What is the algorithmic complexity of the Top K Frequent problem with PriorityQueue? What is the complexity of offer and poll operations?

For the Top K Frequent problem using a PriorityQueue, the algorithmic complexity is usually as follows:

• Counting the frequency of elements — O(N), where N is the number of elements.
• Adding elements to the PriorityQueue (min-heap) with a size limit of K — for each of the M unique elements, the offer operation takes O(log K).

Thus, if M is the number of unique elements, the total complexity will be O(N + M log K).

Operations of PriorityQueue:

• offer (insertion) — O(log n), where n is the current size of the heap.
• poll (removing the root) — O(log n).

In the context of Top K Frequent, the size of the heap is limited to K, so offer and poll operations work in O(log K), which is efficient when K << M.