6.1. Introduction to Kruskal's Algorithm

Try these first

1. 1.

   What is a Minimum Spanning Tree?

   Hint

   Think about connecting points with the smallest lengths.

2. 2.

   List the two primary operations of the Union-Find data structure.

   Hint

   Consider what functions we need to manage sets.

3. 3.

   What is the key function of the Find operation in Union-Find?

   Hint

   Think about how we track elements in a graph.

4. 4.

   True or False: Kruskal's Algorithm ensures that all edges are added to the MST.

   • True
   • False

   Hint

   Consider how cycles affect the tree structure.

5. 5.

   Given a weighted graph, apply Kruskal's algorithm step by step to find the MST. Document the edges added and the state of the Union-Find structure after each step.

   Hint

   Make sure to consider cycle formation with conflicting edges during union operations.

6. 6.

   Illustrate how to optimize Union-Find operations using path compression. Show before and after states of the data structure for a series of union operations.

   Hint

   How does path compression affect future Find operations on the same elements?