System-Design-Question

Word Ladder

Category: dsa Date: 2026-03-27

System Design Discussion: Word Ladder

Problem Statement: Given two words, find a sequence of words where each word differs from the previous one by exactly one character, and the final word is the target word.

Requirements:

Functional Requirements:

1. Given two words, return a list of words that transform one word into the other.
2. Handle words with different lengths.
3. Handle words with special characters or non-ASCII characters.

Non-Functional Requirements:

1. Scalability: handle a large number of users and requests.
2. Performance: respond within 1 second for a typical request.
3. Availability: ensure the system is available 99.99% of the time.

High-Level Architecture: The system will consist of three main components:

1. Client: a RESTful API that accepts user requests and sends them to the Word Ladder Service.
2. Word Ladder Service: a stateless service that performs the word ladder computation using a combination of graph algorithms and memoization.
3. Database: a distributed database that stores the precomputed word ladders and their metadata.

Database Design: We’ll use a graph database like Neo4j to store the word ladders. Each node will represent a word, and each edge will represent a single-character difference between two words.

• Node properties:
  • word: the actual word
  • length: the length of the word
  • precomputed: a boolean indicating whether the word ladder has been precomputed
• Edge properties:
  • source: the source word
  • target: the target word
  • difference: the character difference between the two words

Scaling Strategy:

1. Horizontal scaling: add more instances of the Word Ladder Service as the load increases.
2. Caching: use a distributed caching layer like Redis to store the precomputed word ladders and their metadata.
3. Load balancing: use a load balancer to distribute incoming requests across multiple instances of the Word Ladder Service.

Bottlenecks:

1. Computational complexity: the word ladder computation has a time complexity of O(n!), where n is the length of the word.
2. Memory usage: storing precomputed word ladders and their metadata can consume a significant amount of memory.

Trade-offs:

1. Complexity vs. performance: a more complex algorithm (e.g., using a genetic algorithm) may be faster but also more resource-intensive.
2. Scalability vs. simplicity: a simpler algorithm (e.g., using a brute-force approach) may be easier to understand but also less scalable.

Solution using the First Principle of System Design:

The First Principle of System Design states that “any system must be designed with the goal of achieving a balance between the competing goals of performance, scalability, and availability.”

To achieve this balance, we’ll use a combination of:

1. Graph algorithms: to efficiently compute the word ladders.
2. Memoization: to store precomputed word ladders and reduce the computational complexity.
3. Distributed caching: to store the precomputed word ladders and their metadata.
4. Horizontal scaling: to add more instances of the Word Ladder Service as the load increases.
5. Load balancing: to distribute incoming requests across multiple instances of the Word Ladder Service.

By following this approach, we can achieve a system that is both scalable and performant, while also ensuring high availability.

Learning links:

• Graph databases: Neo4j
• Distributed caching: Redis
• Load balancing: HAProxy
• Graph algorithms: Khan Academy
• System design principles: System Design Primer

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