4.1.6. Conclusion on Spanning Trees

Try these first

1. 1.

   Define a Minimum Spanning Tree (MST).

   Hint

   Consider the concept of connecting all points.

2. 2.

   What does Prim's algorithm do?

   Hint

   Focus on how edges are chosen.

3. 3.

   What is the purpose of Prim's algorithm?

   • To find the shortest path
   • To find the minimum spanning tree
   • To sort vertices

   Hint

   Think about the graph properties it aims to optimize.

4. 4.

   True or False: Prim's algorithm can result in different Minimum Spanning Trees if edge weights are duplicated.

   • True
   • False

   Hint

   Review how edge selection can vary in such cases.

5. 5.

   You are given a graph with weights: (1,2,3), (1,3,4), (2,4,5), (3,4,1). Using Prim's algorithm, outline the steps taken to determine the MST and list the edges selected.

   Hint

   Remember to always choose the edge with the smallest weight that connects the current tree.

6. 6.

   In a scenario where edge weights have duplicates, how would you ensure that the same MST is produced in multiple iterations?

   Hint

   Consider how sorting could help manage your edge choices.