5.5. Complexity Analysis

Try these first

1. 1.

   What is Kruskal's algorithm used for?

   Hint

   Think about trees and how they connect vertices.

2. 2.

   Why is it essential to avoid cycles in a spanning tree?

   Hint

   Consider the definition of a tree.

3. 3.

   What is the first step in Kruskal's algorithm?

   • Sort the edges
   • Pick the largest edge
   • Count the vertices

   Hint

   Recall the order of operations in the algorithm.

4. 4.

   True or False: Kruskal's algorithm can create cycles between paths in a graph.

   • True
   • False

   Hint

   Remember the properties of a tree.

5. 5.

   Given a graph with specific edge weight values, illustrate how you would implement Kruskal's algorithm step by step, providing the final minimum spanning tree.

   Hint

   Sketch the graph and work through each edge systematically.

6. 6.

   Explore how varying the weights of certain edges affects the final spanning tree result within Kruskal’s algorithm framework.

   Hint

   What occurs if you make a high-weight edge low and vice versa?