FEATURE: Implement Topological Sort using DFS and Indegree visualization

[TejasSaraf]

Feature Summary

In a Directed Acyclic Graph (DAG), topological sorting is the process of linearly ranking vertices so that, for each directed edge u-v, vertex u appears before v in the ordering.

Description

DFS-based Approach

• Uses a recursive depth-first search
• Typically implemented using a stack
• Detects cycles during traversal

Indegree-based Approach (Kahn's Algorithm)

• Uses a queue to process nodes
• Iteratively removes nodes with zero in-degree
• Naturally detects cycles if not all nodes are processed

Problems It Solves

1. Dependency Resolution: Topological sort is crucial for solving dependency-related problems in various domains, such as:

• Build systems and package managers
• Task scheduling
• Course prerequisites in academic planning

2. Cycle Detection: Both implementations can detect cycles in a graph, which is essential for identifying circular dependencies.

By implementing and visualizing both approaches, users gain a comprehensive understanding of topological sorting, its applications, and the trade-offs between different algorithms. This feature enhances problem-solving skills and provides practical insights into graph theory and algorithm design.

Proposed Solution

No response

Alternatives Considered

No response

Screenshots/Logs

No response

Additional Information

• [X] I have searched for existing feature requests
• [X] I am willing to help implement this feature
• [X] I can provide more details or clarification if needed

[sakeel-103]

@TejasSaraf Just a reminder msg, To complete your implementation as soon as you can.