Topological Sort Algorithms For A Directed Acyclic Graph

First Version of Topological Sort of a Directed Acyclic Graph

Procedure TopologicalSort
{
  Let N = the number of vertices;
  Let L be an empty list ;
  For step 1 to N
  {
     Let V be a vertex in the graph that has no successors ;
     Insert V into the first position of list L;
     Delete V and its incident edges from the graph;
  }
}

When the algorithm terminates L contains the vertices of the
original graph in a topological order.



Second Version of Topological Sort of a Directed Acyclic Graph

Procedure TopologicalSort
{
  Initialize status = WAITING for all vertices;
  Let L be an empty list ;
  Let S be an empty stack;

  For each vertex V in the graph
    If (V has no predecessors)
     {
        Set status(V) = VISITED ;
        Push V onto S;
     }

    While (S is not empty)
     {
       Let X be the top element of S;
       If (X has an adjacent vertex N 
           with status(N) = WAITING)
        {
          Set status(N) = VISITED ;
          Push N onto S;           
        }
       Else 
        {
          Pop X ;
          Insert X into the first position of list L;
        }
     } /* end while */
}

When the algorithm terminates L contains the vertices of the
original graph in a topological order.