// CSE 143, Winter 2011, Marty Stepp
// This program solves the classic "8 queens" problem using recursive 
// backtracking.
//
// This file isn't quite correct, because it doesn't stop when it places
// the 8th queen.  We will fix it during Monday's lecture.
// (A correct version of the code can be found in your section handout.)

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) {
        solveQueens(b, 1);
    }
    
    // Solves the eight queens problem on the given board, starting from the
    // given column, assuming that any previous columns are already safely
    // placed.
    private static boolean solveQueens(Board b, int column) {
    	if (column > b.size()) {
    		return true;     // base case: already placed all queens safely
    	} else {
    		// assumes that all prior columns have already been placed safely
    		for (int row = 1; row <= 8; row++) {
    			if (b.isSafe(row, column)) {
    				b.place(row, column);                // choose
    				if (solveQueens(b, column + 1)) {    // explore
    					return true;
    				}
    				b.remove(row, column);               // un-choose
    			}
    		}
    		return false;
    	}
    }

}