Design a data structure that supports all following operations in average O(1) time.

Note: Duplicate elements are allowed.
insert(val): Inserts an item val to the collection.
remove(val): Removes an item val from the collection if present.
getRandom: Returns a random element from current collection of elements. The probability of each element being returned is linearly related to the number of same value the collection contains.
Example:

// Init an empty collection.
RandomizedCollection collection = new RandomizedCollection();

// Inserts 1 to the collection. Returns true as the collection did not contain 1.
collection.insert(1);

// Inserts another 1 to the collection. Returns false as the collection contained 1. Collection now contains [1,1].
collection.insert(1);

// Inserts 2 to the collection, returns true. Collection now contains [1,1,2].
collection.insert(2);

// getRandom should return 1 with the probability 2/3, and returns 2 with the probability 1/3.
collection.getRandom();

// Removes 1 from the collection, returns true. Collection now contains [1,2].
collection.remove(1);

// getRandom should return 1 and 2 both equally likely.
collection.getRandom();

 1 public class RandomizedCollection {
 2     HashMap<Integer, HashSet<Integer>> map;
 3     ArrayList<Integer> arr;
 4     java.util.Random random;
 5 
 6     /** Initialize your data structure here. */
 7     public RandomizedCollection() {
 8         map = new HashMap<Integer, HashSet<Integer>>();
 9         arr = new ArrayList<Integer>();
10         random = new java.util.Random();
11     }
12     
13     /** Inserts a value to the collection. Returns true if the collection did not already contain the specified element. */
14     public boolean insert(int val) {
15         boolean res = false;
16         if (!map.containsKey(val)) {
17             map.put(val, new HashSet<Integer>());
18             res = true;
19         }
20         arr.add(val);
21         map.get(val).add(arr.size()-1);
22         return res;
23     }
24     
25     /** Removes a value from the collection. Returns true if the collection contained the specified element. */
26     public boolean remove(int val) {
27         if (!map.containsKey(val)) return false;
28         int lastItem = arr.get(arr.size()-1);
29         int index = arr.size()-1;
30         if (lastItem != val) {
31             HashSet<Integer> lastItemSet = map.get(lastItem);
32             index = map.get(val).iterator().next();
33             arr.set(index, lastItem);
34             lastItemSet.remove(arr.size()-1);
35             lastItemSet.add(index);
36         }
37         
38         if (map.get(val).size() == 1) map.remove(val);
39         else map.get(val).remove(index);
40         arr.remove(arr.size()-1);
41         return true;
42     }
43     
44     /** Get a random element from the collection. */
45     public int getRandom() {
46         return arr.get(random.nextInt(arr.size()));
47     }
48 }
49 
50 /**
51  * Your RandomizedCollection object will be instantiated and called as such:
52  * RandomizedCollection obj = new RandomizedCollection();
53  * boolean param_1 = obj.insert(val);
54  * boolean param_2 = obj.remove(val);
55  * int param_3 = obj.getRandom();
56  */