Leetcode: Insert Delete GetRandom O(1) - Duplicates allowed

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();

The idea is to add a set to the hashMap to remember all the locations of a duplicated number.

 public class RandomizedCollection {
     HashMap<Integer, HashSet<Integer>> map;
     ArrayList<Integer> arr;
     java.util.Random random;

     /** Initialize your data structure here. */
     public RandomizedCollection() {
         map = new HashMap<Integer, HashSet<Integer>>();
         arr = new ArrayList<Integer>();
         random = new java.util.Random();
     }

     /** Inserts a value to the collection. Returns true if the collection did not already contain the specified element. */
     public boolean insert(int val) {
         boolean res = false;
         if (!map.containsKey(val)) {
             map.put(val, new HashSet<Integer>());
             res = true;
         }
         arr.add(val);
         map.get(val).add(arr.size()-1);
         return res;
     }

     /** Removes a value from the collection. Returns true if the collection contained the specified element. */
     public boolean remove(int val) {
         if (!map.containsKey(val)) return false;
         int lastItem = arr.get(arr.size()-1);
         int index = arr.size()-1;
         if (lastItem != val) {
             HashSet<Integer> lastItemSet = map.get(lastItem);
             index = map.get(val).iterator().next();
             arr.set(index, lastItem);
             lastItemSet.remove(arr.size()-1);
             lastItemSet.add(index);
         }

         if (map.get(val).size() == 1) map.remove(val);
         else map.get(val).remove(index);
         arr.remove(arr.size()-1);
         return true;
     }

     /** Get a random element from the collection. */
     public int getRandom() {
         return arr.get(random.nextInt(arr.size()));
     }
 }

 /**
  * Your RandomizedCollection object will be instantiated and called as such:
  * RandomizedCollection obj = new RandomizedCollection();
  * boolean param_1 = obj.insert(val);
  * boolean param_2 = obj.remove(val);
  * int param_3 = obj.getRandom();
  */