Problem 306. Eight Queens Solution Checker

Steve Eddins

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Write a function to verify whether an arrangement of queens on a chessboard is a valid solution to the classic 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:
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.)