2020-12-22

2020-12-22 23:01:51 阅读：230 来源： 互联网

标签：12 22 section mark range 2020 放置皇后 sign

八皇后问题——经典再现

在8×8的方格中，放置8个皇后，使其相互不冲突，即任意一个皇后所在的行、列和斜线均无其它皇后。
以下是其中两种放置方法。

 0   0   0   0   1   0   0   0
 0   0   0   0   0   0   0   2
 0   0   0   3   0   0   0   0
 4   0   0   0   0   0   0   0
 0   0   0   0   0   0   5   0
 0   6   0   0   0   0   0   0
 0   0   0   0   0   7   0   0
 0   0   8   0   0   0   0   0

 1   0   0   0   0   0   0   0
 0   0   0   0   2   0   0   0
 0   0   0   0   0   0   0   3
 0   0   0   0   0   4   0   0
 0   0   5   0   0   0   0   0
 0   0   0   0   0   0   6   0
 0   7   0   0   0   0   0   0
 0   0   0   8   0   0   0   0

计算总共有多少种放置方法，并打印，皇后的编号从1-8。
这是经典的递归问题。与前文蛇形排列极为相似。不多解释。

def dfs(section):
    global n
    if section == 8:  # 递归返回条件，即一种放置方法成功后返回寻找另外一种放置方法，直至找到所有放置方法
        n += 1
        show()
        return
    # 试尝在section行放置皇后
    for k in range(8):  # k是列
        sign = 0
        for p in range(8):
            if mark[p][k] > 0:   # 如果k列已经放置了皇后，往后寻找其它合适位置
                sign = 1
                break
            for q in range(8):
                if mark[p][q] > 0 and abs(p - section) == abs(q - k):  # 如果斜线遭遇其他皇后，往后寻找其它合适位置
                    sign = 1
                    break
            if sign == 1:
                break
        if sign == 0:
            mark[section][k] = section + 1  # 设置皇后编号
            dfs(section + 1)  # 进入下一行递归搜索
            mark[section][k] = 0  # 返回时清除编号


def show():
    for _j in range(8):
        for _i in range(8):
            print("{0:2}".format(mark[_j][_i]), end="  ")
        print("")
    print("")


if __name__ == '__main__':
    n = 0
    mark = [[0 for _ in range(8)] for _ in range(8)]
    for i in range(8):
        mark[0][i] = 1  # 从第一行第一列（下标0,0）开始放置，首标记设置为1
        dfs(1)  # 开始递归搜索
        mark[0][i] = 0  # 重新搜索前先清除标记
    print("共有{0}种放置方法。".format(n))

D:\Python\Python38\python.exe D:/Python/study/eight.py
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 0   0   7   0   0   0   0   0  
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 0   6   0   0   0   0   0   0  
 0   0   0   7   0   0   0   0  
 0   0   0   0   0   8   0   0  

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 0   0   0   0   0   0   0   4  
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 0   0   0   0   0   0   6   0  
 0   0   0   7   0   0   0   0  
 0   0   0   0   0   8   0   0  

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 0   0   0   0   2   0   0   0  
 0   3   0   0   0   0   0   0  
 0   0   0   0   0   0   0   4  
 0   0   0   0   0   5   0   0  
 0   0   0   6   0   0   0   0  
 0   0   0   0   0   0   7   0  
 8   0   0   0   0   0   0   0  

 0   0   1   0   0   0   0   0  
 0   0   0   0   2   0   0   0  
 0   0   0   0   0   0   3   0  
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 0   0   1   0   0   0   0   0  
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 4   0   0   0   0   0   0   0  
 0   0   0   0   5   0   0   0  
 0   0   0   0   0   0   6   0  
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 0   0   0   8   0   0   0   0  

 0   0   1   0   0   0   0   0  
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 0   0   0   1   0   0   0   0  
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 0   0   0   1   0   0   0   0  
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 0   6   0   0   0   0   0   0  
 0   0   0   0   0   7   0   0  
 0   0   8   0   0   0   0   0  

 0   0   0   1   0   0   0   0  
 0   0   0   0   0   0   0   2  
 0   0   0   0   3   0   0   0  
 0   0   4   0   0   0   0   0  
 5   0   0   0   0   0   0   0  
 0   0   0   0   0   0   6   0  
 0   7   0   0   0   0   0   0  
 0   0   0   0   0   8   0   0  

