4.1.3. Update Mechanism in Prim's Algorithm

Try these first

1. 1.

   What is Prim's algorithm used for?

   Hint

   Think of the tree that connects all vertices with minimum weight.

2. 2.

   What happens if two edges in Prim’s algorithm have the same weight?

   Hint

   Consider what options become available in that case.

3. 3.

   What is Prim's algorithm primarily used for?

   • Finding shortest paths in a graph
   • Finding minimum spanning trees
   • Finding maximum flow in a network

   Hint

   Remember the tree connection concept.

4. 4.

   Dijkstra's algorithm is focused on:

   • True
   • False

   Hint

   Reflect on how both handle weights.

5. 5.

   Consider a graph with edges having weights such that two edges have the same weight. If you apply Prim's algorithm, describe how many possible minimum spanning trees might exist. Explain your reasoning.

   Hint

   Reflect on what happens when multiple valid connections arise in a tree.

6. 6.

   Create an example of a graph with five vertices and all edges with equal weights. Determine if Prim's algorithm will yield a unique minimum spanning tree.

   Hint

   Think about the freedom of selection within your setup.