[Leetcode] Insert Delete GetRandom O(1)

Combining hash table and in place manipulation in array.

Description

Implement the RandomizedSet class:

• RandomizedSet() Initializes the RandomizedSet object.
• bool insert(int val) Inserts an item val into the set if not present. Returns true if the item was not present, false otherwise.
• bool remove(int val) Removes an item val from the set if present. Returns true if the item was present, false otherwise.
• int getRandom() Returns a random element from the current set of elements (it's guaranteed that at least one element exists when this method is called). Each element must have the same probability of being returned.

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

Examples

Example 1:

Input
["RandomizedSet", "insert", "remove", "insert", "getRandom", "remove", "insert", "getRandom"]
[[], [1], [2], [2], [], [1], [2], []]
Output
[null, true, false, true, 2, true, false, 2]
Explanation
RandomizedSet randomizedSet = new RandomizedSet();
randomizedSet.insert(1); // Inserts 1 to the set. Returns true as 1 was inserted successfully.
randomizedSet.remove(2); // Returns false as 2 does not exist in the set.
randomizedSet.insert(2); // Inserts 2 to the set, returns true. Set now contains [1,2].
randomizedSet.getRandom(); // getRandom() should return either 1 or 2 randomly.
randomizedSet.remove(1); // Removes 1 from the set, returns true. Set now contains [2].
randomizedSet.insert(2); // 2 was already in the set, so return false.
randomizedSet.getRandom(); // Since 2 is the only number in the set, getRandom() will always return 2.

Solution

insert(): append in array is O(1), so does assigning in hash.

remove(): pop in array is O(1)~O(n). del in hash is O(1).

getRandom(): accessing array is with index is O(1), the requirement can be done by giving a random index within the range of array len. hash cannot use index, so there will be traverse and cost (n).

Array is necessary for using random index to access in O(1). To fulfill removal O(1) constraint, store index of array in hash (val:index). Hash helps us know target position amid array in O(1). Swap target elm with last elm in array. Then, target can be popped in O(1). Note the index info needs modification before swap. We can getRandom without using hash.

• code

ref: https://maxming0.github.io/2020/06/12/Insert-Delete-GetRandom-O1/