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  • [LeetCode]题解(python):051-N-Queens


    题目来源

    https://leetcode.com/problems/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.

    Given an integer n, return all distinct solutions to the n-queens puzzle.

    Each solution contains a distinct board configuration of the n-queens' placement, where 'Q' and '.' both indicate a queen and an empty space respectively.


    题意分析
    Input: n:integer

    Output:a list contains the result

    Conditions:典型的n皇后问题(同一列,同一行,同斜线会互相攻击)


    题目思路


    本题很明显用回溯的方法,经大神指点,这里采用一维数组的方式,如n=4时,list = [2,4,1,3]表示i行第list[i]位置放置皇后,这样就保证了每一行只有一位皇后,然后代码中有个check条件,就是用来判断是不是同一列和斜线的,

    注意如果list[i] == list[j]则表示同一列,abs(i - j) == abs(list[i] - list[j])表示同斜线(很明显同一斜线时两点的横纵坐标差相等)

    之后,回溯就好了


    AC代码(Python)


     1 __author__ = 'YE'
     2 
     3 class Solution(object):
     4     def solveNQueens(self, n):
     5         """
     6         :type n: int
     7         :rtype: List[List[str]]
     8         """
     9         def check(k, j):
    10             for i in range(k):
    11                 if board[i] == j or abs(k - i) == abs(board[i] - j):
    12                     return False
    13             return True
    14 
    15         def dfs(depth, valueList):
    16             if depth == n:
    17                 res.append(valueList)
    18             else:
    19                 for i in range(n):
    20                     if check(depth, i):
    21                         board[depth] = i
    22                         s = '.' * n
    23                         dfs(depth + 1, valueList + [s[:i] + "Q" + s[i+1:]])
    24         res = []
    25 
    26         board = [-1 for i in range(n)]
    27         dfs(0, [])
    28 
    29         return res
    30 
    31 s = Solution()
    32 n = 4
    33 print(s.solveNQueens(n))
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  • 原文地址:https://www.cnblogs.com/loadofleaf/p/5082213.html
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