// This program solves the classic "8 queens" problem using recursive 
// backtracking.

import java.util.*;

public class Queens {
    public static void main(String[] args) {
        giveIntro();
        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 Board(size);
        solve(b);
    }

    // post: explains program to user
    public static void giveIntro() {
        System.out.println("This program solves the classic '8 queens'");
        System.out.println("problem, placing queens on a chessboard so");
        System.out.println("that no two queens threaten each other.");
        System.out.println();
    }
          
    // post: searches for a solution to the 8 queens problem with this
    //       board, reporting result.
    public static void solve(Board solution) {
        if (!solve(solution, solution.size())) {
            System.out.println("No solution.");
        } else {
            System.out.println("One solution is as follows:");
            solution.print();
        }
    }
    
    // pre : queens have been safely placed in columns 1 through (col - 1)
    // post: recursively searchs the board for a solution starting at col,
    //       returning true iff such a solution occurs and storing the
    //       solution in board if it exists
    private static boolean solve(Board solution, int queensLeft) {
        if (queensLeft == 0) {
            return true;
        } else {
            for (int i = 1; i <= solution.size(); i++) {
                if (solution.safe(i, queensLeft)) {
                    // choose
                    solution.place(i, queensLeft);
                    // recurse
                    boolean isFound = solve(solution, queensLeft - 1);
                    if (isFound) {
                        return true;
                    }                
                    // unchoose
                    solution.remove(i, queensLeft);
                }
            }
            return false;
        }
    }
}