// Allison Obourn
// CSE 143 - lecture 16
// Prints all possible combinations of dice and all combinations 
// of dice that sum to a given value 

import java.util.*;

public class Dice {
   public static void main(String[] args) {
       diceRoll(3);
       diceSum(3, 7);
       diceSum(5, 7);
       diceSum(15, 87);
   }

   // 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 combinations of rolling the given number of 
   // six-sided dice. 
   // pre: dice >= 0 and soFar != null
   private static void diceRoll(int dice, List<Integer> soFar) {
      if(dice == 0) {
         System.out.println(soFar);
      } else {
         for(int i = 1; i <= 6; i++) {
            soFar.add(i);
            diceRoll(dice - 1, soFar);
            soFar.remove(soFar.size() - 1);
         }        
      }
   }


   // Prints all possible outcomes of rolling the given
   // number of six-sided dice that add up to exactly
   // the given sum, in [#, #, #] format.
   // pre: dice >= 0
   public static void diceSum(int dice, int sum) {
      diceSum(dice, sum, new ArrayList<Integer>(), 0);
   }
   
   // Prints all possible outcomes of rolling the given
   // number of six-sided dice that add up to exactly
   // the given sum
   // pre: dice >= 0 and soFar != null 
   private static void diceSum(int dice, int sum, List<Integer> soFar, int sumSoFar) {
      if(dice == 0) {
         // initially we calculated the total so far here but that slowed us down
         // there is no need to add up the numbers every time when we can add once
         // each as we recurse
         // int sumSoFar = 0;
         // for(int n : soFar) {
          //  sumSoFar += n;
         //}  
         if(sumSoFar == sum) {
            System.out.println(soFar);
         }
      } else if (sumSoFar + 6 * dice >= sum && sumSoFar + dice <= sum) {
         for(int i = 1; i <= 6; i++) {
            soFar.add(i);
            diceSum(dice - 1, sum, soFar, sumSoFar + i);
            soFar.remove(soFar.size() - 1);
         }        
      }
   }

}