Problem 45498. Trace the path of a harmful chemical in an ecological network

Created by Karl Ezra Pilario

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{"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":"<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>An ecological network consists of the cycles of nature, such as the water cycle, the carbon cycle, the oxygen cycle, etc. Due to human activities, harmful chemicals (or persistent pollutants) are now entering these cycles and may stay there forever. Your job is to track a specific unknown chemical inside an ecological network.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>For this problem, a network involves</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>N</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>sites</w:t></w:r><w:r><w:t> in nature, labelled as</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>Site</w:t></w:r><w:r><w:t> 1,</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>Site</w:t></w:r><w:r><w:t> 2, ...,</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>Site</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>N</w:t></w:r><w:r><w:t>. Researchers have identified an ecological network for you, which is given as a [1 x</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>N</w:t></w:r><w:r><w:t>] row vector called</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>P</w:t></w:r><w:r><w:t>. The network is read as follows: \"A chemical that enters</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>Site i</w:t></w:r><w:r><w:t> always end up at</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>Site</w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t> </w:t></w:r><w:r><w:rPr><w:b/><w:i/></w:rPr><w:t>P</w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>(i)</w:t></w:r><w:r><w:t>\". Consider the following example:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[If a chemical enters Site: 1 2 3 4 5\n it will end up at Site: P = [3 1 5 2 4]]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>If a harmful chemical enters the ecological network from</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>Site 2</w:t></w:r><w:r><w:t>, it will be traced to</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>Site 1</w:t></w:r><w:r><w:t> (which is</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>P</w:t></w:r><w:r><w:t>(2)), then eventually at</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>Site 3</w:t></w:r><w:r><w:t>, then at</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>Site 5</w:t></w:r><w:r><w:t>, then at</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>Site 4</w:t></w:r><w:r><w:t>, then back to</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>Site 2</w:t></w:r><w:r><w:t>. Hence, the path of this chemical is [2 1 3 5 4].</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Write a function that takes a vector</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>P</w:t></w:r><w:r><w:t> and a starting site</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>S</w:t></w:r><w:r><w:t>. Output the path of the chemical after it enters</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>Site</w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t> </w:t></w:r><w:r><w:rPr><w:b/><w:i/></w:rPr><w:t>S</w:t></w:r><w:r><w:t> in the given ecological network. You are ensured that:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>P</w:t></w:r><w:r><w:t> is always a permutation of integers 1 to</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>N</w:t></w:r><w:r><w:t>.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>2 &lt;=</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>N</w:t></w:r><w:r><w:t> &lt;= 100</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>1 &lt;=</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>S</w:t></w:r><w:r><w:t> &lt;=</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>N</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>See sample test cases:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[>> trace_chemical([3 1 5 2 4],2)\n ans = \n 2 1 3 5 4\n>> trace_chemical([3 1 5 2 4],1)\n ans =\n 1 3 5 4 2\n>> trace_chemical([4 1 6 5 2 3],1)\n ans =\n 1 4 5 2]]></w:t></w:r></w:p></w:body></w:document>"},{"partUri":"/matlab/output.xml","contentType":"text/xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\" ?><embeddedOutputs><metaData><evaluationState>manual</evaluationState><layoutState>code</layoutState><outputStatus>ready</outputStatus></metaData><outputArray type=\"array\"/><regionArray type=\"array\"/></embeddedOutputs>"}]}

An ecological network consists of the cycles of nature, such as the water cycle, the carbon cycle, the oxygen cycle, etc. Due to human activities, harmful chemicals (or persistent pollutants) are now entering these cycles and may stay there forever. Your job is to track a specific unknown chemical inside an ecological network.For this problem, a network involves N sites in nature, labelled as Site 1, Site 2, ..., Site N. Researchers have identified an ecological network for you, which is given as a [1 x N] row vector called P. The network is read as follows: "A chemical that enters Site i always end up at Site P(i)". Consider the following example:<pre class="language-matlab">If a chemical enters Site: 1 2 3 4 5
 it will end up at Site: P = [3 1 5 2 4]
</pre>If a harmful chemical enters the ecological network from Site 2, it will be traced to Site 1 (which is P(2)), then eventually at Site 3, then at Site 5, then at Site 4, then back to Site 2. Hence, the path of this chemical is [2 1 3 5 4].Write a function that takes a vector P and a starting site S. Output the path of the chemical after it enters Site S in the given ecological network. You are ensured that:<ul><li>P is always a permutation of integers 1 to N.</li><li>2 &lt;= N &lt;= 100</li><li>1 &lt;= S &lt;= N</li></ul>See sample test cases:<pre class="language-matlab">&gt;&gt; trace_chemical([3 1 5 2 4],2)
 ans = 
 2 1 3 5 4
&gt;&gt; trace_chemical([3 1 5 2 4],1)
 ans =
 1 3 5 4 2
&gt;&gt; trace_chemical([4 1 6 5 2 3],1)
 ans =
 1 4 5 2
</pre>

An ecological network consists of the cycles of nature, such as the water cycle, the carbon cycle, the oxygen cycle, etc. Due to human activities, harmful chemicals (or persistent pollutants) are now entering these cycles and may stay there forever. Your job is to track a specific unknown chemical inside an ecological network.

For this problem, a network involves *N* _sites_ in nature, labelled as _Site_ 1, _Site_ 2, ..., _Site_ *N*. Researchers have identified an ecological network for you, which is given as a [1 x *N*] row vector called *P*. The network is read as follows: "A chemical that enters _Site i_ always end up at _Site *P*(i)_". Consider the following example:

If a chemical enters Site:      1 2 3 4 5
     it will end up at Site: P = [3 1 5 2 4]
  
If a harmful chemical enters the ecological network from _Site 2_, it will be traced to _Site 1_ (which is *P*(2)), then eventually at _Site 3_, then at _Site 5_, then at _Site 4_, then back to _Site 2_. Hence, the path of this chemical is [2 1 3 5 4].

Write a function that takes a vector *P* and a starting site *S*. Output the path of the chemical after it enters _Site *S*_ in the given ecological network. You are ensured that:

* *P* is always a permutation of integers 1 to *N*.
* 2 <= *N* <= 100
* 1 <= *S* <= *N*

See sample test cases:

>> trace_chemical([3 1 5 2 4],2)
     ans = 
         2 1 3 5 4
>> trace_chemical([3 1 5 2 4],1)
     ans =
         1 3 5 4 2
>> trace_chemical([4 1 6 5 2 3],1)
     ans =
         1 4 5 2

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Problem 45498. Trace the path of a harmful chemical in an ecological network

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