n皇后问题（python）

最新推荐文章于 2025-11-25 11:31:36 发布

原创最新推荐文章于 2025-11-25 11:31:36 发布 · 223 阅读

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文章标签：

#算法 #n皇后 #python

本文介绍了一种解决N皇后问题的递归算法，通过深度优先搜索策略在棋盘上放置皇后，确保任意两个皇后不处于同一行、列或对角线上。算法详细展示了如何检查每个位置是否合法，并在找到解决方案时记录结果。

def isValid(board, x, y):
    for i in range(x + 1):
        for j in range(len(board[i])):
            if board[i][j] and (j == y or abs(x - i) == abs(y - j)):
                return False
    return True


def nQueenProblem(board, row, n, res):
    if row == n:
        t = []
        for i in range(len(board)):
            for j in range(len(board[i])):
                if not board[i][j] == 0:
                    t.append(j + 1)
        res.append(t)
        # res.append(copy.deepcopy(board))
        return

    for j in range(n):
        if isValid(board, row, j):
            board[row][j] = 1
            nQueenProblem(board, row + 1, n, res)
            board[row][j] = 0

    return res



if __name__ == '__main__':
    n = 10
    board = []
    for i in range(n):
        board.append([])
        for j in range(n):
            board[i].append(0)
    res = []
    nQueenProblem(board, 0, n, res)
    i = 0
    while i < len(res):
        if i % 5 == 0:
            print '\r'
        print res[i],
        i += 1

    if len(res) == 0:
        print 'No Solution'