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+// # Perl Weekly Challenge #075 Task 1 Coins Sum, Java Program
+// task statement: 
+// You are given a set of coins @C, assuming you have 
+// infinite amount of each coin in the set.
+// Write a script to find how many ways you make 
+// sum $S using the coins from the set @C.
+
+import java.util.Scanner;
+import java.util.ArrayList;
+import java.util.Vector;
+import java.util.Collections;
+import java.util.Arrays;
+
+public class coinssum {
+    static public void main(String[] args) {
+        // int[] coins = new int[] {1, 2, 4};
+        // int total = 5;
+
+        Scanner scn = new Scanner(System.in);
+        System.out.println("Input expected sum of coins:");
+        int total = scn.nextInt();
+        System.out.println("Input number of varieties of coins:");
+        int size = scn.nextInt();
+        int[] coins = new int[size];
+        System.out.println("Input values of the coins:");
+        for (int k = 0; k < size; k++) {
+            coins[k] = scn.nextInt();
+        }
+
+
+// initialize the "ArrayList" for dynamic programming
+        ArrayList<Vector>[] arr_for_dp = new ArrayList[total+1];
+
+        int j = 0;
+        for (int i=0; i <= total; i++) {
+            arr_for_dp[i] = new ArrayList<Vector>();
+            if (i == coins[j]) {
+                Vector temp = new Vector();
+                temp.addElement(new Integer(coins[j]));
+                arr_for_dp[i].add( temp );
+                if (j < coins.length-1) {
+                    j++;
+                }
+            }
+        }
+
+        for (int i=0; i<=total; i++) {
+            for (int k=0; k < coins.length; k++) {
+                if (i-coins[k] > 0) {
+                     for (int p=0; p < arr_for_dp[i-coins[k]].size(); p++) {
+                          Vector partition = arr_for_dp[i-coins[k]].get(p);
+                          Vector partition_p = new Vector<Integer>();
+                          partition_p = (Vector)partition.clone();
+                          partition_p.addElement(coins[k]);
+                          Collections.sort(partition_p);
+                          if ((!arr_for_dp[i].contains(partition_p))) {
+                              arr_for_dp[i].add(partition_p);
+                          }
+                      
+                      }
+                }
+            }
+        }
+
+
+        int ans = arr_for_dp[total].size();
+        if ( ans > 0) {
+            for (int f=0; f<ans; f++) {
+                Vector testvector = arr_for_dp[total].get(f);
+                System.out.println(testvector);
+            }
+        }
+        
+
+        System.out.println(ans);
+
+    }
+
+    
+    
+    
+}
+
+
+
+//references:
+//textbook
+//https://www.w3schools.com/java/java_arraylist.asp
+//https://www.geeksforgeeks.org/array-of-arraylist-in-java/
+//https://www.cis.upenn.edu/~bcpierce/courses/629/jdkdocs/api/java.util.Vector.html