Introduction

Top K Frequent Elements means:

  • finding the k elements
    that appear most frequently
    in an array

Goal:

  • return only the
    k highest frequency elements

Example:

nums =[1,1,1,2,2,3]
k = 2

Output:
[1,2]

Explanation:

Frequency:
1 → 3
2 → 2
3 → 1

Top 2 frequent:
[1,2]

This problem is one of the most important applications of:

Hash Map + Min Heap

Constraints

1 <= nums.length <= 10^5

Approach : Hash Map + Min Heap

Explanations:

Explanation:

The idea is:

  • count frequency
    using Hash Map
  • keep only top k
    frequent elements
    inside Min Heap

Steps:

  1. Count frequencies.
  2. Create Min Heap.
  3. Insert frequency pairs.
  4. Keep heap size k.
  5. Remove smallest frequency.
  6. Extract heap elements.

Condition:

Heap Size > k
Remove minimum frequency element

Observation:

Heap always stores k most frequent elements.

This approach:

  • avoids sorting
    all frequencies
  • efficiently finds
    top k answers

Dry Run

nums:[1,1,1,2,2,3]k = 2

Frequency Map:
1 → 3
2 → 2
3 → 1

Heap:
(1,3)
(2,2)

Heap Size = 2

Add:
(3,1)
Heap Size > 2

Remove:
(3,1)

Remaining:
(1,3)
(2,2)

Answer:
[1,2]

Practice :

Complexity Analysis :

Time Complexity:- O(n log k)
Explanation :
Heap operations take log k time.

Space Complexity:- O(n)
Explanation :
Frequency map and heap storage.

Why This Problem is Important

This problem builds the foundation for:

  • Hash Maps
  • Min Heaps
  • Frequency counting
  • Top-K problems
  • Priority Queues

Real-World Applications

This pattern is used in:

  • Search rankings
  • Trending topics
  • Recommendation engines
  • Analytics systems
  • Log processing

Common Beginner Mistakes

  • Sorting entire array
  • Ignoring frequency map
  • Using wrong heap type
  • Forgetting heap size limit
  • Returning frequencies instead of values

Interview Tip

Interviewers often expect:

  • Hash Map explanation
  • Min Heap optimization
  • Top-K pattern discussion
  • Complexity comparison

Always explain:

  • frequency counting first
  • why heap size stays k
  • why Min Heap is used

Related Questions

  • Kth Largest Element
  • Last Stone Weight
  • Merge K Sorted Lists
  • Find Median from Data Stream
  • K Closest Points to Origin

Final Takeaway

The Top K Frequent Elements problem is one of the most important heap interview questions.

It teaches:

  • Hash Map usage
  • Min Heap optimization
  • Frequency counting
  • Top-K pattern

Understanding this problem builds a strong foundation for:

  • advanced heap problems
  • priority queue algorithms
  • interview-level data structures.