enumeration - N+1 queens algorithm -


i'm looking improve speed of algorithm calculate number of solutions n+1 queens problem (place n+1 queens on nxn chessboard 1 pawn). i'm using brute-force combined backtracking, first place pawn on random location on board (without edges , corners of square without edges) , after start place queens using backtracking. method easy, slow. algorithms faster?

i thinking of first placing pawn , 4 queens on each side of pawn, i'm not sure improve calculation speed.

as looking count all solutions of problem, placing pawn first on random position not do. have place pawn on each position. believe best algorithm here backtracking, still can optimizations. in n-queen problem improtant bit take advantage of symmetry of solutions, guess can here well. having solution, of 4 rotatations , mirror images solutions.


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