeltaW_{ij}=n*o_{i}*\\delta_{j}, \\DeltaWP where o_{i} is Output(HY) and \\delta_{j} is a delta(dPY) ','Fontsize',14);\r\ntext(1,32,'dWP=n*HY''.*dPY  %Matlab for a single case, n=1 learning rate','Fontsize',14,'Color','b');\r\ntext(1,28,'n*[HY1;HY2;1].*[dPY1 dPY2 dPY3 dPY4]=','Fontsize',14);\r\nstr='$$ n*\\left[\\matrix{ dPY1*HY1 \u0026 dPY2*HY1 \u0026 dPY3*HY1 \u0026 dPY4*HY1 \\cr dPY1*HY2 \u0026 dPY2*HY2 \u0026 dPY3*HY2 \u0026 dPY4*HY2 \\cr dPY1*1 \u0026 dPY2*1 \u0026 dPY3*1 \u0026 dPY4*1 } \\right]  $$'; \r\ntext(1,22,str,'Interpreter','latex','Fontsize',12);text(70,25,'=\\DeltaWP','Fontsize',14);\r\ntext(1,15,'The WP values affecting P1/PY1 adjusted by dPY1.  \\DeltaW=dWP','Fontsize',14);\r\n%text(1,15,'Cycle over all four cases','Fontsize',14);\r\ntext(1,11,'dWP=dWP+n*HY''.*dPY;  %Matlab combining single cases','Fontsize',14);\r\ntext(7,7,'Case1','Fontsize',13);text(36,7,'Case3','Fontsize',13);text(63,7,'Case4','Fontsize',13);\r\nstr='$$ \\left[\\matrix{ 0 \u0026 .0076 \u0026 -.0076 \u0026 0 \\cr 0 \u0026 .0356 \u0026 -.0354 \u0026 0 \\cr 0 \u0026 .0255 \u0026 -.0253 \u0026 0 } \\right]  $$'; \r\ntext(0,1,str,'Interpreter','latex','Fontsize',10);\r\nstr='$$ \\left[\\matrix{ 0 } \\right]  $$'; \r\ntext(22,1,str,'Interpreter','latex','Fontsize',10);\r\nstr='$$ \\left[\\matrix{ -.0010 \u0026 -.016 \u0026 -.0517 \u0026 .0741 \\cr -.0010 \u0026 -.016 \u0026 -.0157 \u0026 .0741 \\cr -.0021 \u0026 -.032 \u0026 -.1034 \u0026 .1481 } \\right]  $$'; \r\ntext(25,1,str,'Interpreter','latex','Fontsize',10);\r\nstr='$$ \\left[\\matrix{ .0437 \u0026 0 \u0026 -.0423 \u0026 0 \\cr .0135 \u0026 0 \u0026-.0130 \u0026 0 \\cr .0336 \u0026 0 \u0026 -.0325 \u0026 0 } \\right]  $$'; \r\ntext(56,1,str,'Interpreter','latex','Fontsize',10);\r\ntext(21,1,'+','Fontsize',13);text(24.5,1,'+','Fontsize',13);text(55,1,'+','Fontsize',13);\r\n\r\n\r\n% d_j=o_j(1-o_j)Sigma_k(WP_jk*d_k) if j is a hidden layer, d_k is from next layer\r\n%   next layer WP and d terms combined and scaled by Hidden layer Output function\r\n%   Generate a dHY to apply against WH terms\r\n% dHY=HY(1-HY)*SumdW  \r\n% dHY=HY.*(1-HY).*sum(WP.*dPY,2)' % Matlab per case\r\n% [HY_C1*(1-HY_C1)*SumdW_C1 HY_C2*(1-HY_C2)*SumdW_C2 HY_C3*(1-HY_C3)*SumdW_C3] where\r\n% SumdW_C1 = WP_11*dPY1+WP_12*dPY2+WP_13*dPY3+WP_14*dPY4   \r\n% SumdW_C2 = WP_21*dPY1+WP_22*dPY2   \r\n% SumdW_C3 = WP_31*dPY1+WP_32*dPY2 since HY_C3=1 this term is unused\r\n% dHY = [-.0420  -.0122 0  (9.5*0-1.9*.0255+6*-.0253+.5*0)=-.200 SumdW_11\r\n%                           (-.5*0+8*.0255+7.2*-.0253+.2*0)=.0218 SumdW_12\r\n%        -.0000 -0.0000 0\r\n%        -.1263 -0.2424 0\r\n%        -.0486  0.0602 0]\r\n%  -0.0420   -0.0122         0\r\n%  -0.7085   -0.7898         0  *1e-4\r\n%  -0.1263   -0.2424         0\r\n%  -0.0486   -0.0602         0\r\n\r\n%\r\ntext(82,80,'\\delta_{j}=o_{j}(1-o_{j})\\Sigma_{k}W_{jk}*\\delta_{k} if j is a hidden layer, d_k is from next layer','Fontsize',14);\r\ntext(81,76,'next layer WP, dPY combined and scaled by Hidden layer Output function','Fontsize',12);\r\ntext(82,72,'\\deltaHY=HY(1-HY)*SumdW','Fontsize',14);\r\ntext(82,68,'dHY=HY.*(1-HY).*sum(WP.*dPY,2)''     %Matlab per case','Fontsize',14,'Color','b');\r\ntext(61,64,'[HY_{C1}*(1-HY_{C1})*SumdW_{C1}   HY_{C2}*(1-HY_{C2})*SumdW_{C2}   HY_{C3}*(1-HY_{C3})*SumdW_{C3}] where','Fontsize',12);\r\ntext(80,60,'SumdW_{C1} = WP_{11}*dPY1+WP_{12}*dPY2+WP_{13}*dPY3+WP_{14}*dPY4','Fontsize',12);\r\ntext(80,56,'SumdW_{C2} = WP_{21}*dPY1+WP_{22}*dPY2+WP_{23}*dPY3+WP_{24}*dPY4','Fontsize',12);\r\ntext(80,52.5,'SumdW_{C3} = 0 since HY_{c3}=1','Fontsize',12);\r\ntext(77,49,'dHY = [-.0420  -.0122 0  %(9.5*0-1.9*.0255+6*-.0253+.5*0)= -.2   SumdW_{11}','Fontsize',12);\r\ntext(103,45.5,'%(-.5*0+8*.0255+7.2*-.0253+.2*0)=.0218 SumdW_{12}','Fontsize',12);\r\ntext(103,42.5,'%dHY_{11}=0.3*(.7)*(-.2)= -0.042','Fontsize',12);\r\ntext(103,39.5,'%dHY_{12}=1.4*(-.4)*(.0218)= -0.0122','Fontsize',12);\r\ntext(85,46,'-.0000 -.0000 0','Fontsize',12);\r\ntext(85,43,'-.1263 -.2424 0','Fontsize',12);\r\ntext(85,40,'-.0486 -.0602 0]','Fontsize',12);\r\n\r\n% n*xc'.*dHy  % xc is a single row of x\r\n% dWH=n*XC'.*dHY   %Matlab single case\r\n% n*[XC1;XC2;1].*[dHY1 dHY2 dHY3]=\r\n% n*[dHY1*XC1 dHY2*XC1 dHY3*XC1  =gtWH \r\n%    dHY1*XC2 dHY2*XC2 dHY3*XC2\r\n%    dHY1*1   dHY2*1   dHY3*1 ]  since dHY3=0 end col is 0\r\n% dWH=dWH+n*XC'.*dHY; % matlab for accumulating cases\r\n% The WH values affecting H1/HY1 adjusted by dHY1. gtw=dWH\r\n% The WH values affecting H2/HY2 adjusted by dHY2\r\n% dWH=\r\n%  [ 0         0   0       [-.1263 -.2424 0  [-.0486   -.0602 0\r\n%    0         0   0           0       0  0   -.0486   -.0602 0\r\n%   -.042   -0.0122 0]+[0]+ -.1263 -.2424 0]+ -.0486   -.0602 0]\r\n\r\ntext(85,36,'dWH=n*XC''.*dHY  %Matlab for a single case, n=1','Fontsize',14,'Color','b');\r\ntext(85,32,'n*[XC1;XC2;1].*[dHY1 dHY2 dHY3]=n*','Fontsize',14);\r\nstr='$$ \\left[\\matrix{ dHY1*XC1 \u0026 dHY2*XC1 \u0026 0 \\cr dHY1*XC2 \u0026 dHY2*XC2 \u0026 0 \\cr dHY1*1 \u0026 dHY2*1 \u0026 0 } \\right]  $$'; \r\ntext(91,25,str,'Interpreter','latex','Fontsize',12);text(145,25,'=\\DeltaWH','Fontsize',14);\r\ntext(81,19,'The WH values affecting H1/HY1 adjusted by dHY1. \\DeltaW=dWH','Fontsize',14);\r\ntext(81,15,'The WH values affecting H2/HY2 adjusted by dHY2. \\DeltaW=dWH','Fontsize',14);\r\n%text(71,15,'Cycle over all four cases','Fontsize',14);\r\ntext(81,11,'dWH=dWH+n*XC''.*dHY;  %Matlab combining cases','Fontsize',14);\r\nstr='$$ \\left[\\matrix{ 0 \u0026 0 \u0026 0 \\cr 0 \u0026 0 \u0026 0 \\cr -.042 \u0026 -.0122 \u0026 0 } \\right]  $$'; \r\ntext(82,3,str,'Interpreter','latex','Fontsize',11);\r\nstr='$$ \\left[\\matrix{ 0 \u0026 0 \u0026 0 \\cr 0 \u0026 0 \u0026 0 \\cr 0 \u0026 0 \u0026 0 } \\right]  $$'; \r\ntext(103,3,str,'Interpreter','latex','Fontsize',11);\r\nstr='$$ \\left[\\matrix{ -.1263 \u0026 -.2424 \u0026 0 \\cr 0 \u0026 0 \u0026 0 \\cr -.1263 \u0026 -.2424 \u0026 0 } \\right]  $$'; \r\ntext(114,3,str,'Interpreter','latex','Fontsize',11);\r\nstr='$$ \\left[\\matrix{ -.0486 \u0026 -.0602 \u0026 0 \\cr -.0486 \u0026 -.0602 \u0026 0 \\cr -.0486 \u0026 -.0602 \u0026 0 } \\right]  $$'; \r\ntext(136,3,str,'Interpreter','latex','Fontsize',11);\r\ntext(102.25,3,'+','Fontsize',14);text(113.25,3,'+','Fontsize',14);text(135.5,3,'+','Fontsize',14);\r\n\r\n\r\nend %Back_Propagation_ReLU_Soft\r\n%}","test_suite":"%%\r\nX=[0 0 1; %[x1 x2 1]\r\n   0 1 1;\r\n   1 0 1;\r\n   1 1 1];\r\nEPY=[0 1 0 0; % 0 0 : 1 Counter\r\n     0 0 1 0; % 0 1 : 2\r\n     0 0 0 1; % 1 0 : 3\r\n     1 0 0 0] % 1 1 : 4\r\nfor attempt=1:5  % ReLU not always successful with rand WP WH, get 5 tries\r\n fprintf('Attempt:%i\\n',attempt);\r\nWP=rand(3,4)\r\nWH=[rand(3,2) [0 0 1]']\r\nztic=tic;\r\nfor epoch=1:1000\r\n dWP=WP*0;\r\n dWH=WH*0;\r\n for i=1:4\r\n  [dWPi,dWHi]=Neural_Back_Propagation_ReLU(X(i,:),WH,WP,EPY(i,:));\r\n  dWP=dWP+dWPi;\r\n  dWH=dWH+dWHi;\r\n end\r\n WP=WP+dWP;\r\n WH=WH+dWH;\r\nend % epoch\r\nfprintf('Processing Time: %.3f\\n',toc(ztic));\r\nWH\r\nWP\r\n\r\n  H=X*WH;\r\n  %HY=1./(1+exp(-H)); %[HY1 HY2 1]  .6803 .6637 1 Sigmoid\r\n  %HY(:,end)=1; %Sigmoid\r\n  HY=max(0,H); % ReLU\r\n  \r\n  P=HY*WP;  %\r\n  PY=exp(P)./sum(exp(P),2) %Softmax [PY1 PY2 PY3 PY4]\r\n\r\n  [~,Pexp]=max(EPY,[],2);\r\n  [~,Pclass]=max(PY,[],2);\r\n if isequal(Pexp,Pclass),break;end\r\nend\r\n\r\nvalid=isequal(Pexp,Pclass);\r\nassert(valid)\r\n\r\n%%\r\n%2 Bit Mux 00:0 01:1 10:2 11:3\r\nX=[0 0 1; %[x1 x2 1]\r\n   0 1 1;\r\n   1 0 1;\r\n   1 1 1];\r\nEPY=[1 0 0 0; % 0 0 : 1 2 Bit Mux\r\n     0 1 0 0; % 0 1 : 2\r\n     0 0 1 0; % 1 0 : 3\r\n     0 0 0 1] % 1 1 : 4\r\nfor attempt=1:5  % ReLU not always successful with rand WP WH, get 5 tries\r\n fprintf('Attempt:%i\\n',attempt);\r\nWP=rand(3,4)\r\nWH=[rand(3,2) [0 0 1]']\r\nztic=tic;\r\nfor epoch=1:1000\r\n dWP=WP*0;\r\n dWH=WH*0;\r\n for i=1:4\r\n  [dWPi,dWHi]=Neural_Back_Propagation_ReLU(X(i,:),WH,WP,EPY(i,:));\r\n  dWP=dWP+dWPi;\r\n  dWH=dWH+dWHi;\r\n end\r\n WP=WP+dWP;\r\n WH=WH+dWH;\r\nend % epoch\r\nfprintf('Processing Time: %.3f\\n',toc(ztic));\r\nWH\r\nWP\r\n\r\n  H=X*WH;\r\n  %HY=1./(1+exp(-H)); %[HY1 HY2 1]  .6803 .6637 1 Sigmoid\r\n  %HY(:,end)=1; %Sigmoid\r\n  HY=max(0,H); % ReLU\r\n  \r\n  P=HY*WP;  %\r\n  PY=exp(P)./sum(exp(P),2) %Softmax [PY1 PY2 PY3 PY4]\r\n\r\n  [~,Pexp]=max(EPY,[],2);\r\n  [~,Pclass]=max(PY,[],2);\r\n if isequal(Pexp,Pclass),break;end\r\nend\r\n\r\nvalid=isequal(Pexp,Pclass);\r\nassert(valid)\r\n%%\r\n%Subtractor  3-X  00:3 01:2 10:1 11:0\r\nX=[0 0 1; %[x1 x2 1]\r\n   0 1 1;\r\n   1 0 1;\r\n   1 1 1];\r\nEPY=[0 0 0 1; % 0 0 : 4 3-X, subtract\r\n     0 0 1 0; % 0 1 : 3\r\n     0 1 0 0; % 1 0 : 2\r\n     1 0 0 0] % 1 1 : 1\r\nfor attempt=1:5  % ReLU not always successful with rand WP WH, get 5 tries\r\n fprintf('Attempt:%i\\n',attempt);\r\nWP=rand(3,4)\r\nWH=[rand(3,2) [0 0 1]']\r\nztic=tic;\r\nfor epoch=1:1000\r\n dWP=WP*0;\r\n dWH=WH*0;\r\n for i=1:4\r\n  [dWPi,dWHi]=Neural_Back_Propagation_ReLU(X(i,:),WH,WP,EPY(i,:));\r\n  dWP=dWP+dWPi;\r\n  dWH=dWH+dWHi;\r\n end\r\n WP=WP+dWP;\r\n WH=WH+dWH;\r\nend % epoch\r\nfprintf('Processing Time: %.3f\\n',toc(ztic));\r\nWH\r\nWP\r\n\r\n  H=X*WH;\r\n  %HY=1./(1+exp(-H)); %[HY1 HY2 1]  .6803 .6637 1 Sigmoid\r\n  %HY(:,end)=1; %Sigmoid\r\n  HY=max(0,H); % ReLU\r\n  \r\n  P=HY*WP;  %\r\n  PY=exp(P)./sum(exp(P),2) %Softmax [PY1 PY2 PY3 PY4]\r\n\r\n  [~,Pexp]=max(EPY,[],2);\r\n  [~,Pclass]=max(PY,[],2);\r\n if isequal(Pexp,Pclass),break;end\r\nend\r\n\r\nvalid=isequal(Pexp,Pclass);\r\nassert(valid)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":3097,"edited_by":3097,"edited_at":"2023-08-27T02:57:17.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-08-27T02:09:44.000Z","updated_at":"2023-08-27T02:57:18.000Z","published_at":"2023-08-27T02:57:18.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis challenge is to return the WH_delta and WP_delta, given X, WH, WP, EPY using ReLU on the hidden layer and Softmax on the output layer. Test Cases will accumulate dWP and dWH to solve neural nets for Counter, Subtractor,Mux. Test Cases will have four output cases. ReLU performs well on multiple output cases.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e[dWP,dWH]=Neural_Back_Propagation_ReLU(X,WH,WP,EPY)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"524\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"875\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e 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Puzzle - 039","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 113px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 56.5px; transform-origin: 407px 56.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGive an example of a number i where i\u0026gt;1000 that satisfies the following conditions:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 53px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 26.5px; text-align: left; transform-origin: 384px 26.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" 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data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eand N does not have the digit \"\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\" in it but the sum of the digits of N is equal to 2^3 or \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e8\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y=puzzle_039(n)\r\n  y=3939;\r\nend","test_suite":"%%\r\nn=2;\r\ny = num2str(puzzle_039(n)^3);\r\nassert(all(unique(y)~=num2str(n)))\r\nassert(puzzle_039(n)\u003e1000)\r\naa=0;\r\nfor i=1:length(y)\r\n    aa=aa+str2num(y(i));\r\nend\r\nassert(aa==n^3)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":180632,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":33,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-02-05T21:13:41.000Z","updated_at":"2024-11-18T01:20:53.000Z","published_at":"2021-02-05T21:13:41.