nqueens

 import java.util.ArrayList;

import java.util.List;

public class NQueens {

   
    public static List<List<String>> solveNQueens(int n) {
        List<List<String>> solutions = new ArrayList<>();
        char[][] board = new char[n][n];

       
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                board[i][j] = '.';
            }
        }

        placeQueens(solutions, board, 0, n);
        return solutions;
    }

   
    private static void placeQueens(List<List<String>> solutions, char[][] board, int row, int n) {
        if (row == n) {
            solutions.add(constructSolution(board));
            return;
        }

        for (int col = 0; col < n; col++) {
            if (isSafe(board, row, col, n)) {
                board[row][col] = 'Q'; // Place a queen
                placeQueens(solutions, board, row + 1, n); // Recur for the next row
                board[row][col] = '.'; // Backtrack
            }
        }
    }

   
    private static boolean isSafe(char[][] board, int row, int col, int n) {
     
        for (int i = 0; i < row; 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 < n; i--, j++) {
            if (board[i][j] == 'Q') {
                return false;
            }
        }

        return true;
    }

   
    private static List<String> constructSolution(char[][] board) {
        List<String> solution = new ArrayList<>();
        for (char[] row : board) {
            solution.add(new String(row));
        }
        return solution;
    }

    // Main function
    public static void main(String[] args) {
        int n = 8; // Change the value of n as needed
        List<List<String>> solutions = solveNQueens(n);

        System.out.println("Total Solutions for " + n + "-Queens: " + solutions.size());
        for (List<String> solution : solutions) {
            for (String row : solution) {
                System.out.println(row);
            }
            System.out.println();
        }
    }
}

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