Homework 2

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1. (2 points) Trace a minimal spanning tree search on the following graph, starting at vertex "A".

   

   Entries in the "Visited Vertex" column should have the form name. Entries in the "Added Edges" column should have the form name:edge-length. Circle edges that are visited and cross out edges that are discarded.

   Visited Vertex	Added Edges
   A	AB:4 AC:3 AD:6

2. (2 points) Trace a single source shortest paths search on the following graph, starting at vertex "A".

   

   Entries in the "Visited Vertex" column should have the form name:shortest-path-distance. Entries in the "Added Edges" column should have the form name:edge-length:to-vertex-distance. Circle edges that are visited and cross out edges that are discarded.

   Visited Vertex	Added Edges
   A:0	AB:4:4 AC:3:3 AD:6:6

3. (1 point) Consider the following search loop:

       do whatever you need to do with v
       record that v has been visited
       put the edges leaving v into the dispenser
       while the dispenser is not empty
           retrieve and remove edge e from the dispenser
           let w be the head of e
           if w has not been visited
               do whatever you need to do with e
               do whatever you need to do with w
               record that w has been visited
               put the edges leaving w into the dispenser
           endif
       endwhile
           

   Fill in the dispenser types and run times in the following table. Assume that "do whatever you need to do with …" is constant time for either vertices or edges and recording that a vertex has been visited is also constant time.

   Graph Search Type	Dispenser Type	Run Time
   Breadth-First Search
   Depth-First Search
   Minimal Spanning Tree
   Single Source Shortest Paths