// Jeremy Lipschutz
// Showing an application of recursion, brute-force exploring
// of possibilities

import java.util.*;
public class RecursiveBacktracking {
   public static void main(String[] args) {
      //sillyHangman(3);
      //diceRoll(3);
      
      diceSum(3, 10);
      
   }
   
   // Prints all strings of the given length consisting of a's and b's
   public static void sillyHangman(int length) {
      sillyHangman(length, "");
   }
   
   private static void sillyHangman(int length, String decisions) {
      if(decisions.length() == length) {
         System.out.println(decisions);
      } else {
         sillyHangman(length, decisions + "a");
         sillyHangman(length, decisions + "b");
         /*
         // We can change the test for this for-loop such that we choose not only a's and b's
         // but also more letters like the whole alphabet 
         for(char c = 'a'; c <= 'b'; c++) { // For each decision we have we can recur on this choice
            sillyHangman(length, decisions + c);
         }
         */
      }
   }
   
   /* Iterative solution that does not scale with length :(
   public static void sillyHangman(int length) {
      for(char c1 = 'a'; c1 <= 'b'; c1++) {
         for(char c2 = 'a'; c2 <= 'b'; c2++) {
            for(char c3 = 'a'; c3 <= 'b'; c3++) {
               for(char c4 = 'a'; c4 <= 'b'; c4++) {
                  System.out.println("" + c1 + c2 + c3 + c4);
               }
            }  
         }
      }
   }
   */
   
   // Assumes that n >= 0
   // Prints all possible outcomes of rolling the given number of
   // 6-sided dice in the format [#, #, #]
   public static void diceRoll(int n) {
      diceRoll(new ArrayList<Integer>(), n);
   }
   
   // prints all possible outcomes of rolling the given number of
   // 6-sided dice in the format [#, #, #] with chosen as the rolls
   // that have already been computed
   private static void diceRoll(List<Integer> chosen, int n) {
      if(chosen.size() == n) {
         System.out.println(chosen);
      } else {
         for(int i = 1; i <= 6; i++) { // for each option 1-6 
            chosen.add(i);                    // CHOOSE
            diceRoll(chosen, n);              // EXPLORE
            chosen.remove(chosen.size() - 1); // UNCHOOSE
         }
      }
   }
   
   // Assumes that n >= 0
   // Prints all possible outcomes of rolling the given number of
   // 6-sided dice in the format [#, #, #] that add up to the given sum
   public static void diceSum(int n, int sum) {
      diceSum(new ArrayList<Integer>(), n, sum);
   }
   
   
   // prints all possible outcomes of rolling the given number of
   // 6-sided dice in the format [#, #, #] with chosen as the rolls
   // that have already been computed
   // sum represents the remaining sum that we have left to roll
   private static void diceSum(List<Integer> chosen, int remaining, int sum) {
      if(remaining == 0 && sum == 0) {
         System.out.println(chosen);
      } else if(sum >= remaining && sum <= remaining * 6) {
         for(int i = 1; i <= 6; i++) { // for each option 1-6 
            chosen.add(i);                                // CHOOSE
            diceSum(chosen, remaining - 1, sum - i);      // EXPLORE
            chosen.remove(chosen.size() - 1);             // UNCHOOSE
         }
      }
   }
}