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGive an example of a number i where i\u0026gt;1000 that satisfies the following conditions:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"47\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"105\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eand N does not have the digit 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data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eand N does not have the digit \"\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e4\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\" in it but the sum of the digits of N is equal to 4^3 or \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e64\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y=puzzle_041(n)\r\n  y=4141;\r\nend","test_suite":"%%\r\nn=4;\r\ny = num2str(puzzle_041(n)^3);\r\nassert(all(unique(y)~=num2str(n)))\r\nassert(puzzle_041(n)\u003e1000)\r\naa=0;\r\nfor i=1:length(y)\r\n    aa=aa+str2num(y(i));\r\nend\r\nassert(aa==n^3)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":180632,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":31,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-02-05T21:21:28.000Z","updated_at":"2021-02-05T21:21:28.000Z","published_at":"2021-02-05T21:21:28.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGive an example of a number i where i\u0026gt;1000 that satisfies the following conditions:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"47\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"105\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eand N does not have the digit 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data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = puzzle_045(x)\r\n  y = [123 345 678];\r\nend","test_suite":"%%\r\na=puzzle_045();\r\nassert(length(a)\u003e=3)\r\nassert(length(unique(a))\u003e=3)\r\nassert(sum(a)==1301)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":180632,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":33,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-02-10T22:44:58.000Z","updated_at":"2021-02-10T22:44:58.000Z","published_at":"2021-02-10T22:44:58.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document 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et mise à l'échelle avec des complexes","description":"Ecrire une fonction Zr=scale_rot(A,phi,Z) qui permet une mise à l'échelle d'un facteur A et une rotation d'un angle phi (en rad) d'un polygone. Vous utiliserez les nombres complexes, on considérera que le polygone est représenté par un vecteur complexe Z dont la partie réélle réprésente les abscisses de chaque sommet et la partie imaginaire les ordonnées.\r\nPar exemple prenons le trangle défini par le trois points A(1,0) B(2,1) et C(3,0) il sera repésenté dans Matlab par\r\nX=[1 2 3 1]; Y=[0 1 0 0]; % le 4 eme point =1 er point sert à fermer le contour lorsque l'on trace) \r\nZ=X+1i*Y;\r\nsi on veut par exemple appliquer une rotation de pi et une réduction d'échelle par un facteur 1/2, on appliquera\r\nZr=scale_rot(1/2,pi,Z); \r\nqui nous donne le triangle Ar, Br,Cr sur la figure d'illustration\r\n\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 708px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 354px; transform-origin: 407px 354px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eEcrire une fonction Zr=scale_rot(A,phi,Z) qui permet une mise à l'échelle d'un facteur A et une rotation d'un angle phi (en rad) d'un polygone. Vous utiliserez les nombres complexes, on considérera que le polygone est représenté par un vecteur complexe Z dont la partie réélle réprésente les abscisses de chaque sommet et la partie imaginaire les ordonnées.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ePar exemple prenons le trangle défini par le trois points A(1,0) B(2,1) et C(3,0) il sera repésenté dans Matlab par\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eX=[1 2 3 1]; Y=[0 1 0 0]; % le 4 eme point =1 er point sert à fermer le contour lorsque l'on trace) \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eZ=X+1i*Y;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003esi on veut par exemple appliquer une rotation de pi et une réduction d'échelle par un facteur 1/2, on appliquera\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eZr=scale_rot(1/2,pi,Z); \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003equi nous donne le triangle Ar, Br,Cr sur la figure d'illustration\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 426px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 213px; text-align: left; transform-origin: 384px 213px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"560\" height=\"420\" style=\"vertical-align: baseline;width: 560px;height: 420px\" 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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function Zr=scale_rot(A,phi,Z)\r\n  \r\nend","test_suite":"%%\r\nX=[1 2 3 1]; Y=[0 1 0 0];\r\nZ=X+1i*Y;\r\nZr_correct = 0.5*Z*exp(1i*pi);\r\nassert(isequal(scale_rot(0.5,pi,Z),Zr_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":63915,"edited_by":63915,"edited_at":"2024-09-27T07:22:47.000Z","deleted_by":null,"deleted_at":null,"solvers_count":12,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-10-27T13:53:33.000Z","updated_at":"2024-09-27T07:22:48.000Z","published_at":"2023-10-27T13:53:33.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eEcrire une fonction Zr=scale_rot(A,phi,Z) qui permet une mise à l'échelle d'un facteur A et une rotation d'un angle phi (en rad) d'un polygone. Vous utiliserez les nombres complexes, on considérera que le polygone est représenté par un vecteur complexe Z dont la partie réélle réprésente les abscisses de chaque sommet et la partie imaginaire les ordonnées.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePar exemple prenons le trangle défini par le trois points A(1,0) B(2,1) et C(3,0) il sera repésenté dans Matlab par\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eX=[1 2 3 1]; Y=[0 1 0 0]; % le 4 eme point =1 er point sert à fermer le contour lorsque l'on trace) \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eZ=X+1i*Y;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003esi on veut par exemple appliquer une rotation de pi et une réduction d'échelle par un facteur 1/2, on appliquera\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eZr=scale_rot(1/2,pi,Z); \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003equi nous donne le triangle Ar, Br,Cr sur la figure d'illustration\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":59349,"title":"Determine ground distance from an aircraft to a DME station","description":"In aviation, distance measuring equipment (DME) uses radio signals to determine slant distance from an aircraft to a ground station. Given the altitude of an aircraft in feet (ft) and a DME readout in nautical miles (NM), determine the ground distance in nautical miles from the aircraft to the DME ground station. Assume that 1 NM = 6076 ft and round solutions to the nearest tenth.\r\nFor example, if an aircraft is at 10000 ft and the DME readout is 5 NM, then the ground distance is 4.7 NM.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440001px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 114px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 57px; transform-origin: 407px 57px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eIn aviation, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Distance_measuring_equipment\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003edistance measuring equipment (DME)\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e uses radio signals to determine \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eslant distance\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e from an aircraft to a ground station. Given the altitude of an aircraft in feet (ft) and a DME readout in nautical miles (NM), determine the ground distance in nautical miles from the aircraft to the DME ground station. Assume that 1 NM = 6076 ft and round solutions to the nearest tenth.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFor example, if an aircraft is at 10000 ft and the DME readout is 5 NM, then the ground distance is 4.7 NM.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function d = groundDistance(alt,DME)\r\n    d = [];\r\nend","test_suite":"%%\r\nalt = 18000;\r\nDME = 10;\r\nd_correct = 9.6;\r\nassert(isequal(groundDistance(alt,DME),d_correct))\r\n%%\r\nalt = 29000;\r\nDME = 45.2;\r\nd_correct = 44.9;\r\nassert(isequal(groundDistance(alt,DME),d_correct))\r\n%%\r\nalt = 0;\r\nDME = 1;\r\nd_correct = 1;\r\nassert(isequal(groundDistance(alt,DME),d_correct))\r\n%%\r\nalt = 30380;\r\nDME = 5;\r\nd_correct = 0;\r\nassert(isequal(groundDistance(alt,DME),d_correct))","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":48615,"edited_by":48615,"edited_at":"2023-12-07T22:54:26.000Z","deleted_by":null,"deleted_at":null,"solvers_count":19,"test_suite_updated_at":"2023-12-07T22:54:26.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2023-12-07T22:50:51.000Z","updated_at":"2024-11-18T23:14:53.000Z","published_at":"2023-12-07T22:54:26.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn aviation, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Distance_measuring_equipment\\\"\u003e\u003cw:r\u003e\u003cw:t\u003edistance measuring equipment (DME)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e uses radio signals to determine \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eslant distance\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e from an aircraft to a ground station. Given the altitude of an aircraft in feet (ft) and a DME readout in nautical miles (NM), determine the ground distance in nautical miles from the aircraft to the DME ground station. Assume that 1 NM = 6076 ft and round solutions to the nearest tenth.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, if an aircraft is at 10000 ft and the DME readout is 5 NM, then the ground distance is 4.7 NM.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":59409,"title":"Determine pressure altitude using field elevation and altimeter setting","description":"Given an airfield's elevation in feet (ft) and the current altimeter setting in inches of mercury (inHg), calculate the pressure altitude of the airfield. Use 29.92 inHg as standard pressure and round solutions to the nearest tens of feet.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440001px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 21px; transform-origin: 407px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGiven an airfield's elevation in feet (ft) and the current altimeter setting in inches of mercury (inHg), calculate the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Pressure_altitude#QNE\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003epressure altitude\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e of the airfield. Use 29.92 inHg as standard pressure and round solutions to the nearest tens of feet.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function a = pressureAlt(elevation,altSetting)\r\n  a = [];\r\nend","test_suite":"%%\r\nelevation = 4831;\r\naltSetting = 30.00;\r\na_correct = 4750;\r\nassert(isequal(pressureAlt(elevation,altSetting),a_correct))\r\n%%\r\nelevation = 1602;\r\naltSetting = 29.83;\r\na_correct = 1690;\r\nassert(isequal(pressureAlt(elevation,altSetting),a_correct))\r\n%%\r\nelevation = 0;\r\naltSetting = 29.92;\r\na_correct = 0;\r\nassert(isequal(pressureAlt(elevation,altSetting),a_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":48615,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":14,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-12-08T01:14:46.000Z","updated_at":"2023-12-08T01:14:46.000Z","published_at":"2023-12-08T01:14:46.