Problem 96. Knight's Tour Checker

Created by Cody Team

Solve Later

{"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

Solve

Solution Stats

1812 Solutions
909 Solvers

Last Solution submitted on Oct 03, 2022

Last 200 Solutions

Problem Comments

4 Comments

4 Comments

Show 1 older comment

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

Solution Comments

Solution 8794005

1 Comment

1 Comment

士元梁 on 25 Jul 2022

quite interesting

Solution 6621409

Solution 712537

1 Comment

1 Comment

Hao li on 26 May 2016

nice solution!

Solution 492529

3 Comments

3 Comments

Carl Witthoft on 1 Dec 2015

wtf?

Jan Orwat on 2 Dec 2015

1774||ggl.it :)

Alfonso Nieto-Castanon on 2 Dec 2015

interestingly, 1774-ggl == leet-ssh

Solution 329299

1 Comment

1 Comment

Ted on 5 Oct 2013

should change the test suite to also include moves of 1,1 or 2,2 which this solution would not prevent...

Solution 119322

1 Comment

1 Comment

Nigel Davies on 7 Aug 2012

Why bother?

Problem Recent Solvers909

Problem Tags

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!