> For the complete documentation index, see [llms.txt](https://emory.gitbook.io/dsa-java/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://emory.gitbook.io/dsa-java/minimum-spanning-trees/exercises.md).

# 8.5. Quiz

## 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.

{% hint style="info" %}
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.
{% endhint %}

## Report

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


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