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2 cards from this section. Quick, good the night before a test.
What does Kruskal's algorithm aim to find?
Think about the structure of trees and costs.
What is the purpose of sorting edges in Kruskal's algorithm?
Consider why choosing smaller edges might be beneficial.
What does Kruskal's algorithm prioritize when selecting edges?
Consider what a greedy algorithm would typically choose.
True or False: In Kruskal's algorithm, it's possible to create cycles when adding edges.
Think about the cycle prevention mechanism.
Given a graph with vertices A, B, C, D, E and the following edges: {(A, B, 3), (B, C, 1), (C, D, 4), (A, D, 2), (B, D, 5), (D, E, 2)}. Apply Kruskal's algorithm to find the minimum spanning tree.
Draw the edges and keep track of added edges to visualize cycles.
Create a dense random graph with at least 10 vertices and 15 edges. Then use both Prim's and Kruskal's to determine the minimum spanning tree and compare results.
Compare the number of edges included by each algorithm.
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