[leetcode 51] N-Queens

"""
The n-queens puzzle is the problem of placing n queens on an n x 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.
"""
class Solution:
    def solveNQueens(self, n: int) -> List[List[str]]:
        def DFS(queens, xy_dif, xy_sum):
            p = len(queens)
            if p==n:
                result.append(queens)
                return None
            for q in range(n):
                if q not in queens and p-q not in xy_dif and p+q not in xy_sum: 
                    DFS(queens+[q], xy_dif+[p-q], xy_sum+[p+q])  
        result = []
        DFS([],[],[])
        return [ ["."*i + "Q" + "."*(n-i-1) for i in sol] for sol in result]