How to use Tarjan’s algorithm for strongly connected components?

Tarjan's algorithm is used to find strongly connected components in a directed graph.

Tarjan's algorithm is a depth-first search algorithm that assigns a unique number to each node in the graph. It then uses these numbers to identify strongly connected components. A strongly connected component is a subset of nodes in the graph where every node is reachable from every other node in the subset.

The algorithm works by maintaining a stack of nodes that have been visited but not yet assigned to a strongly connected component. As the algorithm visits each node, it assigns it a unique number and adds it to the stack. It also keeps track of the lowest numbered node that can be reached from the current node.

When the algorithm finishes visiting all the nodes in a strongly connected component, it pops them off the stack and assigns them to the same component. This is done by assigning each node the same component number.

The algorithm continues until all nodes have been assigned to a strongly connected component. The output of the algorithm is a list of strongly connected components, where each component is represented by a list of nodes.

Overall, Tarjan's algorithm is an efficient way to find strongly connected components in a directed graph. It has a time complexity of O(V+E), where V is the number of nodes in the graph and E is the number of edges.