// This program solves the classic "8 queens" problem using recursive 
// backtracking, printing all solutions.

import java.util.*;

public class Queens {
    public static void main(String[] args) {
        giveIntro();
        Scanner console = new Scanner(System.in);
        System.out.print("What size board do you want to use? ");
        int size = console.nextInt();
        System.out.println();
        Board b = new Board(size);
        solve(b);
    }

    // post: explains program to user
    public static void giveIntro() {
        System.out.println("This program solves the classic '8 queens'");
        System.out.println("problem, placing queens on a chessboard so");
        System.out.println("that no two queens threaten each other.");
        System.out.println();
    }

    // pre : queens have been safely placed in columns 1 through (col - 1)
    // post: recursively searchs the board for all solutions starting at col,
    //       and printing any solution it finds
    private static void explore(Board b, int col) {
        if (col > b.size()) {
            b.print();
        } else {
            for (int row = 1; row <= b.size(); row++)
                if (b.safe(row, col)) {
                    b.place(row, col);
                    explore(b, col + 1);
                    b.remove(row, col);
                }
        }
    }
          
    // post: prints all solutions to 8 queens
    public static void solve(Board b) {
        explore(b, 1);
    }
}