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.

1. insert(val): Inserts an item val to the collection.

2. remove(val): Removes an item val from the collection if present.

3. 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();

public class RandomizedCollection {
    ArrayList<Integer> nums;
    // Map of element -> Set of indices at which it is present
    HashMap<Integer, Set<Integer>> map;
    Random random = new Random();

    /** Initialize your data structure here. */
    public RandomizedCollection() {
        nums = new ArrayList<Integer>();
        map = new HashMap<Integer, Set<Integer>>();
    }

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

    /**
     * Removes a value from the collection. Returns true if the collection contained
     * the specified element.
     */
    public boolean remove(int val) {
        boolean contain = map.containsKey(val);
        if (!contain)
            return false;
        int index = map.get(val).iterator().next();
        map.get(val).remove(index);
        if (index < nums.size() - 1) {
            // Swapping
            int lastOne = nums.get(nums.size() - 1);
            nums.set(index, lastOne);
            // Changing indices in set of last element
            map.get(lastOne).remove(nums.size() - 1);
            map.get(lastOne).add(index);
        }
        nums.remove(nums.size() - 1);

        if (map.get(val).isEmpty())
            map.remove(val);
        return true;
    }

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