// Allison Obourn
// CSE 143 - lecture 18
// This program solves the classic "n queens" problem using recursive 
// backtracking.

import java.util.*;

public class Queens {
   public static void main(String[] args) {
      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 GraphicalBoard(size);
      solveQueens(b);
   }

   // Solves the queens problem on the given board.
   // Precondition: b != null
   public static void solveQueens(Board b) {
      solveQueens(b, 1);
   }
   
   // Searches the board for a solution to the n-queens problem starting at
   // col. Stores a solution in b if it exists.
   // Pre: col > 0
   // Pre: the previous col - 1 queens are correctly placed
   private static void solveQueens(Board b, int col) {
      if(col > b.size()) {
         System.out.println(b);
      } else {
         for(int row = 1; row <= b.size(); row++) {
            if(b.isSafe(row, col)) {
               b.place(row, col);
               solveQueens(b, col + 1);
               b.remove(row, col);
            }
         }
      }
   }

}