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Tarjan's algorithm is an algorithm in graph theory for finding the strongly connected components of a graph.

It runs in linear time, matching the time bound for alternative methods including Kosaraju's algorithm and the path-based strong component algorithm.

Tarjan's Algorithm is named for its discoverer, Robert Tarjan.



References

 The article on Wikipedia.


using System;
using System.Collections.Generic;
 
class Node
{
    public int LowLink { get; set; }
    public int Index { get; set; }
    public int N { get; }
 
    public Node(int n)
    {
        N = n;
        Index = -1;
        LowLink = 0;
    }
}
 
class Graph
{
    public HashSet<Node> V { get; }
    public Dictionary<Node, HashSet<Node>> Adj { get; }
 
    /// <summary>
    /// Tarjan's strongly connected components algorithm
    /// </summary>
    public void Tarjan()
    {
        var index = 0; // number of nodes
        var S = new Stack<Node>();
 
        Action<Node> StrongConnect = null;
        StrongConnect = (v) =>
        {
            // Set the depth index for v to the smallest unused index
            v.Index = index;
            v.LowLink = index;
 
            index++;
            S.Push(v);
 
            // Consider successors of v
            foreach (var w in Adj[v])
                if (w.Index < 0)
                {
                    // Successor w has not yet been visited; recurse on it
                    StrongConnect(w);
                    v.LowLink = Math.Min(v.LowLink, w.LowLink);
                }
                else if (S.Contains(w))
                    // Successor w is in stack S and hence in the current SCC
                    v.LowLink = Math.Min(v.LowLink, w.Index);
 
            // If v is a root node, pop the stack and generate an SCC
            if (v.LowLink == v.Index)
            {
                Console.Write("SCC: ");
 
                Node w;
                do
                {
                    w = S.Pop();
                    Console.Write(w.N + " ");
                } while (w != v);
 
                Console.WriteLine();
            }
        };
 
        foreach (var v in V)
            if (v.Index < 0)
                StrongConnect(v);
    }
}