26.2.6. Minimum Spanning Tree

Try these first

1. 1.

   What is a Minimum Spanning Tree?

   Hint

   Think about connectivity and cost.

2. 2.

   Which data structure is commonly used in Prim's Algorithm?

   Hint

   It helps find the smallest weight efficiently.

3. 3.

   What characterizes a Minimum Spanning Tree?

   • Contains cycles
   • Connects all vertices
   • Has maximum weight

   Hint

   Consider the core purpose of an MST.

4. 4.

   True or False: Prim's Algorithm always starts from the smallest edge.

   • True
   • False

   Hint

   Focus on where the algorithm begins.

5. 5.

   Given a graph with specified edge weights, demonstrate how to apply Prim’s Algorithm step by step.

   Hint

   Draw the graph as you go to visualize it.

6. 6.

   Provide a scenario in a real-world application where choosing the wrong algorithm (Prim's or Kruskal's) could lead to inefficiencies. Discuss why.

   Hint

   Consider where the most connections exist between points.