Problem 96. Knight's Tour Checker

Created by Cody Team

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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>Given a matrix a, determine whether or not a legal</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"http://en.wikipedia.org/wiki/Knight's_tour\"><w:r><w:t>knight's tour</w:t></w:r></w:hyperlink><w:r><w:t> is present. The knight's tour always follows the pattern 1, 2, 3, ... but it need not fill the entire matrix. Any unused squares contain zeros. Your function should return true if the counting sequence from 1 to n represents a knight's tour, and false if not.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Example</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>The matrix a as given below is a legal knight's tour. The middle square is unreachable, but since it contains a zero, it satisfies the condition. The function should return TRUE.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[7 2 5\n4 0 8\n1 6 3]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Here is another legal (if short) knight's tour. The test suite will always contain at least one move (i.e. the counting sequence [1 2]). Note the matrix is not required to be square.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[1 0 0\n0 0 2]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Here is an illegal knight's tour. Everything is fine up until the jump from 14 to 15, which is illegal because it jumps from row 4 to row 1.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ 15 5 12 3\n 0 2 9 6\n 8 11 4 13\n 1 14 7 10]]></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>"}]}

Given a matrix a, determine whether or not a legal <a href="http://en.wikipedia.org/wiki/Knight's_tour">knight's tour</a> is present. The knight's tour always follows the pattern 1, 2, 3, ... but it need not fill the entire matrix. Any unused squares contain zeros. Your function should return true if the counting sequence from 1 to n represents a knight's tour, and false if not.ExampleThe matrix a as given below is a legal knight's tour. The middle square is unreachable, but since it contains a zero, it satisfies the condition. The function should return TRUE.<pre class="language-matlab">7 2 5
4 0 8
1 6 3
</pre>Here is another legal (if short) knight's tour. The test suite will always contain at least one move (i.e. the counting sequence [1 2]). Note the matrix is not required to be square.<pre class="language-matlab">1 0 0
0 0 2
</pre>Here is an illegal knight's tour. Everything is fine up until the jump from 14 to 15, which is illegal because it jumps from row 4 to row 1.<pre> 15 5 12 3
 0 2 9 6
 8 11 4 13
 1 14 7 10</pre>

Given a matrix a, determine whether or not a legal <http://en.wikipedia.org/wiki/Knight's_tour knight's tour> is present. The knight's tour always follows the pattern 1, 2, 3, ... but it need not fill the entire matrix. Any unused squares contain zeros. Your function should return true if the counting sequence from 1 to n represents a knight's tour, and false if not.

Example

The matrix a as given below is a legal knight's tour. The middle square is unreachable, but since it contains a zero, it satisfies the condition. The function should return TRUE.

7     2     5
  4     0     8
  1     6     3

Here is another legal (if short) knight's tour. The test suite will always contain at least one move (i.e. the counting sequence [1 2]). Note the matrix is not required to be square.

1     0     0
  0     0     2
 
Here is an illegal knight's tour. Everything is fine up until the jump from 14 to 15, which is illegal because it jumps from row 4 to row 1.

15     5    12     3
  0     2     9     6
  8    11     4    13
  1    14     7    10

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Last Solution submitted on Sep 29, 2023

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James on 15 Jun 2012

I think several of the solutions to this problem would return a false positive on the vector [1 0 0 2].

Jean-Marie Sainthillier on 9 Aug 2012

I like this problem and I like chess.

BluePoseidon1643 on 20 Dec 2016

Fantastic problem since it offers introductions to graph theory, specifically Hamiltonian path problems, time complexity, neural network solutions, and Warnsdorf's Rule. Thanks

Sanzhar Askaruly on 9 Aug 2019

easier than I expected

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