// 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.
  //
  // where are we going?
  //      how many queens we have left to place
  // where have we been?
  //      where are queens placed?
  public static void solve(Board solution) {
    boolean solved = solve(solution, 1);
    if (!solved) {
      System.out.println("No solution found.");
    }
  }
  
  // 
  //   public Board(int size)
  //
  //   public boolean safe(int row, int col)
  //   public void place(int row, int col)
  //   public void remove(int row, int col)
  //   public int size()
  //   public void print()
  //
  // pre: all queens < col are placed and valid
  // solution.size() == 4
  private static boolean solve(Board solution, int col) {
    if (col > solution.size()) {
      solution.print();
      return true;
    } else {
      // try every row from 1 - 8
      for (int row = 1; row <= solution.size(); row++) {
        // is it safe?
        if (solution.safe(row, col)) {
          // choose -- a row to place (row, col), (4, col)
          solution.place(row, col);
          // explore -- recurse
          boolean solved = solve(solution, col + 1);
          if (solved) {
            return solved;
          }
          // unchoose -- take queen off (row, col)
          solution.remove(row, col);
        }
      }
      return false;
    }
  }
}