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.."]
]

public class Solution {
    public List<String[]> solveNQueens(int n) {
        List<String[]> boards = new ArrayList<String[]>();
        if(n<0) return boards;
        char[][] board = new char[n][n];
        for(int i=0;i<n;i++) {
            for(int j=0;j<n;j++) {
                board[i][j] = '.';
            }
        }
        helper(n, boards, board, 0);
        return boards;
    }
   
    private void helper(int n, List<String[]> boards, char[][] board, int row) {
        if(row==n) {
            String[] copy = new String[n];
            for(int i=0;i<n;i++) {
                copy[i] = new String(board[i]);
            }
            boards.add(copy);
        } else if(row<n) {
            for(int i=0;i<n;i++) {
                if(check(board, row, i)) {
                    board[row][i] = 'Q';
                    helper(n, boards, board, row+1);
                    board[row][i] = '.';
                }
            }
        }
    }
   
    private boolean check(char[][] board, int row, int column) {
        for(int i=0;i<row;i++) {
            if(board[i][column]=='Q') return false;
            if((column- (row-i))>=0 && board[i][column- (row-i)]=='Q') return false;
            if((column+(row-i))<board.length && board[i][column+(row-i)]=='Q') return false;
        }
        return true;
    }
}


=========

public class Solution {
    public List<List<String>> solveNQueens(int n) {
        List<List<String>> res = new ArrayList<List<String>>();
        int[] board = new int[n];
        helper(board, 0, res);
        return res;
    }
   
    private void helper(int[] board, int k, List<List<String>> res) {
        if (k == board.length) {
            List<String> ret = new ArrayList<String>();
            for (int i = 0; i < board.length; i++) {
                char cs[] = new char[board.length];
                Arrays.fill(cs, '.');
                cs[board[i]] = 'Q';
                ret.add(new String(cs));
            }
            res.add(ret);
        } else if (k < board.length) {
            for (int i = 0; i < board.length; i++) {
                board[k] = i;
                if (check(board, k)) {
                    helper(board, k + 1, res);
                }
            }
        }
    }
   
    private boolean check(int[] board, int k) {
        for (int i = 0; i < k; i++) {
            if (board[i] == board[k] || Math.abs(board[i] - board[k]) == Math.abs(i - k)) {
                return false;
            }
        }
        return true;
    }
}