 0   0   0   0   1   0   0   0  
 2   0   0   0   0   0   0   0  
 0   0   0   3   0   0   0   0  
 0   0   0   0   0   4   0   0  
 0   0   0   0   0   0   0   5  
 0   6   0   0   0   0   0   0  
 0   0   0   0   0   0   7   0  
 0   0   8   0   0   0   0   0  

 0   0   0   0   1   0   0   0  
 2   0   0   0   0   0   0   0  
 0   0   0   0   0   0   0   3  
 0   0   0   4   0   0   0   0  
 0   5   0   0   0   0   0   0  
 0   0   0   0   0   0   6   0  
 0   0   7   0   0   0   0   0  
 0   0   0   0   0   8   0   0  

 0   0   0   0   1   0   0   0  
 2   0   0   0   0   0   0   0  
 0   0   0   0   0   0   0   3  
 0   0   0   0   0   4   0   0  
 0   0   5   0   0   0   0   0  
 0   0   0   0   0   0   6   0  
 0   7   0   0   0   0   0   0  
 0   0   0   8   0   0   0   0  

 0   0   0   0   1   0   0   0  
 0   2   0   0   0   0   0   0  
 0   0   0   3   0   0   0   0  
 0   0   0   0   0   4   0   0  
 0   0   0   0   0   0   0   5  
 0   0   6   0   0   0   0   0  
 7   0   0   0   0   0   0   0  
 0   0   0   0   0   0   8   0  

 0   0   0   0   1   0   0   0  
 0   2   0   0   0   0   0   0  
 0   0   0   3   0   0   0   0  
 0   0   0   0   0   0   4   0  
 0   0   5   0   0   0   0   0  
 0   0   0   0   0   0   0   6  
 0   0   0   0   0   7   0   0  
 8   0   0   0   0   0   0   0  

 0   0   0   0   1   0   0   0  
 0   2   0   0   0   0   0   0  
 0   0   0   0   0   3   0   0  
 4   0   0   0   0   0   0   0  
 0   0   0   0   0   0   5   0  
 0   0   0   6   0   0   0   0  
 0   0   0   0   0   0   0   7  
 0   0   8   0   0   0   0   0  

 0   0   0   0   1   0   0   0  
 0   2   0   0   0   0   0   0  
 0   0   0   0   0   0   0   3  
 4   0   0   0   0   0   0   0  
 0   0   0   5   0   0   0   0  
 0   0   0   0   0   0   6   0  
 0   0   7   0   0   0   0   0  
 0   0   0   0   0   8   0   0  

 0   0   0   0   1   0   0   0  
 0   0   2   0   0   0   0   0  
 3   0   0   0   0   0   0   0  
 0   0   0   0   0   4   0   0  
 0   0   0   0   0   0   0   5  
 0   6   0   0   0   0   0   0  
 0   0   0   7   0   0   0   0  
 0   0   0   0   0   0   8   0  

 0   0   0   0   1   0   0   0  
 0   0   2   0   0   0   0   0  
 3   0   0   0   0   0   0   0  
 0   0   0   0   0   0   4   0  
 0   5   0   0   0   0   0   0  
 0   0   0   0   0   0   0   6  
 0   0   0   0   0   7   0   0  
 0   0   0   8   0   0   0   0  

 0   0   0   0   1   0   0   0  
 0   0   2   0   0   0   0   0  
 0   0   0   0   0   0   0   3  
 0   0   0   4   0   0   0   0  
 0   0   0   0   0   0   5   0  
 6   0   0   0   0   0   0   0  
 0   0   0   0   0   7   0   0  
 0   8   0   0   0   0   0   0  

 0   0   0   0   1   0   0   0  
 0   0   0   0   0   0   2   0  
 3   0   0   0   0   0   0   0  
 0   0   4   0   0   0   0   0  
 0   0   0   0   0   0   0   5  
 0   0   0   0   0   6   0   0  
 0   0   0   7   0   0   0   0  
 0   8   0   0   0   0   0   0  

