Problem 42708. Placing Beads Neatly in a Box

Created by Ned Gulley

Solve Later

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Your job is to pack them neatly into a square box. \"Neatly\" in this case means that all the black beads are at the bottom, and all the white beads are at the top.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:customXml w:element=\"image\"><w:customXmlPr><w:attr w:name=\"height\" w:val=\"122\"/><w:attr w:name=\"width\" w:val=\"125\"/><w:attr w:name=\"verticalAlign\" w:val=\"baseline\"/><w:attr w:name=\"altText\" w:val=\"\"/><w:attr w:name=\"relationshipId\" w:val=\"rId1\"/></w:customXmlPr></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Half the beads are black, and half are white. The number of beads n will always be an even number perfect square (4, 16, 36, ...). Black beads are 1, and white beads are 0, so a string might look like this.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ str = [0 0 1 1 1 1 0 0 0 0 0 0 1 1 1 1]]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:customXml w:element=\"image\"><w:customXmlPr><w:attr w:name=\"height\" w:val=\"49\"/><w:attr w:name=\"width\" w:val=\"432\"/><w:attr w:name=\"verticalAlign\" w:val=\"baseline\"/><w:attr w:name=\"altText\" w:val=\"\"/><w:attr w:name=\"relationshipId\" w:val=\"rId2\"/></w:customXmlPr></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Return a square matrix bx that indexes into str such that</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ str(bx) = [ 0 0 0 0\n             0 0 0 0\n             1 1 1 1\n             1 1 1 1 ]]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>The matrix bx consists of the numbers 1 through n snaking through the box in a 4-connected sense (see Cody Problem 42705,</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"https://www.mathworks.com/matlabcentral/cody/problems/42705-is-it-a-snake\"><w:r><w:t>Is It a Snake?</w:t></w:r></w:hyperlink><w:r><w:t>).</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Here's one solution for the string shown above.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ bx = [ 1  8  9 10 \n        2  7 12 11\n        3  6 13 14\n        4  5 16 15 ]]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:customXml w:element=\"image\"><w:customXmlPr><w:attr w:name=\"height\" w:val=\"-1\"/><w:attr w:name=\"width\" w:val=\"-1\"/><w:attr w:name=\"verticalAlign\" w:val=\"baseline\"/><w:attr w:name=\"altText\" w:val=\"\"/><w:attr w:name=\"relationshipId\" w:val=\"rId3\"/></w:customXmlPr></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>In general the answers are not unique. I will be checking that bx contains the numbers 1 through n, that they form a snake, and that when used with the string of beads, they result in a tidy ones-on-the-bottom formation.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:rPr><w:i/></w:rPr><w:t>I am grateful to the solvers of problem 42705 for giving me nice short code to use in my test suite for this 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<div 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; "><div style="block-size: 923.92px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 331.989px 461.96px; transform-origin: 331.996px 461.96px; vertical-align: baseline; "><div style="block-size: 62.7273px; 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: 308.991px 31.3636px; text-align: left; transform-origin: 308.999px 31.3636px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="">You are given a string of n black and white beads. Your job is to pack them neatly into a square box. "Neatly" in this case means that all the black beads are at the bottom, and all the white beads are at the top.</span></span></div><div style="block-size: 127.443px; 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: 308.991px 63.7216px; text-align: left; transform-origin: 308.999px 63.7216px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><img class="imageNode" style="vertical-align: baseline" src="data:image/png;base64,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" data-image-state="image-loaded"></div><div style="block-size: 62.7273px; 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: 308.991px 31.3636px; text-align: left; transform-origin: 308.999px 31.3636px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="">Half the beads are black, and half are white. The number of beads n will always be an even number perfect square (4, 16, 36, ...). Black beads are 1, and white beads are 0, so a string might look like this.</span></span></div><div 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: 328.991px 10px; transform-origin: 328.999px 10px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; "><div 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: 0.994318px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.994318px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.994318px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.994318px; 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; "><span 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; "><span style="margin-inline-end: 0px; margin-right: 0px; "> str = [0 0 1 1 1 1 0 0 0 0 0 0 1 1 1 1]</span></span></div></div><div style="block-size: 54.446px; 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: 308.991px 27.2159px; text-align: left; transform-origin: 308.999px 27.223px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; "><img class="imageNode" style="vertical-align: