Insert Delete GetRandom O(1) – Duplicates allowed LeetCode Solution

Difficulty Level Hard
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Problem Statement:

Insert Delete GetRandom O(1) – Duplicates allowed LeetCode Solution: RandomizedCollection is a data structure that contains a collection of numbers, possibly duplicates (i.e., a multiset). It should support inserting and removing specific elements and also removing a random element.

Implement the RandomizedCollection class:

  • RandomizedCollection() Initializes the empty RandomizedCollection object.
  • bool insert(int val) Inserts an item val into the multiset, even if the item is already present. Returns true if the item is not present, false otherwise.
  • bool remove(int val) Removes an item val from the multiset if present. Returns true if the item is present, false otherwise. Note that if val has multiple occurrences in the multiset, we only remove one of them.
  • int getRandom() Returns a random element from the current multiset of elements. The probability of each element being returned is linearly related to the number of same values the multiset contains.

You must implement the functions of the class such that each function works on average O(1) time complexity.

Note: The test cases are generated such that getRandom will only be called if there is at least one item in the RandomizedCollection.

Examples:

Input

["RandomizedCollection", "insert", "insert", "insert", "getRandom", "remove", "getRandom"]
[[], [1], [1], [2], [], [1], []]

Output

[null, true, false, true, 2, true, 1]

Explanation

RandomizedCollection randomizedCollection = new RandomizedCollection();
randomizedCollection.insert(1);   // return true since the collection does not contain 1.
                                  // Inserts 1 into the collection.
randomizedCollection.insert(1);   // return false since the collection contains 1.
                                  // Inserts another 1 into the collection. Collection now contains [1,1].
randomizedCollection.insert(2);   // return true since the collection does not contain 2.
                                  // Inserts 2 into the collection. Collection now contains [1,1,2].
randomizedCollection.getRandom(); // getRandom should:
                                  // - return 1 with probability 2/3, or
                                  // - return 2 with probability 1/3.
randomizedCollection.remove(1);   // return true since the collection contains 1.
                                  // Removes 1 from the collection. Collection now contains [1,2].
randomizedCollection.getRandom(); // getRandom should return 1 or 2, both equally likely.

Approach:

Idea:

The data structure can be implemented with the help of a Hash_map consisting of a pair of <int, Hash_set> and an arrayList. The Hash_map will store the indices of the elements and the list will store the list of elements present so far. The required methods can be implemented as follows:

  • insert: Insert the element to the list and add the index to HashMap[element].
  • remove: First, we find any index of the element to be removed in the HashMap. Now we will update the element in this index with the last element of the list. Since the last element of the list has been assigned a new index, we have to update its value in the HashMap. We also have to get rid of the index of the element we removed from the HashMap.
  • getRandom: Just sample a random element from the list.

Code for Insert Delete GetRandom O(1) – Duplicates allowed LeetCode Solution:

C++ Solution:

class RandomizedCollection {
public:
    unordered_map<int,unordered_set<int>> mp;
    vector<int> arr;
    int size = 0;
    
    RandomizedCollection() {
        
    }
    
    bool insert(int val) {
        bool status = not mp.count(val);
        mp[val].insert(size);
        arr.push_back(val);
        size++;
        return status;
    }
    
    bool remove(int val) {
        bool status = mp.count(val);
        if(status){
            int last_element = arr.back();
            if(val == last_element){
                mp[val].erase(arr.size()-1);
                arr.pop_back();
                size--;
                if(mp[val].size()==0)
                    mp.erase(val);
            }
            else{
                int index;
                for(auto it:mp[val]){
                    index = it;
                    break;
                }
                arr[index] = last_element;
                mp[last_element].erase(arr.size()-1);
                arr.pop_back();
                size--;
                mp[val].erase(index);
                mp[last_element].insert(index);
                if(mp[val].size()==0)
                    mp.erase(val);
            } 
        }
        return status;
    }
    
    int getRandom() {
        return arr[rand()%arr.size()];
    }
};

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

Complexity Analysis of Insert Delete GetRandom O(1) – Duplicates allowed LeetCode Solution:

  • Time Complexity: The time complexity of the above code is O(n) with n being the number of operations.
  • Space Complexity: The space complexity of the above code is O(n).
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