System-Design-Question

Merge K Sorted Lists

Category: dsa Date: 2026-02-15

Merge K Sorted Lists System Design Discussion

1. Requirements (Functional + Non-functional)

• Functional Requirements:
  • Merge K sorted linked lists into one sorted linked list.
  • Support insertion of new linked lists.
  • Support removal of existing linked lists.
• Non-functional Requirements:
  • Scalability: handle a large number of linked lists (hundreds or thousands).
  • Performance: merge linked lists efficiently (O(N log K) time complexity).
  • Availability: ensure system remains operational even in case of node failures.

2. High-Level Architecture

• Data Ingestion: Create a separate node in the system for each linked list. This node will be responsible for receiving new linked lists and inserting them into the system.
• Merge Service: This service will be responsible for merging the linked lists. It will utilize a priority queue data structure to efficiently select the next node from the linked lists to be merged.
• Queue Service: This service will manage the priority queue and ensure that nodes are inserted and removed efficiently.
• Storage Service: This service will store the merged linked list.

High-Level Architecture Diagram

+---------------+
|  Data Ingestion  |
+---------------+
         |
         |
         v
+---------------+       +---------------+
|  Merge Service  |       |  Queue Service  |
+---------------+       +---------------+
         |                   |
         |                   |
         v                   v
+---------------+       +---------------+
|  Priority Queue |       |  Node Store  |
+---------------+       +---------------+
         |                   |
         |                   |
         v                   v
+---------------+       +---------------+
|  Storage Service |       |  Node Removal  |
+---------------+       +---------------+

3. Database Design

• Node Table: Store information about each node, including the linked list it belongs to and its priority in the priority queue.
• Node Store Table: Store the actual node data and its corresponding linked list.
• Storage Table: Store the merged linked list.

Database Schema

CREATE TABLE Node (
    id INT PRIMARY KEY,
    linked_list_id INT,
    priority INT
);

CREATE TABLE Node_Store (
    id INT PRIMARY KEY,
    data INT,
    linked_list_id INT
);

CREATE TABLE Storage (
    id INT PRIMARY KEY,
    data INT
);

4. Scaling Strategy

• Horizontal Scaling: Add more instances of the Merge Service, Queue Service, and Storage Service to handle increased load.
• Load Balancing: Use a load balancer to distribute incoming requests across multiple instances of the services.
• Caching: Implement caching at the Storage Service to reduce the number of database queries.

5. Bottlenecks

• Priority Queue: The priority queue can become a bottleneck when dealing with a large number of linked lists.
• Node Removal: Removing nodes from the priority queue can be expensive.

6. Trade-offs

• Complexity: The system design is complex due to the use of a priority queue and multiple services.
• Scalability: The system can scale horizontally, but may require additional infrastructure and maintenance.

Solution using the First Principle of System Design (The Single Responsibility Principle)

The Single Responsibility Principle (SRP) states that a class or module should have only one reason to change. In the context of this problem, we can apply the SRP as follows:

• Node Class: Responsible for storing and managing the data of a single node.
• Priority Queue Class: Responsible for managing the priority queue and selecting the next node to be merged.
• Merge Class: Responsible for merging the linked lists.
• Storage Class: Responsible for storing the merged linked list.

By applying the SRP, we can ensure that each class or module has a single responsibility and can be modified independently without affecting other parts of the system.

Code Example

class Node:
    def __init__(self, data):
        self.data = data
        self.next = None

class PriorityQueue:
    def __init__(self):
        self.queue = []

    def insert(self, node):
        heapq.heappush(self.queue, node)

    def remove(self):
        return heapq.heappop(self.queue)

class Merge:
    def __init__(self):
        self.queue = PriorityQueue()

    def merge(self, node):
        self.queue.insert(node)

    def get_next_node(self):
        return self.queue.remove()

class Storage:
    def __init__(self):
        self.storage = []

    def store(self, node):
        self.storage.append(node)

Note: This is a simplified example and may not cover all edge cases. In a real-world implementation, you would need to consider additional factors such as error handling and edge cases.

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