[模板题] - 52. N 皇后 II

题目链接	52. N 皇后 II
思路	经典回溯题
题解链接	【视频】回溯秒杀N皇后！一个视频讲透！（Python/Java/C++/Go/JS）
关键点	无
时间复杂度	$O(n!)$
空间复杂度	$O(n)$

代码实现：

class Solution:
    def totalNQueens(self, n: int) -> int:
        m = n * 2 - 1
        answer = 0
        on_path = [False] * n
        diag1 = [False] * m
        diag2 = [False] * m
        
        def dfs(r):
            if r == n:
                nonlocal answer
                answer += 1
                return
            for c, on in enumerate(on_path):
                if not on and not diag1[r + c] and not diag2[r - c]:
                    on_path[c] = diag1[r + c] = diag2[r - c] = True
                    dfs(r+1)
                    on_path[c] = diag1[r + c] = diag2[r - c] = False
 
        dfs(0)
        return answer