0.原題

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 '.'

Example:

Input: 4
Output: [
 [".Q..",  // Solution 1
  "...Q",
  "Q...",
  "..Q."],

 ["..Q.",  // Solution 2
  "Q...",
  "...Q",
  ".Q.."]
]
Explanation: There exist two distinct solutions to the 4-queens puzzle as shown above.

1.程式碼

class Solution:
    def solveNQueens(self, n):
        """
        :type n: int
        :rtype: List[List[str]]
        """
        self.n = n
        self.state1 = [True for _ in range(n)]
        self.state2 = [True for _ in range(2*n-1)]
        self.state3 = [True for _ in range(2*n-1)]
        self.one_result = []
        self.result = []
        self.fun(0)
        return self.result

    def fun(self,row):
        if row == self.n:
            r = self.one_result.copy()
            self.result.append(r)
            return 0
        else:
            for column in range(self.n):
                if self.state1[column] and self.state2[row+column] and self.state3[row-column+self.n-1]:
                    self.state1[column] = False
                    self.state2[row+column] = False
                    self.state3[row-column+self.n-1] = False
                    self.one_result.append(self.place_queen(column))
                    self.fun(row+1)
                    self.one_result.pop()
                    self.state3[row-column+self.n-1] = True
                    self.state2[row+column] = True
                    self.state1[column] = True

    def place_queen(self,column):
        s =''
        for i in range(self.n):
            if i == column:
                s += 'Q'
            else:
                s += '.'
        return s
 

2.思路

本題思路與之前寫過的八皇后問題完全相同，區別僅僅在皇后數量和輸出格式上，本文不在贅述。