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven an airfield's elevation in feet (ft) and the current altimeter setting in inches of mercury (inHg), calculate the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Pressure_altitude#QNE\\\"\u003e\u003cw:r\u003e\u003cw:t\u003epressure altitude\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e of the airfield. Use 29.92 inHg as standard pressure and round solutions to the nearest tens of feet.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":59546,"title":"Getting values from a vector","description":"This exercise is for finding the values that meet your criteria.\r\na = [-5 28 7 83 73];\r\nb = 23 ;\r\nc = (a \u003e b)\r\nThen :\r\nc = \r\n   0   1   0   1   1\r\nWhat we are looking for now is how to get the values :\r\ny =     \r\n    28    83    73\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 287.062px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 143.525px; transform-origin: 407px 143.531px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThis exercise is for finding the values that meet your criteria.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 61.3125px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 30.65px; transform-origin: 404px 30.6562px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.8px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.8px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.8px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.8px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2125px; text-wrap: nowrap; transform-origin: 404px 10.2188px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003ea = [-5 28 7 83 73];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.8px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.8px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.8px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.8px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2125px; text-wrap: nowrap; transform-origin: 404px 10.2188px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eb = 23 ;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.8px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.8px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.8px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.8px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2125px; text-wrap: nowrap; transform-origin: 404px 10.2188px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003ec = (a \u0026gt; b)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThen :\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 40.875px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 20.4375px; transform-origin: 404px 20.4375px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.8px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.8px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.8px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.8px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2125px; text-wrap: nowrap; transform-origin: 404px 10.2188px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003ec = \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.8px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.8px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.8px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.8px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2125px; text-wrap: nowrap; transform-origin: 404px 10.2188px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e   0   1   0   1   1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eWhat we are looking for now is how to get the values :\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 40.875px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 20.4375px; transform-origin: 404px 20.4375px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.8px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.8px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.8px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.8px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2125px; text-wrap: nowrap; transform-origin: 404px 10.2188px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003ey =     \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.8px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.8px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.8px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.8px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2125px; text-wrap: nowrap; transform-origin: 404px 10.2188px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    28    83    73\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = your_fcn_name(x)\r\n  \r\nend","test_suite":"%%\r\nx = [17 85 -20 99];\r\ny_correct = [85 99];\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n%%\r\nx = [-5 28 7 83 73];\r\ny_correct = [28 83 73];\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n%%\r\nx = [55 0 7 53];\r\ny_correct = [55 53];\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n%%\r\nx = [80 0 -90];\r\ny_correct = [80];\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n%%\r\nx = [10 14 -80 30 -95];\r\ny_correct = [30];\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n%%","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":4033021,"edited_by":4033021,"edited_at":"2024-01-10T06:33:06.000Z","deleted_by":null,"deleted_at":null,"solvers_count":34,"test_suite_updated_at":"2024-01-10T06:33:06.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2024-01-09T17:51:26.000Z","updated_at":"2024-11-18T01:17:46.000Z","published_at":"2024-01-09T18:04:51.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis exercise is for finding the values that meet your criteria.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[a = [-5 28 7 83 73];\\nb = 23 ;\\nc = (a \u003e b)]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThen :\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[c = \\n   0   1   0   1   1]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWhat we are looking for now is how to get the values :\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[y =     \\n    28    83    73]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":50524,"title":"Calculate the structural rank of a 2-by-4 matrix.","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 51px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 25.5px; transform-origin: 407px 25.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 10px; transform-origin: 404px 10px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003ex=[1 0 2 0 ;2 0 4 0]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; 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The challenge is to write a code that can take some arbitrary function, f(t,x), and use Euler's method to integrate over  equally-spaced points ( equal intervals) between times  and . You must implement the boundary condition . 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src=\"data:image/png;base64,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\" width=\"44.5\" height=\"18\" style=\"width: 44.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. The challenge is to write a code that can take some arbitrary function, f(t,x), and use Euler's method to integrate over \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eN\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e equally-spaced points (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"39.5\" height=\"18\" style=\"width: 39.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e equal intervals) between times \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"12\" height=\"20\" style=\"width: 12px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"14\" height=\"20\" style=\"width: 14px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. You must implement the boundary condition \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"63\" height=\"19\" style=\"width: 63px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [t,x] = EulerIntegration(t0,tf,N,x0,func)\r\n  t = 0;\r\n  x = 0;\r\nend","test_suite":"%%\r\nt0=0; tf=1.5; \r\nfunc = @(t,x) 2*x*t;\r\nN=50;\r\nt = linspace(t0,tf,N);\r\nh = (tf-t0)/N;\r\nnum_steps = length(t) - 1;\r\nx = zeros(1,num_steps + 1);\r\nx(1) = 1;\r\nfor i = 1:num_steps\r\n    x(i+1) = x(i) + h*func(t(i),x(i));\r\nend\r\n\r\nx0=1;\r\n[t2,x2] = EulerIntegration(t0,tf,N,x0,func)\r\n\r\nassert(isequal(x(1),x2(1)))\r\nn1 = length(x);\r\nn2 = length(x2);\r\nassert(isequal(x(n1),x2(n2)))\r\nassert(isequal(n1,n2))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":5,"created_by":4078801,"edited_by":4078801,"edited_at":"2024-02-29T18:51:13.000Z","deleted_by":null,"deleted_at":null,"solvers_count":11,"test_suite_updated_at":"2024-02-29T18:51:13.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2024-02-28T23:15:52.000Z","updated_at":"2024-10-29T13:31:26.000Z","published_at":"2024-02-28T23:15:52.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eEuler's method approximates the solution to a differential equation as\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex(t+\\\\Delta t) = x(t) + h \\\\cdot f(x, t )\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh = \\\\Delta t\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. The challenge is to write a code that can take some arbitrary function, f(t,x), and use Euler's method to integrate over \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e equally-spaced points (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eN-1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e equal intervals) between times \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et_o\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et_f\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. You must implement the boundary condition \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex(0)=x0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":59736,"title":"Counting the occurrences of a digit in a book","description":"The printer has printed a book with 'p' pages. How many times did they use the character 'd'? In other words, how many times does the digit 'd' appear when writing numbers from 1 to 'p'?","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 343.5px 21px; transform-origin: 343.5px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320.5px 21px; text-align: left; transform-origin: 320.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThe printer has printed a book with '\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep'\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e pages. How many times did they use the character 'd'? In other words, how many times does the digit 'd' appear when writing numbers from 1 to '\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep'\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e?\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function count = printer(d,p)\r\n  \r\nend","test_suite":"%%\r\nd = 4 ;\r\np = 1234 ;\r\ny_correct = 344;\r\nassert(isequal(printer(d,p),y_correct))\r\n%%\r\nd = randi([5, 9]);\r\np = d-1 ;\r\ny_correct = 0;\r\nassert(isequal(printer(d,p),y_correct))\r\n%%\r\nd = randi([1, 8]);\r\np = d ;\r\ny_correct = 1;\r\nassert(isequal(printer(d,p),y_correct))\r\n%%\r\nd = randi([3, 9]);\r\np = 9+d ;\r\ny_correct = 1;\r\nassert(isequal(printer(d,p),y_correct))\r\n%%\r\nd = randi([2, 9]);\r\np = 108+d ;\r\ny_correct = 21;\r\nassert(isequal(printer(d,p),y_correct))\r\n%%\r\nd = randi([2, 9]);\r\np = 1107+d ;\r\ny_correct = 321;\r\nassert(isequal(printer(d,p),y_correct))\r\n%%\r\nd = randi([2, 9]);\r\np = 11106+d ;\r\ny_correct = 4321;\r\nassert(isequal(printer(d,p),y_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":208445,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-03-30T09:24:59.000Z","updated_at":"2024-03-30T09:24:59.000Z","published_at":"2024-03-30T09:24:59.