 0   0   0   0   1   0   0   0  
 0   0   0   0   0   0   2   0  
 3   0   0   0   0   0   0   0  
 0   0   0   4   0   0   0   0  
 0   5   0   0   0   0   0   0  
 0   0   0   0   0   0   0   6  
 0   0   0   0   0   7   0   0  
 0   0   8   0   0   0   0   0  

 0   0   0   0   1   0   0   0  
 0   0   0   0   0   0   2   0  
 0   3   0   0   0   0   0   0  
 0   0   0   4   0   0   0   0  
 0   0   0   0   0   0   0   5  
 6   0   0   0   0   0   0   0  
 0   0   7   0   0   0   0   0  
 0   0   0   0   0   8   0   0  

 0   0   0   0   1   0   0   0  
 0   0   0   0   0   0   2   0  
 0   3   0   0   0   0   0   0  
 0   0   0   0   0   4   0   0  
 0   0   5   0   0   0   0   0  
 6   0   0   0   0   0   0   0  
 0   0   0   7   0   0   0   0  
 0   0   0   0   0   0   0   8  

 0   0   0   0   1   0   0   0  
 0   0   0   0   0   0   2   0  
 0   3   0   0   0   0   0   0  
 0   0   0   0   0   4   0   0  
 0   0   5   0   0   0   0   0  
 6   0   0   0   0   0   0   0  
 0   0   0   0   0   0   0   7  
 0   0   0   8   0   0   0   0  

 0   0   0   0   1   0   0   0  
 0   0   0   0   0   0   2   0  
 0   0   0   3   0   0   0   0  
 4   0   0   0   0   0   0   0  
 0   0   5   0   0   0   0   0  
 0   0   0   0   0   0   0   6  
 0   0   0   0   0   7   0   0  
 0   8   0   0   0   0   0   0  

 0   0   0   0   1   0   0   0  
 0   0   0   0   0   0   0   2  
 0   0   0   3   0   0   0   0  
 4   0   0   0   0   0   0   0  
 0   0   5   0   0   0   0   0  
 0   0   0   0   0   6   0   0  
 0   7   0   0   0   0   0   0  
 0   0   0   0   0   0   8   0  

 0   0   0   0   1   0   0   0  
 0   0   0   0   0   0   0   2  
 0   0   0   3   0   0   0   0  
 4   0   0   0   0   0   0   0  
 0   0   0   0   0   0   5   0  
 0   6   0   0   0   0   0   0  
 0   0   0   0   0   7   0   0  
 0   0   8   0   0   0   0   0  

 0   0   0   0   0   1   0   0  
 2   0   0   0   0   0   0   0  
 0   0   0   0   3   0   0   0  
 0   4   0   0   0   0   0   0  
 0   0   0   0   0   0   0   5  
 0   0   6   0   0   0   0   0  
 0   0   0   0   0   0   7   0  
 0   0   0   8   0   0   0   0  

 0   0   0   0   0   1   0   0  
 0   2   0   0   0   0   0   0  
 0   0   0   0   0   0   3   0  
 4   0   0   0   0   0   0   0  
 0   0   5   0   0   0   0   0  
 0   0   0   0   6   0   0   0  
 0   0   0   0   0   0   0   7  
 0   0   0   8   0   0   0   0  

 0   0   0   0   0   1   0   0  
 0   2   0   0   0   0   0   0  
 0   0   0   0   0   0   3   0  
 4   0   0   0   0   0   0   0  
 0   0   0   5   0   0   0   0  
 0   0   0   0   0   0   0   6  
 0   0   0   0   7   0   0   0  
 0   0   8   0   0   0   0   0  

 0   0   0   0   0   1   0   0  
 0   0   2   0   0   0   0   0  
 3   0   0   0   0   0   0   0  
 0   0   0   0   0   0   4   0  
 0   0   0   0   5   0   0   0  
 0   0   0   0   0   0   0   6  
 0   7   0   0   0   0   0   0  
 0   0   0   8   0   0   0   0  

 0   0   0   0   0   1   0   0  
 0   0   2   0   0   0   0   0  
 3   0   0   0   0   0   0   0  
 0   0   0   0   0   0   0   4  
 0   0   0   5   0   0   0   0  
 0   6   0   0   0   0   0   0  
 0   0   0   0   0   0   7   0  
 0   0   0   0   8   0   0   0  

