# LeetCode | 0051. N-Queens N 皇后【Python】

### Problem

LeetCode

The n-queens puzzle is the problem of placing n queens on an n×n chessboard such that no two queens attack each other.

image

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.

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.
``````

### 问题

n 皇后问题研究的是如何将 n 个皇后放置在 n×n 的棋盘上，并且使皇后彼此之间不能相互攻击。

image

``````输入：4

[".Q..",  // 解法 1
"...Q",
"Q...",
"..Q."],

["..Q.",  // 解法 2
"Q...",
"...Q",
".Q.."]
]

``````

• 皇后彼此不能相互攻击，也就是说：任何两个皇后都不能处于同一条横行、纵行或斜线上。

### 思路

``````回溯模板：
res = []
def backtrack(路径, 选择列表):
if 满足结束条件:
return

for 选择 in 选择列表:
做选择
backtrack(路径, 选择列表)
撤销选择
``````
##### Python3 代码
``````from typing import List

class Solution:
def solveNQueens(self, n: int) -> List[List[str]]:
res = []
# 一维列表
board = ['.' * n for _ in range(n)]

def isValid(board, row, col):
"""
检查是否有皇后互相冲突
"""
# 检查第 row 行 第 col 列是否可以放皇后
# 只需考虑 <= row，因为后面的棋盘是空的
for row_index in range(row):
# 判断当前行是否放了皇后
if row_index == row:
if 'Q' in board[row_index]:
return False
# 判断遍历每行时，第 col 列是否已经放了皇后
if 'Q' == board[row_index][col]:
return False

# 判断左上方是否放了皇后
tmp_row, tmp_col = row, col
while tmp_row > 0 and tmp_col > 0:
tmp_row -= 1
tmp_col -= 1
if 'Q' in board[tmp_row][tmp_col]:
return False

# 判断右上方是否放了皇后
tmp_row, tmp_col = row, col
while tmp_row > 0 and tmp_col < n - 1:
tmp_row -= 1
tmp_col += 1
if 'Q' in board[tmp_row][tmp_col]:
return False

return True

def replace_char(string, char, index):
"""
构建新的字符串进行赋值
"""
string = list(string)
string[index] = char
return ''.join(string)

def backtrack(board, row):
# 1.结束条件
if row == len(board):
# 需要用 list 转化一下
res.append(list(board[:]))
return

# 2.剪枝
# m = len(board[row])
for col in range(n):
# 剪枝
if not isValid(board, row, col):
continue
# 3.回溯并更新 row
board[row] = replace_char(board[row], 'Q', col)
backtrack(board, row + 1)
board[row] = replace_char(board[row], '.', col)

backtrack(board, 0)
return res

if __name__ == "__main__":
n = 4
print(Solution().solveNQueens(n))
``````

Python

N皇后---python解题思路