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe printer has printed a book with '\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e pages. How many times did they use the character 'd'? In other words, how many times does the digit 'd' appear when writing numbers from 1 to '\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":59741,"title":"Pivot index","description":"Let L be a vector of numbers. We are searching for the index n of the pivot element defined as follows: the dot product of the elements in the sub-vector to the left by their distance to the pivot element is equal to the dot product of the elements in the sub-vector to the right by their distance to the pivot element. \r\nExample 1: \r\nIf L = [6,1,10,5,4], then n = 3 since :\r\nLeft sub-vector: L(1:n-1) = [6,1] and distances = [2,1] so dot product = \r\nRight sub-vector: L(n+1:end) = [5,4] and distances = [1,2] so dot product =  \r\nExample 2:\r\nIf L = [10,3,3,2,1], then n = 2 since :\r\nLeft sub-vector: L(1:n-1) = [10] and distances = [1] so dot product = \r\nRight sub-vector: L(n+1:end) = [3,2,1] and distances = [1,2,3] so dot product =  \r\n\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 432.062px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 216.025px; transform-origin: 407px 216.031px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eLet \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eL\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e be a vector of numbers. We are searching for the index n of the pivot element defined as follows: the dot product of the elements in the sub-vector to the left by their distance to the pivot element is equal to the dot product of the elements in the sub-vector to the right by their distance to the pivot element. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eExample 1: \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eIf L = [\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e6\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e10\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e5\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e4\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e], then n = 3 since :\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 83.35px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 41.675px; transform-origin: 391px 41.675px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 41.675px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.8375px; text-align: left; transform-origin: 363px 20.8375px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eLeft sub-vector: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eL(1:n-1) = [6,1] and distances = [\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e] so dot product = \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"116\" height=\"18\" style=\"width: 116px; height: 18px;\"\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 41.675px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.8375px; text-align: left; transform-origin: 363px 20.8375px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eRight sub-vector: L(n+1:end) = [5,4] and distances = [\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e] so dot product =  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"116\" height=\"18\" style=\"width: 116px; height: 18px;\"\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eExample 2:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eIf L = [10,3,3,2,1], then n = 2 since :\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 62.9125px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 31.45px; transform-origin: 391px 31.4562px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 21.2375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.6125px; text-align: left; transform-origin: 363px 10.6187px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eLeft sub-vector: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eL(1:n-1) = [10] and distances = [1] so dot product = \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"75.5\" height=\"18\" style=\"width: 75.5px; height: 18px;\"\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 41.675px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.8375px; text-align: left; transform-origin: 363px 20.8375px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eRight sub-vector: L(n+1:end) = [3,2,1] and distances = [\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e2,3] so dot product =  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"164\" height=\"18\" style=\"width: 164px; height: 18px;\"\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.9px; text-align: left; transform-origin: 384px 10.9px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function n = pivot(L)\r\n\r\nend","test_suite":"%%\r\nL = [6 1 10 5 4];\r\ny_correct = 3;\r\nassert(isequal(pivot(L),y_correct))\r\n%%\r\nL = [10 3 3 2 1];\r\ny_correct = 2;\r\nassert(isequal(pivot(L),y_correct))\r\n%%\r\nx = randi([5,9]);\r\nL = [1:x, x-1:-1:1]\r\ny_correct = x;\r\nassert(isequal(pivot(L),y_correct))\r\n%%\r\nx = randi([20,30]);\r\nL = [x:-1:1, 2:x]\r\ny_correct = x;\r\nassert(isequal(pivot(L),y_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":208445,"edited_by":208445,"edited_at":"2024-03-30T11:44:59.000Z","deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-03-30T10:20:09.000Z","updated_at":"2024-03-30T11:44:59.000Z","published_at":"2024-03-30T10:20:09.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLet \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eL\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e be a vector of numbers. We are searching for the index n of the pivot element defined as follows: the dot product of the elements in the sub-vector to the left by their distance to the pivot element is equal to the dot product of the elements in the sub-vector to the right by their distance to the pivot element. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample 1: \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf L = [\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e6\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e10\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e5\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e4\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e], then n = 3 since :\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eLeft sub-vector: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eL(1:n-1) = [6,1] and distances = [\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e] so dot product = \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e6\\\\times2+1\\\\times1=13\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eRight sub-vector: L(n+1:end) = [5,4] and distances = [\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e] so dot product =  \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e5\\\\times1+4\\\\times2=13\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample 2:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf L = [10,3,3,2,1], then n = 2 since :\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eLeft sub-vector: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eL(1:n-1) = [10] and distances = [1] so dot product = \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e10\\\\times1=10\\n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eRight sub-vector: L(n+1:end) = [3,2,1] and distances = [\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2,3] so dot product =  \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e3\\\\times1+2\\\\times2+1\\\\times3=10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":59761,"title":"Digits eliminate","description":"Complete the function my_f(n,b) to return, for a given integer, the number obtained by removing the digits '0' and 'b'. If there are no other digits, it should return -1.\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 72.8px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 343.5px 36.4px; transform-origin: 343.5px 36.4px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320.5px 21px; text-align: left; transform-origin: 320.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eComplete the function my_f(n,b) to return, for a given integer, the number obtained by removing the digits '0' and 'b'. If there are no other digits, it should return -1.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320.5px 10.9px; text-align: left; transform-origin: 320.5px 10.9px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = my_f(n,b)\r\n\r\nend","test_suite":"%%\r\nn = 203456789\r\nb = 1\r\ny_correct = 23456789;\r\nassert(isequal(my_f(n,b),y_correct))\r\n%%\r\nn = 3300303003\r\nb = 3\r\ny_correct = -1;\r\nassert(isequal(my_f(n,b),y_correct))\r\n%%\r\nb = randi([7, 9])\r\nn = b*10^randi([2, 5])\r\ny_correct = -1;\r\nassert(isequal(my_f(n,b),y_correct))\r\n%%\r\ny_correct = randi([1, 6]);\r\nb = randi([7, 9])\r\nn = b*10^randi([2, 5])+y_correct\r\nassert(isequal(my_f(n,b),y_correct))\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":208445,"edited_by":208445,"edited_at":"2024-03-31T10:03:42.000Z","deleted_by":null,"deleted_at":null,"solvers_count":16,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-03-31T09:37:36.000Z","updated_at":"2024-11-12T07:42:17.000Z","published_at":"2024-03-31T10:03:42.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eComplete the function my_f(n,b) to return, for a given integer, the number obtained by removing the digits '0' and 'b'. If there are no other digits, it should return -1.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":59786,"title":"Missing Number (arithmetic progression)","description":"Given a list of integers forming an arithmetic progression (where the difference between consecutive elements is constant), your task is to find the missing element. However, the sequence provided is unsorted.\r\nComplete the missing_number function. This function should take an unsorted list L as input and return the missing element in the sequence.\r\nFor example, if the input list is [4, 2, 6, 10, 12], the missing element is 8.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 125px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 428px 62.5px; transform-origin: 428px 62.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 405px 21px; text-align: left; transform-origin: 405px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGiven a list of integers forming an arithmetic progression (where the difference between consecutive elements is constant), your task is to find the missing element. However, the sequence provided is unsorted.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 43px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 405px 21.5px; text-align: left; transform-origin: 405px 21.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eComplete the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003emissing_number\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e function. This function should take an unsorted list \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eL\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e as input and return the missing element in the sequence.