Design a data structure that supports all following operations in average O(1) time.
insert(val): Inserts an item val to the set if not already present.remove(val): Removes an item val from the set if present.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 1 is the only number in the set, getRandom always return 1. randomSet.getRandom();
这道题是设计实现一个<插入、删除、随机取>三种操作平均时间复杂度均为O(1)的数据结构，题目难度为Hard。
用Hash Table能够满足插入和删除的平均时间复杂度要求，但是随机取不能满足。如果用vector存储数据，能够满足随机取的时间复杂度要求，但是插入和删除需要查找，不满足时间复杂度要求。单一的数据存储形式不能满足条件，可以将两者结合，用vector来满足随机取的时间复杂度，用Hash Table来满足插入和删除时查找的时间复杂度。将数据存储在vector中，在Hash Table中存储<value, index>对，其中index为value在vector中的下标，这样插入操作就非常简单了，不再详述；删除操作先在Hash Table中查找删除数据在vector中下标，然后将vector尾部数据存入该下标位置，同时更新Hash Table中vector尾部数据的对应下标，最后删除vector尾部数据和Hash Table中对应数据即可；随机取vector中数据能够在O(1)时间复杂度完成，不再详述。具体代码：
class RandomizedSet { vector<int> data; unordered_map<int, int> hash; 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(hash.find(val) != hash.end()) return false; data.push_back(val); hash[val] = data.size() - 1; return true; } /** Removes a value from the set. Returns true if the set contained the specified element. */ bool remove(int val) { if(hash.find(val) == hash.end()) return false; data[hash[val]] = data.back(); hash[data.back()] = hash[val]; data.pop_back(); hash.erase(val); return true; } /** Get a random element from the set. */ int getRandom() { return data[rand()%data.size()]; } }; /** * 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(); */