 0   0   0   0   0   1   0   0  
 0   0   2   0   0   0   0   0  
 3   0   0   0   0   0   0   0  
 0   0   0   0   0   0   0   4  
 0   0   0   0   5   0   0   0  
 0   6   0   0   0   0   0   0  
 0   0   0   7   0   0   0   0  
 0   0   0   0   0   0   8   0  

 0   0   0   0   0   1   0   0  
 0   0   2   0   0   0   0   0  
 0   0   0   0   3   0   0   0  
 0   0   0   0   0   0   4   0  
 5   0   0   0   0   0   0   0  
 0   0   0   6   0   0   0   0  
 0   7   0   0   0   0   0   0  
 0   0   0   0   0   0   0   8  

 0   0   0   0   0   1   0   0  
 0   0   2   0   0   0   0   0  
 0   0   0   0   3   0   0   0  
 0   0   0   0   0   0   0   4  
 5   0   0   0   0   0   0   0  
 0   0   0   6   0   0   0   0  
 0   7   0   0   0   0   0   0  
 0   0   0   0   0   0   8   0  

 0   0   0   0   0   1   0   0  
 0   0   2   0   0   0   0   0  
 0   0   0   0   0   0   3   0  
 0   4   0   0   0   0   0   0  
 0   0   0   5   0   0   0   0  
 0   0   0   0   0   0   0   6  
 7   0   0   0   0   0   0   0  
 0   0   0   0   8   0   0   0  

 0   0   0   0   0   1   0   0  
 0   0   2   0   0   0   0   0  
 0   0   0   0   0   0   3   0  
 0   4   0   0   0   0   0   0  
 0   0   0   0   0   0   0   5  
 0   0   0   0   6   0   0   0  
 7   0   0   0   0   0   0   0  
 0   0   0   8   0   0   0   0  

 0   0   0   0   0   1   0   0  
 0   0   2   0   0   0   0   0  
 0   0   0   0   0   0   3   0  
 0   0   0   4   0   0   0   0  
 5   0   0   0   0   0   0   0  
 0   0   0   0   0   0   0   6  
 0   7   0   0   0   0   0   0  
 0   0   0   0   8   0   0   0  

 0   0   0   0   0   1   0   0  
 0   0   0   2   0   0   0   0  
 3   0   0   0   0   0   0   0  
 0   0   0   0   4   0   0   0  
 0   0   0   0   0   0   0   5  
 0   6   0   0   0   0   0   0  
 0   0   0   0   0   0   7   0  
 0   0   8   0   0   0   0   0  

 0   0   0   0   0   1   0   0  
 0   0   0   2   0   0   0   0  
 0   3   0   0   0   0   0   0  
 0   0   0   0   0   0   0   4  
 0   0   0   0   5   0   0   0  
 0   0   0   0   0   0   6   0  
 7   0   0   0   0   0   0   0  
 0   0   8   0   0   0   0   0  

 0   0   0   0   0   1   0   0  
 0   0   0   2   0   0   0   0  
 0   0   0   0   0   0   3   0  
 4   0   0   0   0   0   0   0  
 0   0   5   0   0   0   0   0  
 0   0   0   0   6   0   0   0  
 0   7   0   0   0   0   0   0  
 0   0   0   0   0   0   0   8  

 0   0   0   0   0   1   0   0  
 0   0   0   2   0   0   0   0  
 0   0   0   0   0   0   3   0  
 4   0   0   0   0   0   0   0  
 0   0   0   0   0   0   0   5  
 0   6   0   0   0   0   0   0  
 0   0   0   0   7   0   0   0  
 0   0   8   0   0   0   0   0  

 0   0   0   0   0   1   0   0  
 0   0   0   0   0   0   0   2  
 0   3   0   0   0   0   0   0  
 0   0   0   4   0   0   0   0  
 5   0   0   0   0   0   0   0  
 0   0   0   0   0   0   6   0  
 0   0   0   0   7   0   0   0  
 0   0   8   0   0   0   0   0  

 0   0   0   0   0   0   1   0  
 2   0   0   0   0   0   0   0  
 0   0   3   0   0   0   0   0  
 0   0   0   0   0   0   0   4  
 0   0   0   0   0   5   0   0  
 0   0   0   6   0   0   0   0  
 0   7   0   0   0   0   0   0  
 0   0   0   0   8   0   0   0  

