## Learning Outcomes

At the end of this lecture, you’ll be able to:

- In the context of Graph Theory, define Cycle, Acyclic Graph, and Tree.
- Describe what spanning tree is and why constructing minimum spanning trees are useful.
- Trace Prim’s algorithm for finding a minimum spanning tree.
- Trace Kruskal’s algorithm for finding a minimum spanning tree.
- Explain how to implement Prim’s algorithm, comparing various approaches to finding the next min edge, and the resulting time/space tradeoffs between them.
- Explain how to implement Kruskal’s algorithm, comparing various approaches to checking for cycles, and the resulting time/space tradeoffs between them.

## Lecture Plan

In this lecture, we'll cover the following lessons:

- Tree: A Connected Acyclic Graph
- Spanning Tree
- Minimum Spanning Tree
- Prim's Algorithm: Description⚡
- Prim's Algorithm: Exercise⚡
- Prim's Algorithm: Analysis⚡
- Kruskal's Algorithm: Description⚡
- Kruskal's Algorithm: Exercise⚡
- Kruskal's Algorithm: Analysis⚡

Lessons marked with ⚡ contain exercise/activity.