FindPath(VertexType A, VertexType B):

Breadth First Search - does a path exist from vertex A to vertex B.

Here we figure out if a path exists from A to B by searching from A in a breadth-first manner. If A and B are the same, the search ends. Else we examine all of the vertices comming directly out of A to see if they are B before going to a deeper level.

In our flight example, we first check for "non-stop" flights before goint to 1-stop and then 2-stop and so on.

Depth versus Breadth first:

• depth first we back up as little as possible. Use a stack - Last In, First Out (LIFO)
• breadth-frist we want to backup as far as possible to find a route originating from the earliest vertices. Here we want First In, First Out (FIFO)....so use a FIFO queue as our data structure during search!!!!!

Example: Does a flight path exist from Austin to Washington?

Intial PsuedoCode:

BreadthFirstSearch(A, B)
{
       Set found to be false

       for All Vertices v comming out of A
              queue.Enqueue(v)  //put on queue all vertices comming out of A 1-stop

      do{
              queue.Dequeue(vertex)     //pop of vertex on top of stack.
              if vertex = B             //if you are at the ending vertex you are done
                  Write final vertex
                  Set found to be true
             else
                  Write this vertex
                  Enqueue all adjacent vertices onto queue
      } while !queue.IsEmpty() AND !found

     if(!found)     //exhuasted all paths and could not find path to B
          Write "Path does not exist"

}

Problem with above code:

• can cycle and revisit a vertex more than once
• could get into an infinite loop

Solution:

• mark vertices we have already visited and do not put them on the path a second time.
• 3 new operators:
        MarkVertex(VertexType vertex)
        IsMarked(VertexType vertex) - returns true/false if vertex marked or not.
        ClearMarks() - sets marks for all vertices to false.

code

Other Issues:

• What is printed out in the code presented here is the result of the search....even the dead-ends that were found before backing up to find the correct path. Consider the question: is there a path from Auston to Washington. This is what are program would print out: Auston -> Dallas -> Houston -> Chicago -> Denver. -> Atlanta -> Washingto But, we dont really want to visit Houston or Chicago!!!!
• This code does not necessarily find the "BEST" path. See shortest path problem.