// CSE 143, Winter 2012
// This program solves the classic "8 queens" problem using recursive 
// backtracking.

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: b != null
    public static void solveQueens(Board b) {
    	explore(b, 1);
    	System.out.println(b);
    }

    // Precondition: queens have been safely placed in columns 1 to col - 1
    // Recursive private helper that searches the board for a solution starting
    // at col.  If there is a solution, return true and store the solution in
    // Board b, otherwise return false.
    private static boolean explore(Board b, int col) {
    	if (col > b.size()) {
    		return true;		// all queens have been safely placed
    	} else {
    		// for each of my choices:
    		for (int row = 1; row <= b.size(); row++) {
        		// 		choose
    			if (b.isSafe(row, col)) {
    				b.place(row, col);
    				// 		explore
    				if (explore(b, col + 1)) {
    					return true;
    				}
    				//		unchoose   	
    				b.remove(row, col);
    			}
    		}

    	}
    	return false;
    }
}