Tarjan's Algorithm
Tarjan's Algorithm is a method used in graph theory to find the strongly connected components (SCCs) of a directed graph. An SCC is a subset of vertices where every vertex is reachable from every other vertex in that subset. The algorithm efficiently identifies these components using depth-first search (DFS) and maintains a stack to track the vertices.
The algorithm operates in linear time, meaning it processes the graph in proportion to the number of vertices and edges. It assigns each vertex a unique index and uses a low-link value to determine the root of each SCC, allowing for the efficient grouping of connected nodes.