// Helene Martin, CSE 143
// 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) {
		if (solveQueens(b, 1)) {
			System.out.println(b);
		} else {
			System.out.println("No solution!");
		}
	}

	// Searches the board for a solution to the n-queens problem starting at
	// col. Stores a solution in b if it exists.
	// pre: the previous col - 1 queens are correctly placed
	private static boolean solveQueens(Board b, int col) {
		if (col > b.size()) {
			return true;
		} else {
			for (int row = 1; row <= b.size(); row++) {
				if (b.isSafe(row, col)) {
					b.place(row, col);
					if (solveQueens(b, col + 1)) {
						return true;
					}
					b.remove(row, col);
				}
			}
			return false;
		}
	}
}