baseline" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAbAAAAAxCAYAAAC71fzjAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAB3RJTUUH5AcdFREcDGe+ogAAAAd0RVh0QXV0aG9yAKmuzEgAAAAMdEVYdERlc2NyaXB0aW9uABMJISMAAAAKdEVYdENvcHlyaWdodACsD8w6AAAADnRFWHRDcmVhdGlvbiB0aW1lADX3DwkAAAAJdEVYdFNvZnR3YXJlAF1w/zoAAAALdEVYdERpc2NsYWltZXIAt8C0jwAAAAh0RVh0V2FybmluZwDAG+aHAAAAB3RFWHRTb3VyY2UA9f+D6wAAAAh0RVh0Q29tbWVudAD2zJa/AAAABnRFWHRUaXRsZQCo7tInAAAH+UlEQVR4nO2dTXIjuRGFcyZ8DhJ9AN+AIUELr3wDTYQbWs4NtINm5RvIO0HtxZxAs1VRjj6BZq8q8iBOLyTQ1WqyiEyg0ET3+yK4UbCUfIXMfKg/1E/MzAQAAAA0xs/f+gcAAAAAGmBgAAAAmgQGBgAAoElgYAAAAJoEBgYAAKBJYGAAAACaBAYGAACgSWBgAAAAmgQGBgAAoElgYAAAAJoEBgYAAKBJYGAAAACaBAYGAACgSWBgAAAAmgQGBgAAoEn+Mtc/Hv7s6f73T0REtNluiIjofHVGdmXJ/PVD8Tib7YaWiyVtthv6ePkPsn+/KB6DqJ6WyPnqjNyvV8VjEH2pxSzMLPtsbi3rz2satpvq41I6x4iI7v8VvtIy17gQ0a5mzGJZdFyIiNZ/dDRsB3r6/B8iqqMlxplDy/rz0y7GcrEkuzpvUsv7fklE1bSUrksiIuLC9M8v7K89G2PYe8/eew4hcAiBnXNsFobdpeP++SUrTvfwyGZhdnFijBACW2vZLAz7a5+tx197JqK9n1Ja+ucXNgszGSfc3s2qhYiKabErezCGXdmiWqy1X+eYMWxXtpiWfblcMsfC7d3eXI5azMIU0eIu3WRdlqyXGlrsmZ1VSxyXqVzuHh6LaJmKUUJL9/A4GafEuDAf75cltIwpamBxMJxzh7/T9+y9z9ph4faOjTHcdd1kHGP0O+xYIy41+OH2LikGEVXToi3K7uExWYu7PJwjx7Ary9Za7vt+v95RjuVq8d4f/E7f92ytraZFa/ypWmIcLdHsD2lhZg4hZDUyqRZtXU41+1JNuX9+Sa6XGlpye0wNLe8pamB2ZTmEkPTdmMhSId3DIxuTVmSxwWgGJbXh5wyKpOHnJJgkgXO0TM1WS5mYXdnJCdKYvu9VJhbHZWqCNI7hvVdrsdYmfbeGFmZWa3GXTqTFnsmPXmKTlGjRGPKxMxX7PtLJhaThj+vyFLUws7j2cyZKY4oZ2LEjr31478UNWZLAzLpi0Qw60evhvgTpoMePRIvkCK8FLalNcrfN20RJqkWcY1Z2alSjpes6sRa7srNrkUwqd9sotaROkHfbCCewmkmlpiFLJ8jxI5lcaEwyapFMYKUTZI2WQxQzMCL5v5LOKjUmyfzaxCQNWTMY0oasNRapuWiNRTIuNbVImnHE2vQJTP/8IjYWZnlDlhrLbjuBFo1JMv+/LpN/k8JYmFlklN3DI9uzOlq0uZxqlFqTlNaL1lik5qKNUeIorIiBhds7lbEwMzvnkgfeLKbPrx9CksQ5zViSxFpjkQx8LS05hUJESbO9WPQaJBMYd+lUzZhZZi5aLV3X/ZBa/LWvpmVuc9Ge4Ym1X0NLrR6TexPMT29Cs7j65YrO/3ZOzjnxtvf39/Sb/y3pu8N2IO3P/fDhA9F/02LkYBYm6Xs14nxvWpxzFEIQ///1ek1XH9NuRx62A/V9T8Yc/03vubi4oOFlSIqh1TIMA12cp93ynKPl6uqK1o/rpBjWWuq6ThxDqiWEoOoxNzc39Cl8SoqRw6nVSy414vhrTzf/vFFvP9tzYBJSd4KmEMfbrtdr9faplEicU4lzalqWy6Xq/xtjqmj5nnJsuVzOXpfSccmp/x+xXlqIM362UkMRA1suljQMg3r71JlLDsMw/JBHLXPHqBVn2A709PSk+v8xN5P1DIO+KQti5JC6z7RaNpvNyWnRItKCuhTFqWWmB8k6AflG9/CouljM/HoNLPU8qPbCN3P6eXrN7eDjT+p1o5yLxRItOTFSL+TmXANLveOpf34R3+kWCSEka8nJMWNOS4u7dJPPS01xalr8tc/SktJjtHftSesl5xoYUdpt7rlaUntMDS1TFDGwnCQmSruIz/y6s7R3IaYmV+7Ap2rJufgp0ZJjxqekhbnOnXvayZj0TtccLZI79zR12XVdcgNjPm0tfd+LtczdjHN7TA0tp9ZjDvHNnwOTPtdwbAWOr7Z5S+Aaz06JtXwnz4HV1CJtYlJjiauWSBuyxCSZdVpqPjt1qs+BSY/CNFrmNpaoZU6TZM4zyh/uObDYxFITTHIL7ZhY+Km302tW4pAsvRQ/mtUrNOZSQ4vUWJjrrioiyTHN6hVxoiTJMW0uS1YV0YyLdNLnnFNpkZwdydWSasg5WuauF82kT5tjNbRo+mUJiq+FeMzESqxTN14seCqOMUbt8pIEy9Uy94yl1lqIkmLRFGPUEpctmjIY772qGMdaUnJMa17MXy58PaeW2Pjn1pKyRmkIIVtLXMT34HcKjUtqLmuv40h7jJZT1HKSayEyf1mUzrndKtFx1WjtzHtfnLh46Ps4JVcjPzb42iLZp2VqwHP3WaqWuVejL7WyfmyW47GP419ay74ci6vR52oZ14u19istc6xGv09LqVXP/bXfrfF4SEuJFdwP9RjnXLEeE27vjuZyKS1TddnSyvo1tIwp8iDzPuK7muL7gOK7Z3IeWjsUZ9gOb58NmcVylvcOjd87NaeW9/tsjnf1jGPEOO7yY/F3aH3PWojKjv+30BJ1EJXXMmwHWn9+fewh1kyNeiGaR8un3/+9+1uNXJ6rx+x7t1mL9RKZzcAAAACAOfn5W/8AAAAAQAMMDAAAQJPAwAAAADQJDAwAAECTwMAAAAA0CQwMAABAk8DAAAAANAkMDAAAQJPAwAAAADQJDAwAAECTwMAAAAA0CQwMAABAk8DAAAAANAkMDAAAQJPAwAAAADTJ/wAewOoB4sX+EwAAAABJRU5ErkJggg==" data-image-state="image-loaded"></div><div style="block-size: 20.9091px; 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: 308.991px 10.4545px; text-align: left; transform-origin: 308.999px 10.4545px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="">Return a square matrix bx that indexes into str such that</span></span></div><div style="background-color: rgb(247, 247, 247); block-size: 80px; 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: 328.991px 40px; transform-origin: 328.999px 40px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; "><div style="background-color: rgba(0, 0, 0, 0); block-size: 20px; 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: 0.994318px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.994318px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.994318px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.994318px; 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: 328.991px 10px; transform-origin: 328.999px 10px; white-space: nowrap; "><span 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; "><span style="margin-inline-end: 0px; margin-right: 0px; "> str(bx) = [ 0 0 0 0</span></span></div><div style="background-color: rgba(0, 0, 0, 0); block-size: 20px; 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: 0.994318px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.994318px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.994318px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.994318px; 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: 328.991px 10px; transform-origin: 328.999px 10px; white-space: nowrap; "><span 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; "><span style="margin-inline-end: 0px; margin-right: 0px; ">             0 0 0 0</span></span></div><div style="background-color: rgba(0, 0, 0, 0); block-size: 20px; 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: 0.994318px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.994318px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.994318px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.994318px; 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: 328.991px 10px; transform-origin: 328.999px 10px; white-space: nowrap; "><span 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; "><span style="margin-inline-end: 0px; margin-right: 