// Marty Stepp, CSE 143, Winter 2009
// This program solves the classic "8 queens" problem using recursive 
// backtracking.

import java.util.*;

public class Queens {
    public static void main(String[] args) {
        Board b = new GraphicalBoard(8);
        solveQueens(b);
    }
    
    // Solves the eight queens problem on the given board.
    // Precondition: board is of size 8
    public static void solveQueens(Board b) {
        solveQueens(b, 0);
    }
     
    // Recursive helper to solve the eight queens problem on the given board.
    // Precondition: The given number 'count' of queens are already placed
    private static void solveQueens(Board b, int count) {
        if (count == 8) {
            // base case: all queens are placed; print board
            System.out.println(b);
        } else {
            // recursive case: loop through all squares, looking for a 
            // place to put one queen
            for (int row = 1; row <= 8; row++) {
                for (int col = 1; col <= 8; col++) {
                    if (b.isSafe(row, col)) {
                        b.place(row, col);           // make a choice
                        solveQueens(b, count + 1);   // explore the rest
                        b.remove(row, col);          // un-make the choice
                    }
                }
            }
        }
    }
}