4.1.5. Handling Ties in Edge Weights

Try these first

1. 1.

   What is a minimum spanning tree?

   Hint

   Think about how edges connect vertices.

2. 2.

   Explain the problem faced when multiple edges have the same weight in Prim's algorithm.

   Hint

   Consider how we can maintain order when selecting edges.

3. 3.

   What does Prim's algorithm aim to achieve?

   • Find the shortest path
   • Construct a minimum spanning tree
   • Sort the graph

   Hint

   Consider what 'minimum spanning tree' implies.

4. 4.

   True or False: Dijkstra's Algorithm and Prim's Algorithm are completely different.

   • True
   • False

   Hint

   Think about their structures and methods of operation.

5. 5.

   Consider a complete graph with 4 vertices where every edge has a weight of 5. How many distinct minimum spanning trees can be formed?

   Hint

   Think about how many sets of edges can connect the vertices without cycles.

6. 6.

   Given the following edges and weights: (A,B,4), (A,C,4), (B,C,6), (C,D,5), if you apply Prim's algorithm starting from A, describe the minimum spanning tree formed and indicate the potential variations.

   Hint

   Consider each step and what tied edges can lead to different outcomes.