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 405px 11px; text-align: left; transform-origin: 405px 11px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFor example, if the input list is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e[4, 2, 6, 10, 12]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, the missing element is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e8\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function n = missing_number(L)\r\n\r\nend","test_suite":"%%\r\nL = [4, 2, 6, 10, 12];\r\nn_correct = 8;\r\nassert(isequal(missing_number(L),n_correct))\r\n%%\r\nk_init = randi([1, 100]); \r\ndelta = randi([2, 20]); \r\nnum_elements = randi([10, 15]); \r\nL = k_init:k_init + (num_elements - 1) * delta;\r\nidx_to_remove = randi([2, num_elements - 1]); \r\nn_correct = L(idx_to_remove);\r\nL(idx_to_remove) = [];\r\nL = L(randperm(length(L)));\r\nassert(isequal(missing_number(L),n_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":208445,"edited_by":208445,"edited_at":"2024-05-19T08:08:32.000Z","deleted_by":null,"deleted_at":null,"solvers_count":13,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-03-31T12:27:31.000Z","updated_at":"2024-11-01T14:06:25.000Z","published_at":"2024-03-31T12:27:31.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a list of integers forming an arithmetic progression (where the difference between consecutive elements is constant), your task is to find the missing element. However, the sequence provided is unsorted.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eComplete the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emissing_number\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e function. This function should take an unsorted list \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eL\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e as input and return the missing element in the sequence.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, if the input list is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[4, 2, 6, 10, 12]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, the missing element is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e8\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":59801,"title":"Limiting Element Occurrences","description":"You are given a list 'v' of numbers. This list may contain repeated numbers. Your objective is to create a new list that maintains the same elements in the same order as the original list. However, if a number appears more than 'k times in the original list, only the first 'k' occurences of that number will be included in the new list. Any additional instances of that number beyond the k-th occurrence will be discarded. Note that, if k equals 0, the resulting list would be empty.\r\nExample: if v = [ 1, 3, 5, 3, 1, 3, 5, 3, 1 ] and k = 2, the function should output [ 1, 3, 5, 3, 1,  5 ].","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 117.67px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.989px 58.8352px; transform-origin: 406.996px 58.8352px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 87.6705px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.991px 43.8352px; text-align: left; transform-origin: 383.999px 43.8352px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou are given a list 'v' of numbers. This list may contain repeated numbers. Your objective is to create a new list that maintains the same elements in the same order as the original list. However, if a number appears more than\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e '\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ek\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003etimes in the original list, only the first\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e 'k' occurences of that number will be included in the new list. Any additional instances of that number beyond the\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e k\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e-\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth occurrence will be discarded. Note that, if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ek\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e equals 0, the resulting list would be empty.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0085px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.991px 10.4972px; text-align: left; transform-origin: 383.999px 10.5043px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eExample: if v = [ 1, 3, 5, 3, 1, 3, 5, 3, 1 ] and k = 2, the function should output [ 1, 3, 5, 3, 1,  5 ].\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function L = remove_after_kth(v, k)\r\n\r\nend","test_suite":"%%\r\nk = 2\r\nv =  [ 1, 3, 5, 3, 1, 3, 5, 3, 1 ] \r\nL_correct = [ 1, 3, 5, 3, 1,  5 ]\r\nassert(isequal(remove_after_kth(v, k),L_correct))\r\n%%\r\nk = randi([3,7])\r\nr = k+randi([1,10 ]);\r\nval = randi([40,70]);\r\nv = val*ones(1,r)\r\nL_correct = val*ones(1,k)\r\nassert(isequal(remove_after_kth(v, k),L_correct))\r\n%%\r\nk = 3\r\nv = [1:5,4:-1:1,2:5,4:-1:1,2:5]\r\nL_correct = [1:5,4:-1:1,2:5,1,5]\r\nassert(isequal(remove_after_kth(v, k),L_correct))\r\n%%\r\nk = randi([5,10])\r\nv = [1, 1, 1, 2, 2, 2]\r\nL_correct = v\r\nassert(isequal(remove_after_kth(v, k),L_correct))\r\n%%\r\nk = 0\r\nv = randi([1,5],1,20)\r\n% L_correct = []\r\n% assert(isequal(remove_after_kth(v, k),L_correct))\r\nassert(isempty(remove_after_kth(v, k)))\r\n%%\r\nk = randi([3,7])\r\nr = k+randi([1,10 ]);\r\nval = 1:5;\r\nv = repmat(val,1,k+5) \r\nL_correct = repmat(val,1,k)  \r\nassert(isequal(remove_after_kth(v, k),L_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":4,"created_by":208445,"edited_by":208445,"edited_at":"2024-05-13T15:52:54.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":"2024-05-13T15:52:54.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2024-04-01T07:36:09.000Z","updated_at":"2024-11-01T14:30:43.000Z","published_at":"2024-04-01T07:36:15.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou are given a list 'v' of numbers. This list may contain repeated numbers. Your objective is to create a new list that maintains the same elements in the same order as the original list. However, if a number appears more than\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e '\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003etimes in the original list, only the first\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e 'k' occurences of that number will be included in the new list. Any additional instances of that number beyond the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e k\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e-\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eth occurrence will be discarded. Note that, if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e equals 0, the resulting list would be empty.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample: if v = [ 1, 3, 5, 3, 1, 3, 5, 3, 1 ] and k = 2, the function should output [ 1, 3, 5, 3, 1,  5 ].\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":59811,"title":"Sort by absolute value","description":"Given a list of numbers, arrange them in ascending order based on their absolute values. \r\nFor example, for the list [-30, -5, 11, 14], the sorted list would be [-5, 11, 14, -30].","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 51px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 428px 25.5px; transform-origin: 428px 25.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 405px 10.5px; text-align: left; transform-origin: 405px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGiven a list of numbers, arrange them in ascending order based on their absolute values. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 405px 10.5px; text-align: left; transform-origin: 405px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFor example, for the list [-30, -5, 11, 14], the sorted list would be [-5, 11, 14, -30].\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = sortAbsolute(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = [-30, -5, 11, 14]\r\ny_correct = [-5, 11, 14, -30]\r\ny = sortAbsolute(x)\r\nassert(isequal(y,y_correct))\r\n%%\r\nx = [46, -83, 43, 28, -96, -84, -4, -21, 50, -65, -47]\r\ny_correct = [-4, -21, 28, 43, 46, -47, 50, -65, -83, -84, -96]\r\ny = sortAbsolute(x)\r\nassert(isequal(y,y_correct))\r\n%%\r\nk = randi([3,10]);\r\nx = [1:k,0]\r\ny_correct = [0,1:k]\r\ny = sortAbsolute(x)\r\nassert(isequal(y,y_correct))\r\n%%\r\nk = randi([3,10]);\r\nx = -[0:k]\r\ny_correct = x\r\ny = sortAbsolute(x)\r\nassert(isequal(y,y_correct))\r\n%%\r\nk = randi([7,15]);\r\nx = -[k:-1:1]\r\ny_correct = -[1:k]\r\ny = sortAbsolute(x)\r\nassert(isequal(y,y_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":208445,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":22,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-04-01T08:33:44.000Z","updated_at":"2024-11-20T13:07:15.000Z","published_at":"2024-04-01T08:33:44.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a list of numbers, arrange them in ascending order based on their absolute values. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, for the list [-30, -5, 11, 14], the sorted list would be [-5, 11, 14, -30].\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":59816,"title":"Sun angle","description":"Determine the angle of the sun above the horizon based on the time of day. \r\nAssumptions: the sun rises in the East at 6h00, corresponding to an angle of 0° degrees; reaches its zenith at 12h00, with an angle of 90° degrees; and sets at 18h00, with an angle of 180° degrees.\r\n\r\nInput: The time of day represented as a list [hh, mm], where  and . \r\nOutput: The angle of the sun above the horizon, in degrees, rounded to 2 decimal places. If the input time falls within the night hours (before 6h00 or after 18h00), your function should return 'Night'.\r\nExample:\r\nsun_angle([7,0]) should return 15.00\r\nsun_angle([12,15]) should return 93.75","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 389.875px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 194.938px; transform-origin: 407px 194.938px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eDetermine the angle of the sun above the horizon based on the time of day. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAssumptions: the sun rises in the East at 6h00, corresponding to an angle of 0° degrees; reaches its zenith at 12h00, with an angle of 90° degrees; and sets at 18h00, with an angle of 180° degrees.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 147px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 73.5px; text-align: left; transform-origin: 384px 73.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"264\" height=\"147\" style=\"vertical-align: middle;width: 264px;height: 147px\" 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data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eInput: The time of day represented as a list [hh, mm], where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"77.5\" height=\"18\" style=\"width: 77.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"86\" height=\"18\" style=\"width: 86px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eOutput: The angle of the sun above the horizon, in degrees, rounded to 2 decimal places. If the input time falls within the night hours (before 6h00 or after 18h00), your function should return 'Night'.