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();

Referrence Source)

Replaced HashSet with LinkedHashSet because the set.iterator() might be costly when a number has too many duplicates. Using LinkedHashSet can be considered as O(1) if we only get the first element to remove.

// arr = all the elems in the list
// index = a map storing the index of the elem in the list

class RandomizedCollection {

    Map<Integer, LinkedHashSet<Integer>> index;
    List<Integer> arr;
    java.util.Random rd = new java.util.Random();

    /** Initialize your data structure here. */
    public RandomizedCollection() {
        index = new HashMap<>();
        arr = new ArrayList<>();
    }

    /** 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 = index.containsKey(val);
        if(!res){
            index.put(val,new LinkedHashSet<Integer>());
            // maintains the order of insersion
        }
            (index.get(val)).add(arr.size());
            arr.add(val);
        return !res;
    }

    /** Removes a value from the collection. Returns true if the collection contained the specified element. */
    public boolean remove(int val) {
        if(!index.containsKey(val)) return false;
        LinkedHashSet<Integer> set = index.get(val);
        // linked hash set is faster using its iterator to get next()
        int idx = set.iterator().next();

        int replacement = arr.get(arr.size()-1);
        // replace with the last elem in the array
        arr.set(idx,replacement);
        set.remove(idx);

        // if the last elem in the array is the element to delete
        if(idx==arr.size()-1){
            arr.remove(idx);
        }else{
            // if not, set the index of replacement elem to the index of removed elem
            // delete the last elem from the array
            (index.get(replacement)).remove(arr.size() - 1);
            (index.get(replacement)).add(idx);
            arr.remove(arr.size()-1);
        }

        if(set.isEmpty()) index.remove(val);
        return true;

    }

    /** Get a random element from the collection. */
    public int getRandom() {
        // Random rd = new Random();
        // this should be initiate in the beginning to avoid multiple space 
        int idx = rd.nextInt(arr.size());
        return arr.get(idx);
    }
    // return arr.get( rd.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();
 */