Problem 42842. The sliding puzzle: 15

Created by HH

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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>If you are unfamiliar with the sliding puzzle, enter the command</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>fifteen</w:t></w:r><w:r><w:t> in your MATLAB command window (or search online, of course). In this problem you are tasked with solving the puzzle.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Given a scrambled classic 4-by-4 sliding puzzle, return a set of moves that solves it.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>The puzzle is represented by a size [4 4] array, p, with integers from 1 to 15 representing the different tiles, and 0 representing the open slot. A single move is represented by an integer that is the linear index of the the tile you wish to slide into an adjacent open slot. A solution is represented by a row vector, m, of moves, the application of which results in a correctly arranged puzzle.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>The solution does not have to be efficient. It must simply result in a correctly solved puzzle. Illegal moves, such as trying to slide a tile that is not adjacent to the open slot, will be ignored.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Example: (the leading zeros are added only for easier visualization)</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ p = [ 01 02 03 04;\n\n 05 10 06 07;\n\n 09 00 11 08;\n\n 13 14 15 12]\n\n m = [6 10 14 15 16]]]></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>"}]}

If you are unfamiliar with the sliding puzzle, enter the command fifteen in your MATLAB command window (or search online, of course). In this problem you are tasked with solving the puzzle.Given a scrambled classic 4-by-4 sliding puzzle, return a set of moves that solves it.The puzzle is represented by a size [4 4] array, p, with integers from 1 to 15 representing the different tiles, and 0 representing the open slot. A single move is represented by an integer that is the linear index of the the tile you wish to slide into an adjacent open slot. A solution is represented by a row vector, m, of moves, the application of which results in a correctly arranged puzzle.The solution does not have to be efficient. It must simply result in a correctly solved puzzle. Illegal moves, such as trying to slide a tile that is not adjacent to the open slot, will be ignored.Example: (the leading zeros are added only for easier visualization)<pre> p = [ 01 02 03 04;</pre><pre> 05 10 06 07;</pre><pre> 09 00 11 08;</pre><pre> 13 14 15 12]</pre><pre> m = [6 10 14 15 16]</pre>

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105 Solutions
19 Solvers

Last Solution submitted on Jul 26, 2020

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3 Comments

Are Mjaavatten on 14 Jul 2018

The most challenging cody problem I have tried so far. Had to teach myself some stuff that I knew little about before, That is a quality indicator!

HH on 15 Jul 2018

Thanks, Are. Now try problem 44376. https://www.mathworks.com/matlabcentral/cody/problems/44376

Sophia Nguyen on 21 Feb 2020

I have tried repeatedly. The code works well and only took 2s max in my computer, but the system keeps outputting error caused by long running matlab code.

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15 fifteen puzzle sliding

Problem 42842. The sliding puzzle: 15

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Problem 42842. The sliding puzzle: 15

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