numQueens = 8 solutions = [] def printBoard(placed): for c in placed: r = ['. '] * 8 r[c] = 'o ' print ''.join(r) print '-' * 16 def isDiagonal(r1, c1, r2, c2): d = r2 - r1 # Always positive since r1 is always less. return c2 - d == c1 or c2 + d == c1 def isInvalid(placed, c): for o_r, o_c in enumerate(placed): if isDiagonal(o_r, o_c, len(placed), c): return True def placeQueen(valid, placed): if len(placed) == numQueens: return solutions.append(placed[:]) for i, c in enumerate(valid): if isInvalid(placed, c): continue placed.append(c) placeQueen(valid[:i] + valid[i+1:], placed) placed.pop() placeQueen(range(8), []) for solution in solutions: printBoard(solution)
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