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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) {
res.add(construct(board));
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]);
res.add(str);
}
return res;
}
}
