// @Title: N 皇后 (N-Queens)
// @Author: qisiii
// @Date: 2024-09-21 17:56:11
// @Runtime: 2 ms
// @Memory: 43.9 MB
// @comment: 
// @flag: 
class Solution {
    public List<List<String>> solveNQueens(int n) {
        char[][] matrix = new char[n][n];
        for (char[] row : matrix) {
            Arrays.fill(row, '.');
        }
        List<List<String>> result = new ArrayList<>();
        dfs(result, matrix, n, 0);
        return result;
    }

    private void dfs(List<List<String>> result, char[][] matrix, int n, int row) {
        if (row == n) {
            List<String> temp = new ArrayList<>();
            for (int i = 0; i < n; i++) {
                StringBuilder sb = new StringBuilder();
                for (int j = 0; j < n; j++) {
                    sb.append(matrix[i][j]);
                }
                temp.add(sb.toString());
            }
            result.add(temp);
            return;
        }
        for (int j = 0; j < n; j++) {
            if (isValid(row, j,matrix)) {
                matrix[row][j] = 'Q';
                dfs(result, matrix, n, row + 1);
                matrix[row][j] = '.';
            }
        }
    }

    private boolean isValid(int row, int column, char[][] matrix) {
        for (int j = 0; j < row; j++) {
            if (matrix[j][column] == 'Q') {
                return false;
            }
        }
        for (int i = row - 1, j = column - 1; i >= 0 && j >= 0; i--, j--) {
            if (matrix[i][j] == 'Q') {
                return false;
            }
        }
        for (int i = row - 1, j = column + 1; i >= 0 && j < matrix.length; i--, j++) {
            if (matrix[i][j] == 'Q') {
                return false;
            }
        }
        return true;
    }
}