0px; ">             1 1 1 1</span></span></div><div style="background-color: rgba(0, 0, 0, 0); block-size: 20px; 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: 0.994318px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.994318px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.994318px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.994318px; 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: 328.991px 10px; transform-origin: 328.999px 10px; white-space: nowrap; "><span 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; "><span style="margin-inline-end: 0px; margin-right: 0px; ">             1 1 1 1 ]</span></span></div></div><div style="block-size: 41.8182px; 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: 308.991px 20.9091px; text-align: left; transform-origin: 308.999px 20.9091px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="">The matrix bx consists of the numbers 1 through n snaking through the box in a 4-connected sense (see Cody Problem 42705,</span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style=""> </span></span><a target='_blank' href = "https://www.mathworks.com/matlabcentral/cody/problems/42705-is-it-a-snake"><span style=""><span style="">Is It a Snake?</span></span></a><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="">).</span></span></div><div style="block-size: 20.9091px; 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: 308.991px 10.4545px; text-align: left; transform-origin: 308.999px 10.4545px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="">Here's one solution for the string shown above.</span></span></div><div style="background-color: rgb(247, 247, 247); block-size: 80px; 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: 328.991px 40px; transform-origin: 328.999px 40px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; "><div style="background-color: rgba(0, 0, 0, 0); block-size: 20px; 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: 0.994318px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.994318px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.994318px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.994318px; 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: 328.991px 10px; transform-origin: 328.999px 10px; white-space: nowrap; "><span 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; "><span style="margin-inline-end: 0px; margin-right: 0px; "> bx = [ 1  8  9 10 </span></span></div><div style="background-color: rgba(0, 0, 0, 0); block-size: 20px; 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: 0.994318px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.994318px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.994318px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.994318px; 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: 328.991px 10px; transform-origin: 328.999px 10px; white-space: nowrap; "><span 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; "><span style="margin-inline-end: 0px; margin-right: 0px; ">        2  7 12 11</span></span></div><div style="background-color: rgba(0, 0, 0, 0); block-size: 20px; 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: 0.994318px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.994318px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.994318px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.994318px; 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: 328.991px 10px; transform-origin: 328.999px 10px; white-space: nowrap; "><span 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; "><span style="margin-inline-end: 0px; margin-right: 0px; ">        3  6 13 14</span></span></div><div style="background-color: rgba(0, 0, 0, 0); block-size: 20px; 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: 0.994318px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.994318px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.994318px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.994318px; 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: 328.991px 10px; transform-origin: 328.999px 10px; white-space: nowrap; "><span 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; "><span style="margin-inline-end: 0px; margin-right: 0px; ">        4  5 16 15 ]</span></span></div></div><div style="block-size: 134.446px; 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: 308.991px 67.2159px; text-align: left; transform-origin: 308.999px 67.223px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; "><img class="imageNode" style="vertical-align: baseline" src="data:image/png;base64,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" data-image-state="image-loaded"></div><div style="block-size: 62.7273px; 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: 308.991px 31.3636px; text-align: left; transform-origin: 308.999px 31.3636px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="">In general the answers are not unique. I will be checking that bx contains the numbers 1 through n, that they form a snake, and that when used with the string of beads, they result in a tidy ones-on-the-bottom formation.</span></span></div><div style="block-size: 41.8182px; 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: 308.991px 20.9091px; text-align: left; transform-origin: 308.999px 20.9091px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="font-style: italic; ">I am grateful to the solvers of problem 42705 for giving me nice short code to use in my test suite for this problem!</span></span></div></div></div>