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eExample:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 40.875px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 20.4375px; transform-origin: 391px 20.4375px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003esun_angle([7,0]) should return 15.00\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003esun_angle([12,15]) should return 93.75\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function angle = sun_angle(time)\r\n\r\nend","test_suite":"%%\r\ntime = [6,0]\r\nangle = sun_angle(time)\r\nangle_correct = 0\r\nassert(isequal(angle,angle_correct))\r\n%%\r\ntime = [12,0]\r\nangle = sun_angle(time)\r\nangle_correct = 90\r\nassert(isequal(angle,angle_correct))\r\n%%\r\ntime = [18,0]\r\nangle = sun_angle(time)\r\nangle_correct = 180\r\nassert(isequal(angle,angle_correct))\r\n%%\r\nnn = [0:5,18:23];\r\nhh = nn(randi([1,numel(nn)]));\r\nmm = randi([1,59]);\r\ntime = [hh,mm]\r\nangle = sun_angle(time)\r\nangle_correct = 'Night'\r\nassert(isequal(angle,angle_correct))\r\n%%\r\ntime = [7,0]\r\nangle = sun_angle(time)\r\nangle_correct = 15\r\nassert(isequal(angle,angle_correct))\r\n%%\r\ntime = [17,0]\r\nangle = sun_angle(time)\r\nangle_correct = 165\r\nassert(isequal(angle,angle_correct))\r\n%%\r\ntime = [7,20]\r\nangle = sun_angle(time)\r\nangle_correct = 20\r\nassert(isequal(angle,angle_correct))\r\n%%\r\ntime = [12,15]\r\nangle = sun_angle(time)\r\nangle_correct = 93.75\r\nassert(isequal(angle,angle_correct))\r\n%%\r\ntmp = randi([0,180]);\r\ntime = [6+floor(tmp/15),0];\r\ntime(2) =  round((tmp - (time(1)-6) * 15) * 4);\r\ntime\r\nangle = sun_angle(time)\r\nangle_correct = tmp\r\nassert(isequal(angle,angle_correct))\r\n%%\r\ntime = [randi(5),0]\r\nangle = sun_angle(time)\r\nangle_correct = 'Night'\r\nassert(isequal(angle,angle_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":208445,"edited_by":208445,"edited_at":"2024-07-01T17:28:03.000Z","deleted_by":null,"deleted_at":null,"solvers_count":13,"test_suite_updated_at":"2024-07-01T17:28:03.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2024-04-01T08:56:06.000Z","updated_at":"2024-11-06T00:07:48.000Z","published_at":"2024-04-01T09:17:29.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDetermine the angle of the sun above the horizon based on the time of day. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAssumptions: the sun rises in the East at 6h00, corresponding to an angle of 0° degrees; reaches its zenith at 12h00, with an angle of 90° degrees; and sets at 18h00, with an angle of 180° degrees.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"147\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"264\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"middle\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInput: The time of day represented as a list [hh, mm], where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e0 \\\\le \\\\text{hh} \\\\le 23\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e0 \\\\le \\\\text{mm} \\\\le 59\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOutput: The angle of the sun above the horizon, in degrees, rounded to 2 decimal places. If the input time falls within the night hours (before 6h00 or after 18h00), your function should return 'Night'.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003esun_angle([7,0]) should return 15.00\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003esun_angle([12,15]) should return 93.75\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.png\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":59846,"title":"Sequencing Odd Even numbers ","description":"Given an input value n, create a vector which contains all odd numbers  \u0026 even numbers centered around mean of vector. If the mean is even/decimal number, round and rescale the even values of vecto. Similarly if the mean of vector is odd, rescale the odd numbers and present it as Odd-Even format ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 62.9883px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.484px 31.4844px; transform-origin: 406.494px 31.4941px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.496px 31.4844px; text-align: left; transform-origin: 383.506px 31.4941px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven an input value n, create a vector which contains all odd numbers  \u0026amp; even numbers centered around mean of vector. If the mean is even/decimal number, round and rescale the even values of vecto. Similarly if the mean of vector is odd, rescale the odd numbers and present it as Odd-Even format \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [odd m even] = odd_even_num(n)\r\n  y = 1:n;\r\n  odd = y(1:2:end);\r\n  even = y(2:2:end);\r\n  m = round(mean(y));\r\n  if mod(m,2) == 0\r\n      even = rescale(even);\r\n       y = [even m odd]\r\n  elseif mod(m,3)== 0 \r\n      odd = rescale(odd);\r\n      y = [odd m even] \r\n  end  \r\nend","test_suite":"%%\r\nn = 10;\r\ny_correct = [1.0000    3.0000    5.0000    7.0000    9.0000    6.0000         0    0.2500    0.5000    0.7500    1.0000]\r\nassert(isequal(odd_even_num(n),y_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":584788,"edited_by":584788,"edited_at":"2024-04-06T10:01:03.000Z","deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":"2024-04-06T07:54:10.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2024-04-06T07:42:57.000Z","updated_at":"2024-11-01T22:33:34.000Z","published_at":"2024-04-06T07:42:57.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven an input value n, create a vector which contains all odd numbers  \u0026amp; even numbers centered around mean of vector. If the mean is even/decimal number, round and rescale the even values of vecto. Similarly if the mean of vector is odd, rescale the odd numbers and present it as Odd-Even format \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60176,"title":"Find the number of diagonals in a n sided polygon.","description":"Find the number of diagonals in a n sided polygon.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 21px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 10.5px; transform-origin: 407px 10.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFind the number of diagonals in a n sided polygon.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = count_diagonals(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx =12;\r\ny_correct =54;\r\nassert(isequal(count_diagonals(x),y_correct))\r\n\r\nx =4;\r\ny_correct =2;\r\nassert(isequal(count_diagonals(x),y_correct))\r\n\r\nx =3;\r\ny_correct =0;\r\nassert(isequal(count_diagonals(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":3469688,"edited_by":3469688,"edited_at":"2024-05-02T19:23:51.000Z","deleted_by":null,"deleted_at":null,"solvers_count":15,"test_suite_updated_at":"2024-05-02T19:23:51.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2024-05-02T18:52:26.000Z","updated_at":"2024-11-04T22:23:28.000Z","published_at":"2024-05-02T19:23:51.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the number of diagonals in a n sided polygon.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":51173,"title":"Squares inside a square! ","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 99.7778px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.5px 49.8889px; transform-origin: 406.5px 49.8889px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 40.8889px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 20.4444px; text-align: left; transform-origin: 383.5px 20.4444px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eIf you have a square has a side (x) that is divided into four squares. Two of those squares carries smaller squares inside them. Each side carries 5 squares. Find the area of one of these small squares. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.4444px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 10.2222px; text-align: left; transform-origin: 383.5px 10.2222px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.4444px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 10.2222px; text-align: left; transform-origin: 383.5px 10.2222px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = squares_inside_square(x)\r\n  y = ;\r\nend","test_suite":"%%\r\nx = 500;\r\ny_correct = 2500;\r\nassert(isequal(squares_inside_square(x),y_correct))\r\n\r\n%%\r\nx = 100;\r\ny_correct = 100;\r\nassert(isequal(squares_inside_square(x),y_correct))\r\n\r\n%%\r\nx = 50;\r\ny_correct = 25;\r\nassert(isequal(squares_inside_square(x),y_correct))\r\n\r\n%%\r\nx = 30;\r\ny_correct = 9;\r\nassert(isequal(squares_inside_square(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":3,"created_by":995198,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":54,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-03-24T11:45:55.000Z","updated_at":"2024-11-05T19:25:27.000Z","published_at":"2021-03-24T11:45:55.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf you have a square has a side (x) that is divided into four squares. Two of those squares carries smaller squares inside them. Each side carries 5 squares. Find the area of one of these small squares. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60181,"title":"Integer Persistence, Product","description":"Let's construct a sequence  as follows:  is a given natural number, and  is the product of the digits of . The persistence of  is defined as the smallest index  such that . \r\nComplete the function persistance(u0) which, for a given , returns its persistence.\r\n\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 137.159px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 386.491px 68.5795px; transform-origin: 386.499px 68.5795px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 43.5227px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 363.494px 21.7614px; text-align: left; transform-origin: 363.501px 21.7614px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eLet's construct a sequence \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"46\" height=\"18.5\" style=\"width: 46px; height: 18.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e as follows: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"15.5\" height=\"18.5\" style=\"width: 15.5px; height: 18.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is a given natural number, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"28.5\" height=\"18.5\" style=\"width: 28.5px; height: 18.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the product of the digits of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB8AAAAlCAYAAAC6TzLyAAAAAXNSR0IArs4c6QAAAmZJREFUWEft1l/ojncYBvAPWspmB8NioiihjaIMOVBSGi20LAfKn5oSsbK1WjjyL4TIUGQpB/60lcaBwqkkB0gciOLA35a1YZn43nW/9fb2/vbr93r4nbzfeuvt6fne131f131f99NDN54e3YitDd4t7Ldpb9P+XhloN9x7pbsG9n+0f4wx+LL8TuNmQ4afYARe4nIr2TcDH4bvsRh98Rqf4nEDwDasxnlMqwq8FmcLfsRVjG0I3gv3MBBrsKFq8N8xB7uxsiH4LPyRzybjQpXgIcdD9C+Vf1Mq/60h+El8jb8Q2r+qEvyLpLuZ3p/jCnoikpjdCnDc6ajbVyTdzfSuyRH3V5XKd1UNfiLpbtR7OpZnLwRmsHC9SvCO9O6DA9nlMQX3MahV4I5oj2quNZnvoPdgGa99mFQM5ggW1IF/gB8wrvTC+DL/U8sY/lc84pf8vxHb65NtpvmyvFCv96KscieelrkOoIU4jCUImaLze2fi8c5XZQrWYgfO5PRM6Qz81wx8KAPHrIfbzcWEupkegpH5bHMGDfA/sRUf4Wf8iwc5Gd91Bl7r5rhwqXR9P8zIymYWsFMZIGT4DPPr5jxs9mzKsx53CjvDcSvfO9oZeJhH6PQis11XbPafvPQhzmFU6fTj6XzP6gJuwk/p+UF3nKXYm/vhSWfgb9PAwdTgrPZ5Bookh2JiY+Aqv2TCZh8VrWPbRfVxwgXj2Z5cPrExb9SSqBJ8Ho5lhRcTIMYudn30xehM7O93Ab4/fT6MJ3ZCnAG5I24XJ/wWd9+l5l3qlypp7xJwR/ba5SCtXmhX3ipzb3XvDRG8cSbnMUYnAAAAAElFTkSuQmCC\" width=\"15.5\" height=\"18.5\" style=\"width: 15.5px; height: 18.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The persistence of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"15.5\" height=\"18.5\" style=\"width: 15.5px; height: 18.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is defined as the smallest index \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e such that \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"49\" height=\"18.5\" style=\"width: 49px; height: 18.