// This program solves the classic "8 queens" problem using recursive
// backtracking, printing all solutions.

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();
    }

    // Solves the n-queens problem using the given board,
    // prints out all possible ways of arranging n queens
    // on the board such that none can attack each other
    // where n is the size of the board.
    public static void solve(Board b) {
        explore(b, 1);
    }

    // pre: b != null, 0 < col <= b.size() + 1
    //      each column from 1 to col - 1 is valid
    // explores every possible way of placing a
    // queen in the given column and the rest of
    // the board after this column such that they are valid
    // placements. If col > b.size(), then the board is
    // fully placed and the solution is printed
    private static void explore(Board b, int col) {
        // base case
        if (col == b.size() + 1) {
            b.print();
        } else {  // recursive case
            // for each choice: each possible row in this col
            for (int row = 1; row <= b.size(); row++) {
                // important to check to make sure our precondition holds
                // for the next recursive call
                if (b.safe(row, col)) {
                    b.place(row, col);    // choose
                    explore(b, col + 1);  // explore
                    b.remove(row, col);   // unchoose
                }
            }
        }
    }
}