 0   0   0   0   0   0   1   0  
 0   2   0   0   0   0   0   0  
 0   0   0   3   0   0   0   0  
 4   0   0   0   0   0   0   0  
 0   0   0   0   0   0   0   5  
 0   0   0   0   6   0   0   0  
 0   0   7   0   0   0   0   0  
 0   0   0   0   0   8   0   0  

 0   0   0   0   0   0   1   0  
 0   2   0   0   0   0   0   0  
 0   0   0   0   0   3   0   0  
 0   0   4   0   0   0   0   0  
 5   0   0   0   0   0   0   0  
 0   0   0   6   0   0   0   0  
 0   0   0   0   0   0   0   7  
 0   0   0   0   8   0   0   0  

 0   0   0   0   0   0   1   0  
 0   0   2   0   0   0   0   0  
 3   0   0   0   0   0   0   0  
 0   0   0   0   0   4   0   0  
 0   0   0   0   0   0   0   5  
 0   0   0   0   6   0   0   0  
 0   7   0   0   0   0   0   0  
 0   0   0   8   0   0   0   0  

 0   0   0   0   0   0   1   0  
 0   0   2   0   0   0   0   0  
 0   0   0   0   0   0   0   3  
 0   4   0   0   0   0   0   0  
 0   0   0   0   5   0   0   0  
 6   0   0   0   0   0   0   0  
 0   0   0   0   0   7   0   0  
 0   0   0   8   0   0   0   0  

 0   0   0   0   0   0   1   0  
 0   0   0   2   0   0   0   0  
 0   3   0   0   0   0   0   0  
 0   0   0   0   4   0   0   0  
 0   0   0   0   0   0   0   5  
 6   0   0   0   0   0   0   0  
 0   0   7   0   0   0   0   0  
 0   0   0   0   0   8   0   0  

 0   0   0   0   0   0   1   0  
 0   0   0   2   0   0   0   0  
 0   3   0   0   0   0   0   0  
 0   0   0   0   0   0   0   4  
 0   0   0   0   0   5   0   0  
 6   0   0   0   0   0   0   0  
 0   0   7   0   0   0   0   0  
 0   0   0   0   8   0   0   0  

 0   0   0   0   0   0   1   0  
 0   0   0   0   2   0   0   0  
 0   0   3   0   0   0   0   0  
 4   0   0   0   0   0   0   0  
 0   0   0   0   0   5   0   0  
 0   0   0   0   0   0   0   6  
 0   7   0   0   0   0   0   0  
 0   0   0   8   0   0   0   0  

 0   0   0   0   0   0   0   1  
 0   2   0   0   0   0   0   0  
 0   0   0   3   0   0   0   0  
 4   0   0   0   0   0   0   0  
 0   0   0   0   0   0   5   0  
 0   0   0   0   6   0   0   0  
 0   0   7   0   0   0   0   0  
 0   0   0   0   0   8   0   0  

 0   0   0   0   0   0   0   1  
 0   2   0   0   0   0   0   0  
 0   0   0   0   3   0   0   0  
 0   0   4   0   0   0   0   0  
 5   0   0   0   0   0   0   0  
 0   0   0   0   0   0   6   0  
 0   0   0   7   0   0   0   0  
 0   0   0   0   0   8   0   0  

 0   0   0   0   0   0   0   1  
 0   0   2   0   0   0   0   0  
 3   0   0   0   0   0   0   0  
 0   0   0   0   0   4   0   0  
 0   5   0   0   0   0   0   0  
 0   0   0   0   6   0   0   0  
 0   0   0   0   0   0   7   0  
 0   0   0   8   0   0   0   0  

 0   0   0   0   0   0   0   1  
 0   0   0   2   0   0   0   0  
 3   0   0   0   0   0   0   0  
 0   0   4   0   0   0   0   0  
 0   0   0   0   0   5   0   0  
 0   6   0   0   0   0   0   0  
 0   0   0   0   0   0   7   0  
 0   0   0   0   8   0   0   0  

共有92种放置方法。

Process finished with exit code 0

标签：12,22,section,mark,range,2020,放置,皇后,sign
来源： https://blog.csdn.net/qsgctysj/article/details/111568850

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ICode9

2020-12-22

八皇后问题——经典再现