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22.8267px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 363.494px 11.4062px; text-align: left; transform-origin: 363.501px 11.4134px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eComplete the function \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003epersistance(u0)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e which, for a given \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"15.5\" height=\"18.5\" style=\"width: 15.5px; height: 18.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, returns its persistence.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22.8267px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 363.494px 11.4062px; text-align: left; transform-origin: 363.501px 11.4134px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0085px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 363.494px 10.4972px; text-align: left; transform-origin: 363.501px 10.5043px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function idx = persistance(n)\r\n\r\nend","test_suite":"%% Test Case 1: n = 7\r\nassert(persistance(7) == 0);\r\n\r\n%% Test Case 2: n = 18\r\nassert(persistance(18) == 1);\r\n\r\n%% Test Case 3: n = 23\r\nassert(persistance(23) == 1);\r\n\r\n%% Test Case 4: n = 97\r\nassert(persistance(97) == 3);\r\n\r\n%% Test Case 5: n = 1009\r\nassert(persistance(1009) == 1);\r\n\r\n%% Test Case 6: n = 12345\r\nassert(persistance(12345) == 2);\r\n\r\n%% Random Test Case 1\r\nn = randi([1, 9])\r\nassert(persistance(n) == 0);\r\n\r\n%% Random Test Case 2\r\nL = [10:24,100:111,200:211,300:311,1000:1111];\r\nn = L(randi([1, numel(L)]))\r\nassert(persistance(n) == 1);\r\n\r\n%% Random Test Case 3\r\nL = [679, 688, 697, 769, 796, 868, 886, 967, 976, 9969, 9996];\r\nn = L(randi([1, numel(L)]))\r\nassert(persistance(n) == 5);\r\n\r\n%% Random Test Case 4\r\nn = randi([93, 98])\r\nassert(persistance(n) == 3);\r\n\r\n%% Random Test Case 5\r\nformat long\r\nnbDig = randi([5, 10]);\r\nnb = randi([0, 1], 1, nbDig);\r\nn = str2double(strrep(num2str(nb), ' ', ''))\r\nassert(persistance(n) == 1);\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":3,"created_by":208445,"edited_by":208445,"edited_at":"2024-05-03T17:21:46.000Z","deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":"2024-05-03T17:21:46.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2024-05-03T16:44:48.000Z","updated_at":"2024-05-03T17:21:46.000Z","published_at":"2024-05-03T17:21:46.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLet's construct a sequence \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e(u_n)_{n\\\\in\\\\mathbb{N}}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e as follows: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eu_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is a given natural number, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eu_{n+1}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the product of the digits of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eu_n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. The persistence of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eu_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is defined as the smallest index \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e such that \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eu_n\u0026lt;10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eComplete the function \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003epersistance(u0)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e which, for a given \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eu_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, returns its persistence.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60201,"title":"Find the largest sum of any contiguous subarray","description":"Given an array of N integers, find the contiguous subarray (which must contain at least one number) with the maximum sum and return its sum. \r\nHere are some examples:\r\nmax_subarray([1,2,3,-2,5]) should return 9 because the sum of the subarray [1,2,3,-2,5] is 9, and the sum of any other subarray is always less.\r\nmax_subarray([-1,-2,-3,-4]) should return -1 because the maximum sum subarray is [-1].\r\nmax_subarray([5,-1,6,-2,7]) should return 15 because the maximum sum subarray is [5, -1, 6, -2, 7].\r\nmax_subarray([-2, 1, -3, 4, -1, 2, 1, -5, 4]) should return 6 because the maximum sum subarray is [4, -1, 2, 1].\r\nmax_subarray([-2, -5, 6, -2, -3, 1, 5, -6]) should return 7 because the maximum sum subarray is [6, -2, -3, 1, 5].","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 273.253px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 386.491px 136.619px; transform-origin: 386.499px 136.626px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42.017px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 363.494px 21.0085px; text-align: left; transform-origin: 363.501px 21.0085px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven an array of N integers, find the contiguous subarray (which must contain at least one number) with the maximum sum and return its sum. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0085px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 363.494px 10.4972px; text-align: left; transform-origin: 363.501px 10.5043px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHere are some examples:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003col style=\"block-size: 191.236px; font-family: Helvetica, Arial, sans-serif; list-style-type: decimal; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 370.497px 95.6108px; transform-origin: 370.497px 95.6179px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 41.7898px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 342.5px 20.8949px; text-align: left; transform-origin: 342.5px 20.8949px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003emax_subarray([1,2,3,-2,5])\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e should return \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e9\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e because the sum of the subarray \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e[1,2,3,-2,5]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e9\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and the sum of any other subarray is always less.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 21.3494px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 342.5px 10.6676px; text-align: left; transform-origin: 342.5px 10.6747px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003emax_subarray([-1,-2,-3,-4])\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e should return \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e-1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e because the maximum sum subarray is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e[-1]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 42.6989px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 342.5px 21.3494px; text-align: left; transform-origin: 342.5px 21.3494px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003emax_subarray([5,-1,6,-2,7])\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e should return \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e15\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e because the maximum sum subarray is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e[5, -1, 6, -2, 7]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 42.6989px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 342.5px 21.3494px; text-align: left; transform-origin: 342.5px 21.3494px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003emax_subarray([-2, 1, -3, 4, -1, 2, 1, -5, 4])\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e should return \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e6\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e because the maximum sum subarray is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e[4, -1, 2, 1]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 42.6989px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 342.5px 21.3494px; text-align: left; transform-origin: 342.5px 21.3494px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003emax_subarray([-2, -5, 6, -2, -3, 1, 5, -6])\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e should return \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e7\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e because the maximum sum subarray is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e[6, -2, -3, 1, 5]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = max_subarray(x)\r\n  \r\nend","test_suite":"%% \r\nassert(isequal(max_subarray([5,-1,6,-2,7]),15))\r\n\r\n%% \r\nassert(isequal(max_subarray([-2, 1, -3, 4, -1, 2, 1, -5, 4]),6))\r\n\r\n%% \r\nassert(isequal(max_subarray([-2, -5, 6, -2, -3, 1, 5, -6]),7))\r\n\r\n%% If the array contains all non-negative numbers, a maximum subarray is the entire array.\r\nx = randi([0,100],1,30)\r\ny_correct = sum(x)\r\nassert(isequal(max_subarray(x),y_correct))\r\n\r\n%% If the array contains all non-positive numbers, then a solution is any subarray of size 1 containing the maximal value of the array\r\nx = -randi([0,100],1,30)\r\ny_correct = max(x)\r\nassert(isequal(max_subarray(x),y_correct))\r\n\r\n%%\r\nell1 = randi([10,30]);\r\nx1 = -randi([0,100],1,ell1);\r\nell2 = randi([5,76]);\r\nx2 = randi([0,100],1,ell2);\r\nx = [x1,x2]\r\ny_correct = sum(x2)\r\nassert(isequal(max_subarray(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":208445,"edited_by":208445,"edited_at":"2024-05-04T14:13:44.000Z","deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":"2024-05-04T14:13:44.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2024-05-04T14:09:16.000Z","updated_at":"2024-11-20T07:56:33.000Z","published_at":"2024-05-04T14:13:44.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven an array of N integers, find the contiguous subarray (which must contain at least one number) with the maximum sum and return its sum. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHere are some examples:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emax_subarray([1,2,3,-2,5])\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e should return \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e9\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e because the sum of the subarray \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[1,2,3,-2,5]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e9\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and the sum of any other subarray is always less.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emax_subarray([-1,-2,-3,-4])\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e should return \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e-1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e because the maximum sum subarray is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[-1]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emax_subarray([5,-1,6,-2,7])\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e should return \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e15\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e because the maximum sum subarray is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[5, -1, 6, -2, 7]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emax_subarray([-2, 1, -3, 4, -1, 2, 1, -5, 4])\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e should return \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e6\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e because the maximum sum subarray is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[4, -1, 2, 1]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emax_subarray([-2, -5, 6, -2, -3, 1, 5, -6])\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e should return \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e7\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e because the maximum sum subarray is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[6, -2, -3, 1, 5]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60216,"title":"Perfect shuffle","description":"We call \"perfect shuffle\" the process of cutting a deck of cards into two equal halves, and then perfectly interleaving them: one card from the left stack, one card from the right stack, one card from the left stack, and so on.