Top K Frequent Elements

Problem

Given an integer array nums and an integer k, return the k most frequent elements. You may return the answer in any order.

Your algorithm's time complexity must be better than O(n log n).

Input: Array nums, integer k. Output: Array of k integers — most frequent elements.

Input: nums = [1,1,1,2,2,3], k = 2 → Output: [1,2]

Input: nums = [1], k = 1 → Output: [1]

Bucket Sort (Optimal) — Count freq with hash map. Build buckets[freq] = [nums...]. Walk buckets from highest freq down, collect until k. Time: O(n).
Min-Heap of size k — Iterate freq map, push (freq, num) into heap, pop when size > k. Final heap = top k. Time: O(n log k).
Quickselect — Partition by frequency. Avg O(n), worst O(n²).

Given an integer array nums and an integer k, return the k most frequent elements. You may return the answer in any order.

Your algorithm's time complexity must be better than O(n log n).

Input: Array nums, integer k. Output: Array of k integers — most frequent elements.

Input: nums = [1,1,1,2,2,3], k = 2 → Output: [1,2]

Input: nums = [1], k = 1 → Output: [1]

Bucket Sort (Optimal) — Count freq with hash map. Build buckets[freq] = [nums...]. Walk buckets from highest freq down, collect until k. Time: O(n).
Min-Heap of size k — Iterate freq map, push (freq, num) into heap, pop when size > k. Final heap = top k. Time: O(n log k).
Quickselect — Partition by frequency. Avg O(n), worst O(n²).