4.1.4. Complexity Analysis

Try these first

1. 1.

   Define what a Minimum Spanning Tree is.

   Hint

   Think about the characteristics of trees in graphs.

2. 2.

   What does Dijkstra's Algorithm do?

   Hint

   Consider what 'shortest paths' means in graph traversal.

3. 3.

   What is the primary goal of Prim's algorithm?

   • Finding shortest paths
   • Constructing a minimum spanning tree
   • Searching a graph

   Hint

   Focus on what Prim's algorithm aims to achieve in graphs.

4. 4.

   True or False: Dijkstra's algorithm can also construct minimum spanning trees.

   • True
   • False

   Hint

   Consider the different goals of the two algorithms.

5. 5.

   Given a graph with 6 vertices and various weighted edges, demonstrate the application of both Prim's and Dijkstra's algorithms to outline the difference in results.

   Hint

   Draw the graph and start applying each algorithm step by step.

6. 6.

   In a case where edge weights are duplicated across a graph, discuss the implications for minimum spanning tree uniqueness.

   Hint

   Reflect on how uniqueness is impacted by equal options.