54 leetcode - N-Queens

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最新推荐文章于 2025-01-18 19:45:42 发布

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文章标签： leetcode 算法八皇后 n-queens Queens

本文链接：https://blog.youkuaiyun.com/lis_12/article/details/53840764

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本文介绍了一种使用Python解决N皇后问题的方法。通过递归和回溯算法找到所有可能的解决方案，使得N个皇后放置在N×N的棋盘上互不攻击。提供了完整的Python代码实现，并展示了4皇后问题的两种解决方案。

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#!/usr/bin/python
# -*- coding: utf-8 -*-
'''
N-Queens
The n-queens puzzle is the problem of placing n queens on an n×n chessboard such that no two queens attack each other.
There exist two distinct solutions to the 4-queens puzzle:

[
 [".Q..",  // Solution 1
  "...Q",
  "Q...",
  "..Q."],

 ["..Q.",  // Solution 2
  "Q...",
  "...Q",
  ".Q.."]
]
'''
class Solution(object):
    def __check(self,result,start_index,next_val):
        for index,val in enumerate(result[:start_index]):
            if (val == next_val) or (abs(index - start_index) == abs(val - next_val)): #将不符合N皇后规则的去掉
                return False

        return True

    def __solveNQueens(self,n,result,start_index,ret,fmt):
        if start_index == n:
            tmp = []
            for val in result:
                fmt[val] = 'Q'
                tmp.append(''.join(fmt))
                fmt[val] = '.'
            ret.append(tmp)
        else:
            #index代表行数,val代表列数
            for i in range(n):
                if self.__check(result,start_index,i) == True:
                    result[start_index] = i
                    self.__solveNQueens(n,result,start_index + 1,ret,fmt)

    def solveNQueens(self, n):
        """
        :type n: int
        :rtype: List[List[str]]
        """
        if n == 1:
            return [['Q']]

        if n < 4:
            return []

        ret = []
        fmt = ["."] * n
        self.__solveNQueens(n,[0]*n,0,ret,fmt)
        return ret

if __name__ == "__main__":
    s = Solution()
    for i in s.solveNQueens(4):
        for j in i:
            print j
        print "=========="