Top K Frequent Elements

Problem Description

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

Key Insights

• The problem requires counting the frequency of each element in the array.
• We need to identify the top k elements based on their frequency.
• Different data structures can be used, such as hash tables for counting and heaps for retrieving the top elements efficiently.
• The algorithm should have a time complexity better than O(n log n).

Space and Time Complexity

Time Complexity: O(n) for counting frequencies and O(k log n) for retrieving the top k elements using a heap, making the overall complexity O(n + k log n).
Space Complexity: O(n) for storing the frequency count.

Solution

To solve the problem, we can use the following steps:

1. Count the frequency of each element in the array using a hash table (or dictionary).
2. Use a min-heap to keep track of the top k frequent elements. The heap will store pairs of (frequency, element).
3. If the size of the heap exceeds k, we remove the element with the smallest frequency.
4. Finally, we extract the elements from the heap as our result.

Code Solutions