5.2. Kruskal's Algorithm Process

Try these first

1. 1.

   What is the first step in Kruskal's algorithm?

   Hint

   Think about what prepares the algorithm for adding edges.

2. 2.

   What does Kruskal's algorithm do if adding an edge forms a cycle?

   Hint

   Consider the rules about cycles in graph theory.

3. 3.

   What does Kruskal's algorithm primarily focus on?

   • Finding the maximum spanning tree
   • Finding the minimum spanning tree
   • Finding all paths in a graph

   Hint

   Think about the tree characteristics.

4. 4.

   True or False: Kruskal's algorithm adds edges in descending order of weight.

   • True
   • False

   Hint

   Revisit the process of how values are arranged in the algorithm.

5. 5.

   Given a graph with vertices A, B, C, and edges AB (10), AC (15), BC (5), outline the steps Kruskal's algorithm would take to find the MST.

   Hint

   Sort first and then methodically check each edge for cycles.

6. 6.

   Demonstrate how Kruskal’s algorithm can be optimized using path compression and union by rank in the union-find data structure.

   Hint

   Focus on how these techniques streamline the component merging process.