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();

重复后remove 时没办法找到对应的合适的位置, 所以要用map<interger, hashset<>>中hashset来保存多个位置

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();
 */