The Matlab function fifteen initializes the 4x4 array with randperm(16), which produces 50% unsolvable puzzles. A two stage parity check from wikipedia details the method of distance of the empty cell to index 16 plus the number of swaps to produce a 1:16 sequence must be Even to be a valid puzzle. The 16 is the empty space.
Given a 4x4 matrix determine if it is valid(1) or invalid(0).
1 2 3 4 1 2 3 4 5 6 7 8 5 6 7 8 9 10 11 12 9 10 11 12 13 15 14 16 Invalid(0) 13 14 16 15 Valid(1)
Who can come up with the best fifteen_check to fix the fifteen function?
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