You are given a string of n black and white beads. Your job is to pack them neatly into a square box. "Neatly" in this case means that all the black beads are at the bottom, and all the white beads are at the top.

<<http://starchamber.com/matlab/images/beads.png>>

Half the beads are black, and half are white. The number of beads n will always be an even number perfect square (4, 16, 36, ...). Black beads are 1, and white beads are 0, so a string might look like this.

str = [0 0 1 1 1 1 0 0 0 0 0 0 1 1 1 1]
 
Return a square matrix bx that indexes into str such that

str(bx) = [ 0 0 0 0
             0 0 0 0
             1 1 1 1
             1 1 1 1 ]

The matrix bx consists of the numbers 1 through n snaking through the box in a 4-connected sense (see Cody Problem 42705, <https://www.mathworks.com/matlabcentral/cody/problems/42705-is-it-a-snake Is It a Snake?>).

Here's one solution for the string shown above.

bx = [ 1  8  9 10 
        2  7 12 11
        3  6 13 14
        4  5 16 15 ]
 
In general the answers are not unique. I will be checking that bx contains the numbers 1 through n, that they form a snake, and that when used with the string of beads, they result in a tidy ones-on-the-bottom formation.

_I am grateful to the solvers of problem 42705 for giving me nice short code to use in my test suite for this problem!_

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Alfonso Nieto-Castanon on 23 Jan 2016

note: the "is it sneaky?" part of the testsuite is not really a complete test (e.g. the matrix [1 2 3; 4 5 6; 7 8 9] would pass that). Using "complex(I,J)" instead of "I+J" would fix this.

Ned Gulley on 25 Jan 2016

Thanks Alfonso! Advice taken.

Ned Gulley on 25 Jan 2016

You also gave me a new test for "Is it Snaky (42705)" that knocked out the current leader.

Carl Witthoft on 27 Jan 2016

Can you clarify: does the partial sequence 1-1-0-1 force a failure? Your diagram doesn't seem to allow diagonal paths, so it seems that a single 0 or 1 causes failure.

Ned Gulley on 28 Jan 2016

Hi Carl: All sequences are generated from successful packings. So you wouldn't get 1-1-0-1 because, as you note, it couldn't be packed successfully. In other words, this situation shouldn't come up.

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Problem 42708. Placing Beads Neatly in a Box

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