Leetcode 380: Insert Delete GetRandom O(1)

https://leetcode.com/problems/insert-delete-getrandom-o1/description/

Design a data structure that supports all following operations in average O(1) time.

1. insert(val): Inserts an item val to the set if not already present.
2. remove(val): Removes an item val from the set if present.
3. getRandom: Returns a random element from current set of elements. Each element must have the same probability of being returned.

Example:

// Init an empty set.
RandomizedSet randomSet = new RandomizedSet();

// Inserts 1 to the set. Returns true as 1 was inserted successfully.
randomSet.insert(1);

// Returns false as 2 does not exist in the set.
randomSet.remove(2);

// Inserts 2 to the set, returns true. Set now contains [1,2].
randomSet.insert(2);

// getRandom should return either 1 or 2 randomly.
randomSet.getRandom();

// Removes 1 from the set, returns true. Set now contains [2].
randomSet.remove(1);

// 2 was already in the set, so return false.
randomSet.insert(2);

// Since 2 is the only number in the set, getRandom always return 2.
randomSet.getRandom();

Notes:

The key to this question is that: how can we achieve O(1) in getRandom()? since there is exiting data structures for insert() and remove() in O(1), for example, hashmap.

Vector or array can localize the element or getRandom() in O(1) (by using rand() for getRandom()), but how can we achieve O(1) in deleting one element?

It is known that we can pop_back() of a vector in O(1). So if we do not care about the deleted element any more, we can do a trick here:

Swap the A[i] with the A.back(). Then we can pop_back(). Both steps are in O(1). So we just need to use a hashmap to memorize the location of the A[i], then we can perform all swap and delete in O(1).

See the code below:

class RandomizedSet {
public:
    /** Initialize your data structure here. */
    RandomizedSet() {
       
    }

    /** Inserts a value to the set. Returns true if the set did not already contain the specified element. */
    bool insert(int val) {
        if(!ump.count(val)) {
            ump[val] = data.size();
            data.push_back(val);
            return true;
        }
        return false;
    }

    /** Removes a value from the set. Returns true if the set contained the specified element. */
    bool remove(int val) {
        if(ump.count(val)) {
            int indx = ump[val], last = data.back();
            data[indx] = last;
            ump[last] = indx;
            ump.erase(val);
            data.pop_back();
            return true;
        }
        return false;
    }

    /** Get a random element from the set. */
    int getRandom() {
        int len = data.size();
        return data[rand()%len];
    }

private:
    unordered_map<int, int> ump;
    vector<int> data;
};

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