Problem 306. Eight Queens Solution Checker

Created by Steve Eddins

Solve Later

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That is, no two queens can share the same row, column, or diagonal. The diagram below is one possible solution:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></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=\"relationshipId\" w:val=\"rId1\"/></w:customXmlPr></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Your function should take an 8-by-8 matrix of 0s and 1s, where the 1s represent the position of the queens, and return a logical 1 if the solution is valid or a logical 0 otherwise.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>EXAMPLE 1</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ in1 = [ ...\n 0 0 0 1 0 0 0 0\n 0 0 0 0 0 0 1 0\n 0 0 1 0 0 0 0 0\n 0 0 0 0 0 0 0 1\n 0 1 0 0 0 0 0 0\n 0 0 0 0 1 0 0 0\n 1 0 0 0 0 0 0 0\n 0 0 0 0 0 1 0 0 ];\n\n isEightQueensSolution(in1)]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>returns 1.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>EXAMPLE 2</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ in2 = [ ...\n 0 0 0 1 0 0 0 0\n 0 0 0 0 0 0 1 0\n 0 0 1 0 0 0 0 0\n 0 0 0 0 0 0 0 1\n 0 1 0 0 0 0 0 0\n 1 0 0 0 0 0 0 0\n 0 0 0 0 1 0 0 0\n 0 0 0 0 0 1 0 0 ];\n\n isEightQueensSolution(in2)]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>returns 0. (Notice that the queens on the bottom two rows share a diagonal.)</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 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"}]}

Write a function to verify whether an arrangement of queens on a chessboard is a valid solution to the classic <a href="http://en.wikipedia.org/wiki/Eight_queens_puzzle">eight queens problem</a>.In the eight queens problem, eight queens must be placed on a chessboard such that no two queens attack each other. That is, no two queens can share the same row, column, or diagonal. The diagram below is one possible solution:<img src="http://blogs.mathworks.com/images/steve/cody/eight-queens-sample-solution.png">Your function should take an 8-by-8 matrix of 0s and 1s, where the 1s represent the position of the queens, and return a logical 1 if the solution is valid or a logical 0 otherwise.EXAMPLE 1<pre> in1 = [ ...
 0 0 0 1 0 0 0 0
 0 0 0 0 0 0 1 0
 0 0 1 0 0 0 0 0
 0 0 0 0 0 0 0 1
 0 1 0 0 0 0 0 0
 0 0 0 0 1 0 0 0
 1 0 0 0 0 0 0 0
 0 0 0 0 0 1 0 0 ];</pre><pre> isEightQueensSolution(in1)</pre>returns 1.EXAMPLE 2<pre> in2 = [ ...
 0 0 0 1 0 0 0 0
 0 0 0 0 0 0 1 0
 0 0 1 0 0 0 0 0
 0 0 0 0 0 0 0 1
 0 1 0 0 0 0 0 0
 1 0 0 0 0 0 0 0
 0 0 0 0 1 0 0 0
 0 0 0 0 0 1 0 0 ];</pre><pre> isEightQueensSolution(in2)</pre>returns 0. (Notice that the queens on the bottom two rows share a diagonal.)

Write a function to verify whether an arrangement of queens on a chessboard is a valid solution to the classic <http://en.wikipedia.org/wiki/Eight_queens_puzzle eight queens problem>.

In the eight queens problem, eight queens must be placed on a chessboard such that no two queens attack each other. That is, no two queens can share the same row, column, or diagonal. The diagram below is one possible solution:

<<http://blogs.mathworks.com/images/steve/cody/eight-queens-sample-solution.png>>

Your function should take an 8-by-8 matrix of 0s and 1s, where the 1s represent the position of the queens, and return a logical 1 if the solution is valid or a logical 0 otherwise.

*EXAMPLE 1*

in1 = [ ...
       0 0 0 1 0 0 0 0
       0 0 0 0 0 0 1 0
       0 0 1 0 0 0 0 0
       0 0 0 0 0 0 0 1
       0 1 0 0 0 0 0 0
       0 0 0 0 1 0 0 0
       1 0 0 0 0 0 0 0
       0 0 0 0 0 1 0 0 ];
   
   isEightQueensSolution(in1)

returns 1.

*EXAMPLE 2*

in2 = [ ...
       0 0 0 1 0 0 0 0
       0 0 0 0 0 0 1 0
       0 0 1 0 0 0 0 0
       0 0 0 0 0 0 0 1
       0 1 0 0 0 0 0 0
       1 0 0 0 0 0 0 0
       0 0 0 0 1 0 0 0
       0 0 0 0 0 1 0 0 ];
   
   isEightQueensSolution(in2)

returns 0. (Notice that the queens on the bottom two rows share a diagonal.)

Solve

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Last Solution submitted on Aug 30, 2021

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2 Comments

2 Comments

@bmtran (Bryant Tran) on 11 Feb 2012

This question is kind of a duplicate of Ned's N-queens checker: http://www.mathworks.com/matlabcentral/cody/problems/113-n-queens-checker

Steve Eddins on 12 Feb 2012

Oops, I didn't know about that one!

Solution Comments

Solution 2071007

1 Comment

1 Comment

Paresh yeole on 27 Dec 2019

Why the first test case fails? It passes in the matlab.

Solution 1327523

1 Comment

1 Comment

yurenchu on 4 Nov 2017

This is a flawed solution. For example, when the queen positions are {a2, b4, c2, c6, d8, e3, f1, g7, h5} (which is the same as the image in the description, but with a 9th queen added at c2), this code would return 'True' while the correct answer is obviously 'False'.

Solution 347969

3 Comments

3 Comments

Andrew Newell on 25 Apr 2014

The beauty of this solution is that you can use it for any other side board (e.g., isEightQueensSolution([1 0; 0 1]) ).

alex on 31 Aug 2015

how can i view this solution, also, can you please explain to me why the tenth test case is false, i dont think it is wrong.

Steve Eddins on 1 Sep 2015

Alex, the tenth case case is false because there are only seven queens on the board.

Solution 37413

5 Comments

5 Comments

Show 2 older comments

Steve Eddins on 11 Feb 2012

Doesn't this kind of trick get boring after a while?

@bmtran (Bryant Tran) on 11 Feb 2012

actually, this is the first time i've used it without essentially copying Alfonso's code, so it's still new and fresh for me =P

Benjamin Kraus on 12 Feb 2012

Can someone explain to me how this function works (even if it is a trick)? I'm trying to parse through the code, but how it works isn't clear to me.

@bmtran (Bryant Tran) on 12 Feb 2012

the sparse function places the values (third input) into the row and column specified, 1st and second inputs respectively. if there are any overlapping coordinates then it sums them, so I created a matrix that, when fed into sparse, would sum the rows, sum the columns, and sum the diagonals in each direction. Then I Cody-fied it (teehee) by changing these indices into a string of characters, which Cody sizes as small, and subtracting a base character from it. does that make sense now?

@bmtran (Bryant Tran) on 12 Feb 2012

it might make more sense to look at one of my other solutions that uses the str2num function instead of the letter thing...

Solution 37396

1 Comment

1 Comment

Mark on 30 May 2012

I think you also need to check the diagonals of fliplr(a). The tests did not include multiple queens on any of those diagonals.

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