51. N-Queens

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.

For example, There exist two distinct solutions to the 4-queens puzzle:

[
 [".Q..",  // Solution 1
  "...Q",
  "Q...",
  "..Q."],

 ["..Q.",  // Solution 2
  "Q...",
  "...Q",
  ".Q.."]
]

Related issue: 52 N-Queens II backtacking

public class Solution {

    List<List<String>> res = new ArrayList<>();
    public List<List<String>> solveNQueens(int n) {
        char[][] board = new char[n][n];
        for(int i=0; i< n;i++){
            for(int j=0; j< n; j++){
                board[i][j] = '.';
            }
        }

        bt(board, 0, n);
        return res;
    }

    private void bt(char[][] board, int row, int n){
        if(row == n){
            //save into database.
            List<String> t = new ArrayList<>();
            for(char[] s : board){
                t.add(new String(s));
            }
            res.add(t);
        }

        for(int col=0; col < n; col++){
            if(isValid(board, row, col)){ // if is not valid, then there is no solution added.
                board[row][col] = 'Q';
                bt(board, row+1, n);
                board[row][col] = '.';
            }
        }

    }

    private boolean isValid(char[][] board, int row, int col){
        for(int i= row-1; i >=0; i--){
            if(board[i][col] == 'Q' )return false;
        }
        for(int i=row-1, j=col-1; i >=0 && j>=0; i--,j--){
            if(board[i][j] == 'Q') return false;
        }


        for(int i=row-1, j=col+1; i>=0 && j<board.length; i--,j++){
            if(board[i][j] == 'Q') return false;
        }

        return true;
    }
}