leetcode 每日一题 51. N皇后

回溯法

思路：

参考37.解数独。在约束条件判断中，主对角线row-col = 常数， 副对角线 row+col = 常数。

代码:

class Solution:
    def solveNQueens(self, n: int) -> List[List[str]]:
        def could_place(row,col):
            return not(cols[col]+hill_diagonal[row-col]+dale_diagonal[row+col])
        def place_queen(row,col):
            queens.add((row,col))
            cols[col] = 1
            hill_diagonal[row-col] = 1
            dale_diagonal[row+col] = 1
        def remove_queen(row,col):
            queens.remove((row,col))
            cols[col] = 0
            hill_diagonal[row-col] = 0
            dale_diagonal[row+col] = 0
        def add_solution():
            solution = []
            for _,col in sorted(queens):
                solution.append('.'*col + 'Q'+'.'*(n-col-1))
            res.append(solution)
        def backtrack(row = 0):
            for col in range(n):
                if could_place(row,col):
                    place_queen(row,col)
                    if row + 1 == n:
                        add_solution()
                    else:
                        backtrack(row+1)
                    remove_queen(row,col)
        cols = [0]*n
        hill_diagonal = [0]*(2*n-1)
        dale_diagonal = [0]*(2*n-1)
        queens = set()
        res = []
        backtrack()
        return res