N Queen Problem.java

import java.util.*;
class TUF {
    public static 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] = '.';
        List < List < String >> res = new ArrayList < List < String >> ();
        int leftRow[] = new int[n];
        int upperDiagonal[] = new int[2 * n - 1];
        int lowerDiagonal[] = new int[2 * n - 1];
        solve(0, board, res, leftRow, lowerDiagonal, upperDiagonal);
        return res;
    }



    static void solve(int col, char[][] board, List < List < String >> res, int leftRow[], int lowerDiagonal[], int upperDiagonal[]) {
        if (col == board.length) {
            res.add(construct(board));
            return;
        }

        for (int row = 0; row < board.length; row++) {
            if (leftRow[row] == 0 && lowerDiagonal[row + col] == 0 && upperDiagonal[board.length - 1 + col - row] == 0) {
                board[row][col] = 'Q';
                leftRow[row] = 1;
                lowerDiagonal[row + col] = 1;
                upperDiagonal[board.length - 1 + col - row] = 1;
                solve(col + 1, board, res, leftRow, lowerDiagonal, upperDiagonal);
                board[row][col] = '.';
                leftRow[row] = 0;
                lowerDiagonal[row + col] = 0;
                upperDiagonal[board.length - 1 + col - row] = 0;
            }
        }
    }


    static List < String > construct(char[][] board) {
        List < String > res = new LinkedList < String > ();
        for (int i = 0; i < board.length; i++) {
            String s = new String(board[i]);
            res.add(s);
        }
        return res;
    }
    public static void main(String args[]) {
        int N = 4;
        List < List < String >> queen = solveNQueens(N);
        int i = 1;
        for (List < String > it: queen) {
            System.out.println("Arrangement " + i);
            for (String s: it) {
                System.out.println(s);
            }
            System.out.println();
            i += 1;
        }

    }
}