import java.util.*;

// More examples of recursive backtracking
public class Backtracking2 {
   public static void main(String[] args) {
      List<Integer> prices = new ArrayList<>();
      prices.add(1);
      prices.add(2);
      prices.add(3);
      prices.add(5);
      waysToSpend(prices, 3);
   }
   
   // Prints out all the ways to spend the given dollarsLeft using the list
   // of item prices. Items can be purchased more than once, and the order
   // in which the purchases are made matters.
   public static void waysToSpend(List<Integer> prices, int dollarsLeft) {
      waysToSpend(prices, dollarsLeft, new Stack<>());
   }
   
   // Prints out all the ways to spend the given dollarsLeft using the list
   // of item prices, where chosen is the prefix of all the answers printed.
   private static void waysToSpend(List<Integer> prices, int dollarsLeft,
                                   Stack<Integer> chosen) {
      if (dollarsLeft == 0) {
         System.out.println(chosen);
      } else if (dollarsLeft > 0) {  // prevent exploring a dead end!
         for (int price : prices) {
            chosen.push(price);                                    //    choose
            waysToSpend(prices, dollarsLeft - price, chosen);      //    explore
            chosen.pop();                                          //    unchoose
         }
      }
   }
   
}