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Topological Sort - Technical Overview

1. Definition: Topological sort is an ordering of the vertices in a directed acyclic graph (DAG) such that for every directed edge u → v, vertex u comes before vertex v.

2. Purpose: It is used for scheduling tasks, resolving dependencies, and organizing data.

3. Algorithm Steps:

• Calculate in-degree for each vertex.
• Enqueue vertices with in-degree of zero.
• While the queue is not empty, dequeue a vertex and append it to the sorted order.
• Decrease the in-degree of its neighbors. Enqueue any neighbor that reaches an in-degree of zero.
• Check for cycles by comparing the sorted order's length to the number of vertices.

4. Complexity: The time complexity is O(V + E), where V is the number of vertices and E is the number of edges.