# N 皇后

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。

给你一个整数 n ,返回所有不同的 n 皇后问题 的解决方案。

每一种解法包含一个不同的 n 皇后问题 的棋子放置方案,该方案中 'Q''.' 分别代表了皇后和空位。

 

示例 1:

输入:n = 4
输出:
[[".Q..","...Q","Q...","..Q."],["..Q.","Q...","...Q",".Q.."]]
解释:
如上图所示,4 皇后问题存在两个不同的解法。

示例 2:

输入:n = 1
输出:
[["Q"]]

 

提示:

以下程序实现了这一功能,请你填补空白处内容: ```java import java.util.List; import java.util.ArrayList; public class Solution { public List> solveNQueens(int n) { List> res = new ArrayList>(); int[] queenList = new int[n]; placeQueen(queenList, 0, n, res); return res; } private void placeQueen(int[] queenList, int row, int n, List> res) { if (row == n) { ArrayList list = new ArrayList(); for (int i = 0; i < n; i++) { String str = ""; for (int col = 0; col < n; col++) { if (queenList[i] == col) { str += "Q"; } else { str += "."; } } list.add(str); } res.add(list); } for (int col = 0; col < n; col++) { if (isValid(queenList, row, col)) { queenList[row] = col; ________________________; } } } private boolean isValid(int[] queenList, int row, int col) { for (int i = 0; i < row; i++) { int pos = queenList[i]; if (pos == col) { return false; } if (pos + row - i == col) { return false; } if (pos - row + i == col) { return false; } } return true; } } ``` ## template ```java import java.util.List; import java.util.ArrayList; public class Solution { public List> solveNQueens(int n) { List> res = new ArrayList>(); int[] queenList = new int[n]; placeQueen(queenList, 0, n, res); return res; } private void placeQueen(int[] queenList, int row, int n, List> res) { if (row == n) { ArrayList list = new ArrayList(); for (int i = 0; i < n; i++) { String str = ""; for (int col = 0; col < n; col++) { if (queenList[i] == col) { str += "Q"; } else { str += "."; } } list.add(str); } res.add(list); } for (int col = 0; col < n; col++) { if (isValid(queenList, row, col)) { queenList[row] = col; placeQueen(queenList, row + 1, n, res); } } } private boolean isValid(int[] queenList, int row, int col) { for (int i = 0; i < row; i++) { int pos = queenList[i]; if (pos == col) { return false; } if (pos + row - i == col) { return false; } if (pos - row + i == col) { return false; } } return true; } } ``` ## 答案 ```java placeQueen(queenList, row + 1, n, res); ``` ## 选项 ### A ```java placeQueen(queenList, row, n, res); ``` ### B ```java placeQueen(queenList, row + 1, n + 1, res); ``` ### C ```java placeQueen(queenList, row, n + 1, res); ```