// 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();
   }
         
   // prints all solutions to place n-queens on the board
   public static void solve(Board b) {
      solve(b, 1);
   }
   
   // Assumes that we have successfully placed col - 1 queens in the previous columns
   // Prints all solutions to place n-queens on the board
   private static void solve(Board b, int col) {
      if (col == b.size() + 1) { // Success
         b.print();
      } else { // In-Bounds Case
         for (int row = 1; row <= b.size(); row++) {
            if (b.safe(row, col)) {
               b.place(row, col);
               solve(b, col + 1);
               b.remove(row, col);
            }
         }
      }
   }
}