LFU Cache Implementation

Design and implement a data structure for Least Frequently Used (LFU) cache. It should support the following operations:

• LFUCache(int capacity): Initializes the LFU Cache with positive size capacity.
• Get(int key): Returns the value of the key if present, otherwise returns -1.
• Put(int key, int value): Updates the value of the key if present, or inserts the key if not present. When the cache reaches its capacity, it should invalidate the least frequently used item. If there is a tie (i.e., two or more keys with the same frequency), the least recently used key should be invalidated.

Example 1

  
Input:

  ["LFUCache", "put", "put", "get", "put", "get", "get", "put", "get", "get", "get"]

  [[2], [1, 1], [2, 2], [1], [3, 3], [2], [3], [4, 4], [1], [3], [4]]
  
Output:

  [null, null, null, 1, null, -1, 3, null, -1, 3, 4]
  
Explanation: 

      
LFUCache cache = new LFUCache(2);  // Cache capacity is 2
      
cache.put(1, 1);
      
cache.put(2, 2);
      
cache.get(1);      // returns 1
      
cache.put(3, 3);   // evicts key 2
      
cache.get(2);      // returns -1 (not found)
      
cache.get(3);      // returns 3
      
cache.put(4, 4);   // evicts key 1
      
cache.get(1);      // returns -1 (not found)
      
cache.get(3);      // returns 3
      
cache.get(4);      // returns 4
    

Example 2

  
Input:

  ["LFUCache", "put", "put", "put", "get", "get"]

  [[2], [1, 1], [2, 2], [3, 3], [2], [1]]
  
Output:

  [null, null, null, null, 2, -1]
  
Explanation: 

      
LFUCache cache = new LFUCache(2);  // Cache capacity is 2
      
cache.put(1, 1);
      
cache.put(2, 2);
      
cache.put(3, 3);   // evicts key 1
      
cache.get(2);      // returns 2
      
cache.get(1);      // returns -1 (not found)
    

Constraints

  
0 ≤ capacity ≤ 10^4
  
0 ≤ key ≤ 10^5
  
0 ≤ value ≤ 10^9
  
At most 2 * 10^5 calls will be made to get and put
  
Time Complexity: O(1) for all operations
  
Space Complexity: O(capacity)