NQueenCountWays.java

package backtracking;

public class NQueenCountWays {
    static int count = 0;

    public static void nQueens(char[][] board, int row) {
        // base
        if (row == board.length) {
            // printBoard(board);
            count++;
            return;
        }

        // column loop
        for (int j = 0; j < board.length; j++) {
            if (isSafe(board, row, j)) {
                board[row][j] = 'Q';
                nQueens(board, row + 1); // func call
                board[row][j] = '.'; // backtracking step
            }
        }
    }

    public static boolean isSafe(char[][] board, int row, int col) {
        // vertical up
        for (int i = row - 1; i >= 0; i--) {
            if (board[i][col] == 'Q') {
                return false;
            }
        }

        // diag left up
        for (int i = row - 1, j = col -1; i >= 0 && j >= 0; i--, j--) {
            if (board[i][j] == 'Q') {
                return false;
            }
        }

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

        return true;
    }

    // public static void printBoard(char[][] board) {
    //     System.out.println("----- Chess Board -----");
    //     for (int i = 0; i < board.length; i++) {
    //         for (int j = 0; j < board.length; j++) {
    //             System.out.print(board[i][j] + " ");
    //         }
    //         System.out.println();
    //     }
    // }

    public static void main(String[] args) {
        int n = 4;
        char[][] board = new char[n][n];

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

        nQueens(board, 0);

        System.out.println("Total ways to solve n queens = " + count);
    }
}

// Count total number of ways in which we can solve N Queens problem.