N_queens.java

public class N_queens {

    public static void nQueens(char board[][], int row) {
        // base
        if (row == board.length) {
            // printBoard(board);
            count ++;
            return;
        }
        // //column
        // for(int j = 0;j<board.length;j++){
        //     board[row][j] = 'Q';
        //     nQueens(board, row+1);
        //     board[row][j] = 'x';
        // }

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

    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 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();
        }
    }

    // count number of solutions
    static int count = 0;
    public static void main(String args[]) {
        int n = 5;
        char board[][] = new char[n][n];
        // initialize
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                board[i][j] = 'x';
            }
        }

        nQueens(board, 0);
        System.out.println("total ways to olve n queens = " + count);
    }
}