力扣：51. N 皇后

class Solution {
    
    int[] dp;
    List<List<String>> list ;
    Set<Integer> x ;
    Set<Integer> y;
    Set<Integer> z;
    public List<List<String>> solveNQueens(int n) {
        dp = new int[n];
        // 初始化
        Arrays.fill(dp, -1);
        list = new ArrayList<>();
        x = new HashSet<>();
        y = new HashSet<>();
        z = new HashSet<>();
        calculation(n, 0, dp, x, y ,z);
        return list;
    }

    private void calculation(int n, int row, int[] dp, Set<Integer> x, Set<Integer> y, Set<Integer> z){
        if (n == row){
            List<String> board = buildBoard(dp, n);
            list.add(board);
            return;
        } else {
            for (int i = 0 ; i < n; i++){
                if (x.contains(i)){
                    continue;
                }

                int y1 = row - i;
                if (y.contains(y1)){
                    continue;
                }

                int z1 = row + i;
                if (z.contains(z1)){
                    continue;
                }
                dp[row] = i;
                x.add(i);
                y.add(y1);
                z.add(z1);
                calculation(n, row + 1, dp, x, y, z);
                dp[row] = -1;
                x.remove(i);
                y.remove(y1);
                z.remove(z1); 
            }
        }
    }

    private List<String> buildBoard(int[] dp, int n){
        List<String> res = new ArrayList<>();
        for (int i = 0; i < n; i++){
            char[] board = new char[n];
            Arrays.fill(board, '.');
            board[dp[i]] = 'Q';
            res.add(new String(board));
        }
        return res;
    }
}