 # [LeetCode] 51. N-Queens

## Problem

The n-queens puzzle is the problem of placing n queens on an n×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.

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.

``````

## Solution

``````class Solution {
public List<List<String>> solveNQueens(int n) {
char[][] board = new char[n][n];
for (int i = 0; i < n; i++) {
Arrays.fill(board[i], '.');
}
List<List<String>> res = new ArrayList<>();
dfs(board, 0, res);
return res;
}

private void dfs(char[][] board, int col, List<List<String>> res) {
if (col == board.length) {
return;
}

for (int row = 0; row < board.length; row++) {
if (validate(board, row, col)) {
board[row][col] = 'Q';
dfs(board, col+1, res);
board[row][col] = '.';
}
}
}

private boolean validate(char[][] board, int row, int col) {
for (int i = 0; i < board.length; i++) {
for (int j = 0; j < col; j++) {
if (board[i][j] == 'Q' && (
i+j == row+col || row+j == col+i || row == i
)) return false;
}
}

return true;
}

private List<String> construct(char[][] board) {
List<String> res = new ArrayList<>();
for (int i = 0; i < board.length; i++) {
String str = new String(board[i]);
}
return res;
}
}
``````