Top K Frequent Elements
Category: dsa
Date: 2026-03-05
Top K Frequent Elements System Design Discussion
1. Requirements
Functional Requirements:
- Given an array of integers and an integer
k, return the top k most frequent elements in the array.
- Handle arrays of varying sizes and frequencies of elements.
- Provide a solution that is efficient in terms of time and space complexity.
Non-Functional Requirements:
- Scalability: Handle large input arrays with millions of elements.
- Responsiveness: Ensure the system responds quickly to user queries.
- Fault Tolerance: Handle edge cases such as empty arrays or invalid input.
2. High-Level Architecture
The high-level architecture for Top K Frequent Elements system design involves the following components:
- Input Interface: Handles user input (array of integers and
k value).
- Frequency Counter: Computes the frequency of each element in the input array.
- Heap Data Structure: Stores the top
k most frequent elements.
- Output Interface: Returns the top
k most frequent elements to the user.
3. Database Design (Not Applicable)
Since this is a system design problem, we will not be using a traditional database. However, if we were to use a database, it would be a NoSQL database such as Apache Cassandra or Amazon DynamoDB to handle the frequency counter and heap data structure.
4. Scaling Strategy
To scale the system, we can use the following strategies:
- Horizontal Partitioning: Divide the input array into smaller chunks and process each chunk in parallel using multiple machines.
- Distributed Hash Table (DHT): Use a DHT such as Apache Cassandra or Amazon DynamoDB to distribute the frequency counter and heap data structure across multiple machines.
- Load Balancing: Use a load balancer to distribute incoming requests across multiple machines.
5. Bottlenecks
The following are potential bottlenecks in the system:
- Frequency Counter: Computing the frequency of each element in the input array can be computationally expensive for large input arrays.
- Heap Data Structure: Maintaining the heap data structure can be expensive for large
k values.
- Input Interface: Handling large input arrays can be slow and memory-intensive.
6. Trade-offs
The following are trade-offs in the system:
- Time Complexity vs. Space Complexity: Using a hash table to compute the frequency of each element reduces space complexity but increases time complexity.
- Scalability vs. Responsiveness: Using a distributed architecture improves scalability but can decrease responsiveness.
- Fault Tolerance vs. Performance: Using a fault-tolerant architecture can decrease performance but improves robustness.
First Principle of System Design Solution
The first principle of system design states that a system should be designed to handle the maximum possible traffic, assuming all users will be online at the same time.
Top K Frequent Elements Solution
To solve the Top K Frequent Elements problem, we can use a combination of the following data structures:
- Hash Table: To compute the frequency of each element in the input array.
- Heap Data Structure: To store the top
k most frequent elements.
The algorithm works as follows:
- Compute the frequency of each element in the input array using a hash table.
- Create a min-heap data structure to store the top
k most frequent elements.
- Iterate over the hash table and for each element, insert it into the min-heap if it is not full.
- If the min-heap is full, remove the smallest element from the heap and insert the new element.
- Return the top
k most frequent elements from the min-heap.
Time Complexity: O(n log k) where n is the size of the input array.
Space Complexity: O(n + k) where n is the size of the input array.
Learning Links: