8.5. Quiz

This section provides exercises for better understanding of minimum spanning trees.

Complexity

Explain the worst-case complexities of the following algorithms in terms of V and E according to our implementations:

• Prim's algorithm

• Kruskal's algorithm

• Chu-Liu-Edmonds' algorithm

Comparison

Provide an example of a graph where Prim's and Kruskal's algorithms find different minimum spanning trees from the same graph and explain how these trees are found. If you cannot find an example, explain why these algorithms always find the same minimum spanning tree given the same graph.

Different MSTs can be found from the same graph only if there are multiple edges with the minimum weight for any of which can be polled from the priority queue. Consider cases where the compareTo() method is overridden differently from the original implementation.

Report

Write a report quiz7.pdf that includes the complexity and comparison analyses.