Seth.

Tarjan's Algorithm - Technical Overview

1. Algorithm Description: Tarjan's Algorithm finds all strongly connected components (SCCs) of a directed graph.

2. Steps of Tarjan's Algorithm:

• Initialize an index and a low-link value for each node.
• Use a stack to track the nodes and mark nodes as visited.
• For each unvisited node, recursively visit its neighbors, updating low-link values.
• If the node is a root node (its low-link value equals its index), pop nodes off the stack to form an SCC.

3. Time Complexity: O(V + E) where V is the number of vertices and E is the number of edges.

4. Space Complexity: O(V) due to the storage of indices, low-link values, and the stack.

5. Usage: Tarjan's Algorithm is used in network analysis, compilers, and various applications in graph theory.