// Erika Wolfe, CSE 143
// Examples of recursive backtracking
// Added a check in diceSum to avoid exploring
// dead end paths. 

import java.util.*;

public class Backtracking2 {
    public static void main(String[] args) {
        // fourAB();
        // diceRoll(2);
        diceSum(2, 7);
    }

    // This method will print all strings of length 4 composed of 
    // only a's and b's
    public static void fourAB() {
        fourAB("");
    }
    
    // This method will print all strings of length 4 composed of 
    // only a's and b's with the prefix soFar
    private static void fourAB(String soFar) {
        if (soFar.length() == 4) {
            System.out.println(soFar);
        } else {
            // soFar = soFar + "a";
            fourAB(soFar + "a");
            fourAB(soFar + "b");
        }
    }
    

    // Prints all possible outcomes of rolling the given
    // number of six-sided dice in [#, #, #] format.
    // pre: dice >= 0
    public static void diceRoll(int dice) {
        diceRoll(dice, new ArrayList<Integer>());
    }
    
    // Prints all possible outcomes of rolling the given
    // number of six-sided dice in [#, #, #] format.
    // chosen contains the dice we've chosen so far 
    // pre: dice >= 0
    private static void diceRoll(int dice, List<Integer> chosen) {
        // how do I know when I'm done? 
        if (dice == 0) {
            System.out.println(chosen);
        } else {
            // how do I make a single choice?  what are the options? 
            for (int i = 1; i <= 6; i++) {
                chosen.add(i); // choose 
                diceRoll(dice - 1, chosen);  // explore 
                chosen.remove(chosen.size() - 1);  // unchoose 
            }
        }
    }

    // Prints all possible outcomes of rolling the given
    // number of six-sided dice that add up to exactly
    // the given sum, in [#, #, #] format.
    public static void diceSum(int dice, int sum) {
        diceSum(dice, sum, 0, new ArrayList<Integer>());
    }
    
    private static void diceSum(int dice, int sum, int sumSoFar, List<Integer> chosen) {
        // how do I know when I'm done? 
        if (dice == 0) {
            if (sum == sumSoFar) {
                System.out.println(chosen);
            }
        } else if (sumSoFar + dice <= sum && sumSoFar + dice * 6 >= sum) {
            // how do I make a single choice?  what are the options? 
            for (int i = 1; i <= 6; i++) {
                chosen.add(i); // choose 
                diceSum(dice - 1, sum, sumSoFar + i, chosen);  // explore 
                chosen.remove(chosen.size() - 1);  // unchoose 
            }
        }
    }
}