// Erika Wolfe, CSE 143
// Examples of recursive backtracking

import java.util.*;

public class Backtracking {
    public static void main(String[] args) {
        fourAB();
        System.out.println();
        diceRoll(3);
        System.out.println();
        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("");
    }
    
    // Prints all strings of length 4 composed of only a's and b's
    // that start with the given prefix soFar
    private static void fourAB(String soFar) {
        if (soFar.length() == 4) {
            System.out.println(soFar);
        } else {
            fourAB(soFar + "a"); 
            // no need to unchoose because soFar + "a" returns a new String
            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 with the dice in chosen 
    // as the prefix.
    private static void diceRoll(int dice, List<Integer> chosen) {
        if (dice == 0) {
            System.out.println(chosen);
        } else {            
            for (int i = 1; i <= 6; i++) {     // for all possible choices (1-6)
                chosen.add(i);                      // choose
                diceRoll(dice - 1, chosen);         // explore
                chosen.remove(chosen.size() - 1);   // unchoose
                // unchoose is necessary because all recursive calls have a 
                // reference to the same list 
            }
        }
    }

    // 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>());
    }
     
    // Prints all the possible outcomes of rolling the given number
    // of six-sided dice that add up to exactly the given sum, in [#, #, #] format.
    // sumSoFar is the sum of all the numbers in chosen. chosen is 
    // the prefix for all the answers printed. 
    private static void diceSum(int dice, int sum, int sumSoFar, List<Integer> chosen) {
        if (dice == 0 && sumSoFar == sum) {
            System.out.println(chosen);
        } else if (sumSoFar <= sum) {  // needs to be else if - otherwise continues recursing
                                       // when dice is negative if base case wasn't hit        
            for (int i = 1; i <= 6; i++) {   // for all possible choices
                chosen.add(i);                                 // choose
                diceSum(dice - 1, sum, sumSoFar + i, chosen);  // explore
                chosen.remove(chosen.size() - 1);              // unchoose
            }
        }
    }
}