Tarjan

Tarjan is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

This page uses content from Wikipedia. The original article was at Graph. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)

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.

C#

<lang csharp>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); } }</lang>

zkl

<lang zkl>class Tarjan{

  // input: graph G = (V, Es)
  // output: set of strongly connected components (sets of vertices)
  // Ick: class holds global state for strongConnect(), otherwise inert
  const INDEX=0, LOW_LINK=1, ON_STACK=2;
  fcn init(graph){
     var index=0, stack=List(), components=List(), 
         G=List.createLong(graph.len(),0);

     // convert graph to ( (index,lowlink,onStack),(id,links)), ...)
     // sorted by id
     foreach v in (graph){ G[v[0]]=T( L(Void,Void,False),v) }

     foreach v in (G){ if(v[0][INDEX]==Void) strongConnect(v) }

     println("List of strongly connected components:");
     foreach c in (components){ println(c.reverse().concat(",")) }

     returnClass(components);	// over-ride return of class instance
  }
  fcn strongConnect(v){  // v is ( (index,lowlink,onStack), (id,links) )
     // Set the depth index for v to the smallest unused index
     v0:=v[0]; v0[INDEX]=v0[LOW_LINK]=index;
     index+=1;
     v0[ON_STACK]=True;
     stack.push(v);

      // Consider successors of v
     foreach idx in (v[1][1,*]){  // links of v to other vs
        w,w0 := G[idx],w[0];	// well, that is pretty vile

if(w[0][INDEX]==Void){ strongConnect(w); // Successor w not yet visited; recurse on it v0[LOW_LINK]=v0[LOW_LINK].min(w0[LOW_LINK]); } else if(w0[ON_STACK]) // Successor w is in stack S and hence in the current SCC v0[LOW_LINK]=v0[LOW_LINK].min(w0[INDEX]);

     }
     // If v is a root node, pop the stack and generate an SCC
     if(v0[LOW_LINK]==v0[INDEX]){
        strong:=List();  // start a new strongly connected component

do{ w,w0 := stack.pop(), w[0]; w0[ON_STACK]=False; strong.append(w[1][0]); // add w to strongly connected component }while(w.id!=v.id); components.append(strong); // output strongly connected component

     }
  }

}</lang> <lang zkl> // graph from https://en.wikipedia.org/wiki/Tarjan%27s_strongly_connected_components_algorithm

  // with vertices id zero based (vs 1 based in article)
  // ids start at zero and are consecutive (no holes), graph is unsorted

graph:= // ( (id, links/Edges), ...)

  T( T(0,1), T(2,0),     T(5,2,6), T(6,5),
     T(1,2), T(3,1,2,4), T(4,5,3), T(7,4,7,6) );

Tarjan(graph);</lang>

Output:

0,1,2
5,6
3,4
7