graph breadth first traversal

Breadth 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 Queue has been created and initialized to an empty state.



Procedure BreadthFirstTraversal
{

  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;
   Place V in the Queue ;
   While ( the Queue is not empty )
   { /* begin while-loop */
      
      Let X be the front element of the Queue;
      Remove X from the Queue;
      For each N adjacent to X with status(N) = WAITING
        { 
           Process N;
           Set status(N) to VISITED;
           Place N in the Queue;
           /* If calculating a spanning tree 
              then here mark the edge between N and X */
        }

   } /* end while-loop */
} /* 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 X". (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.