\r\nLet \"deck\" be an array with an even number of elements. Write a function \"perfect_shuffle(deck)\" that returns a new array constructed according to this shuffle.\r\nFor example, perfect_shuffle([1, 2, 3, 4, 5, 6]) should return [1, 4, 2, 5, 3, 6].\r\nRemark: For an array of 1024 elements, after 10 shuffles, we get back to the initial arrangement.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 153.026px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 441.989px 76.5057px; transform-origin: 441.996px 76.5128px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42.017px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 418.991px 21.0085px; text-align: left; transform-origin: 418.999px 21.0085px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWe call \"perfect shuffle\" the process of cutting a deck of cards into two equal halves, and then perfectly interleaving them: one card from the left stack, one card from the right stack, one card from the left stack, and so on.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42.017px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 418.991px 21.0085px; text-align: left; transform-origin: 418.999px 21.0085px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eLet \"deck\" be an array with an even number of elements. Write a function \"perfect_shuffle(deck)\" that returns a new array constructed according to this shuffle.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0085px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 418.991px 10.4972px; text-align: left; transform-origin: 418.999px 10.5043px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example, perfect_shuffle([1, 2, 3, 4, 5, 6]) should return [1, 4, 2, 5, 3, 6].\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0085px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 418.991px 10.4972px; text-align: left; transform-origin: 418.999px 10.5043px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eRemark: For an array of 1024 elements, after 10 shuffles, we get back to the initial arrangement.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = perfect_shuffle(x)\r\n  \r\nend","test_suite":"%%  \r\nx = [1, 2, 3, 4, 5, 6];\r\ny_correct = [1, 4, 2, 5, 3, 6];\r\ny = perfect_shuffle(x);\r\nassert(isequal(y, y_correct));\r\n\r\n%%  \r\nx = [1, 4, 2, 5, 3, 6];\r\ny_correct = [1, 5, 4, 3, 2, 6];\r\ny = perfect_shuffle(x);\r\nassert(isequal(y, y_correct));\r\n\r\n%%  \r\nx = [10, 20, 30, 40, 50, 60, 70, 80];\r\ny_correct = [10, 50, 20, 60, 30, 70, 40, 80];\r\ny = perfect_shuffle(x);\r\nassert(isequal(y, y_correct));\r\n\r\n%% \r\nx = randperm(6);\r\ny_correct = x;\r\nfor i = 1:4\r\n    y_correct = perfect_shuffle(y_correct);\r\nend\r\nassert(isequal(y_correct, x));\r\n\r\n%% \r\nx = randperm(1024);\r\ny_correct = x;\r\nfor i = 1:10\r\n    y_correct = perfect_shuffle(y_correct);\r\nend\r\nassert(isequal(y_correct, x));\r\n\r\n\r\n%% \r\nnn = [6, 30, 22, 126, 16, 124, 120, 118, 116, 114, 112, 110, 100, 98];\r\nii = [4, 28,  6, 100,  4,  20,  24,  12,  44,  28,  36,  36,  30, 48];\r\nidx = randi(length(nn)); % random index\r\nn = nn(idx) % number of elements\r\nj = ii(idx) % number of shuffles to get back to the initial arrangement for n elements\r\nx = randperm(n); % array of n elements\r\ny_correct = x;\r\nfor i = 1:j\r\n    y_correct = perfect_shuffle(y_correct);\r\nend\r\nassert(isequal(y_correct, x));\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":208445,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":12,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-05-05T08:41:11.000Z","updated_at":"2024-05-05T08:41:11.000Z","published_at":"2024-05-05T08:41:11.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWe call \\\"perfect shuffle\\\" the process of cutting a deck of cards into two equal halves, and then perfectly interleaving them: one card from the left stack, one card from the right stack, one card from the left stack, and so on.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLet \\\"deck\\\" be an array with an even number of elements. Write a function \\\"perfect_shuffle(deck)\\\" that returns a new array constructed according to this shuffle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, perfect_shuffle([1, 2, 3, 4, 5, 6]) should return [1, 4, 2, 5, 3, 6].\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRemark: For an array of 1024 elements, after 10 shuffles, we get back to the initial arrangement.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60221,"title":"Battery Charge Indicator","description":"Write a function called battery_charge that visually represents the charge of a battery.\r\nThe function takes an integer parameter percentage between 0 and 100 representing the battery charge percentage. It returns an array bars where each element contains a single character (visually representing the battery charge). \r\nThe array starts with '[', ends with ']', and contains from 0 to 10 characters '❚' or ' ' (space) to visually represent the battery charge. The number of '❚' characters is rounded, meaning that for percentages like 9% and 11%, only one ❚ will be used.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 132.116px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 441.989px 66.0511px; transform-origin: 441.996px 66.0582px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 22.8267px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 418.991px 11.4062px; text-align: left; transform-origin: 418.999px 11.4134px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function called \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ebattery_charge\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e that visually represents the charge of a battery.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 45.6534px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 418.991px 22.8267px; text-align: left; transform-origin: 418.999px 22.8267px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe function takes an integer parameter \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003epercentage\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e between 0 and 100 representing the battery charge percentage. It returns an array \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ebars\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e where each element contains a single character (visually representing the battery charge). \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 45.6534px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 418.991px 22.8267px; text-align: left; transform-origin: 418.999px 22.8267px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe array starts with '\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e['\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, ends with '\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e]'\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and contains from 0 to 10 characters '\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e❚' or ' '\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (space) to visually represent the battery charge. The number of '\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e❚'\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e characters is rounded, meaning that for percentages like 9% and 11%, only one \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e❚\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e will be used.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function bars = battery_charge(percentage)\r\n  \r\nend","test_suite":"%% Verify the charge bar for 9%\r\nexpected_result = [ '[', '❚', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ']' ]\r\nobtained_result = battery_charge(9) \r\nassert(isequal(obtained_result, expected_result));\r\n\r\n%% Verify the charge bar for 11%\r\nexpected_result = [ '[', '❚', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ']' ]\r\nobtained_result = battery_charge(11) \r\nassert(isequal(obtained_result, expected_result));\r\n\r\n%% Verify the charge bar for 16%\r\nexpected_result = [ '[', '❚', '❚', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ']' ]\r\nobtained_result = battery_charge(16) \r\nassert(isequal(obtained_result, expected_result));\r\n\r\n%% Verify the charge bar for 99%\r\nexpected_result = [ '[', '❚', '❚', '❚', '❚', '❚', '❚', '❚', '❚', '❚', '❚', ']' ]\r\nobtained_result = battery_charge(99) \r\nassert(isequal(obtained_result, expected_result));\r\n\r\n%% Verify the charge bar for 4%\r\nexpected_result = [ '[', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ']' ]\r\nobtained_result = battery_charge(4) \r\nassert(isequal(obtained_result, expected_result));\r\n\r\n%% Random test case\r\npercentage = randi([6, 87]); \r\nobtained_result = battery_charge(percentage);\r\nassert(length(obtained_result) == 12, 'Incorrect length');\r\nassert(obtained_result(1) == '[', 'Missing opening bracket');\r\nassert(obtained_result(end) == ']', 'Missing closing bracket');\r\nexpected_bars = min(round(percentage/10), 10);\r\nobtained_bars = sum(obtained_result == '❚');\r\nassert(obtained_bars == expected_bars, 'Incorrect number of bars');\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":208445,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":12,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-05-05T09:20:21.000Z","updated_at":"2024-11-16T11:33:39.000Z","published_at":"2024-05-05T09:20:21.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function called \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ebattery_charge\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e that visually represents the charge of a battery.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe function takes an integer parameter \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003epercentage\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e between 0 and 100 representing the battery charge percentage. It returns an array \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ebars\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e where each element contains a single character (visually representing the battery charge). \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe array starts with '\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e['\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, ends with '\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e]'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and contains from 0 to 10 characters '\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e❚' or ' '\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (space) to visually represent the battery charge. The number of '\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e❚'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e characters is rounded, meaning that for percentages like 9% and 11%, only one \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e❚\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e will be 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