graph depth first traversal

Depth First Traversal of a Graph

Set-Up:

Each vertex of the graph has a status variable which has one of two values: {WAITING, VISITED}
A Stack has been created and initialized to an empty state.



Procedure DepthFirstTraversal
{

  Set the status of each vertex to WAITING ;
  For each vertex V in the graph
    If    status(V) is WAITING
    Then  VisitComponentOf(V) ;
}


Iterative Version of Procedure VisitComponentOf

Procedure VisitComponentOf(vertex V) 

{ /* Begin Procedure VisitComponentOf */

   Process V ;   
   Set status(V) to VISITED;
   Push V onto the Stack ;
   While ( the Stack is not empty )
   { /* begin while-loop */

      Let X be the top element of the Stack ;
      If   ( X has an adjacent vertex N 
             with status(N) = WAITING )
      Then 
         { 
            Process N;
            Set status(N) to VISITED;
            Push N onto the Stack;
            /* If calculating a spanning tree 
               then here mark the edge between N and X */
         }
      Else Pop X from the Stack ;

   } /* end while-loop */
} /* End Procedure VisitComponentOf */


Recursive Version of Procedure VisitComponentOf

Procedure VisitComponentOf(vertex V) 

{ /* Begin Procedure VisitComponentOf */

    Process V ;
    Set status(V) to VISITED ;
    For each N adjacent to V
       If status(N) is WAITING
       {
          VisitComponentOf(N) ;
          /* If calculating a spanning tree 
             then here mark the edge between N and X */
       }

} /* End Procedure VisitComponentOf */

Note: The algorithms do not completely determine the traversal order (the order in which the status of the vertices will be set to VISITED). This is because the algorithms do not specify in what order the vertices will be examined when implementing a phrase like "For each N adjacent to V". (In test situations, the student should assume that traversal begins at the "Start Vertex" and that the adjacent vertices should be examined in ascending key order.