Lecture 27: Minimum Spanning Trees, Cut Property, Kruskal's Algorithm [Advanced Data Structures]

In this lecture, I discuss what a minimum spanning tree is, optimization problems, the cut property of minimum spanning trees (and its proof), and Kruskal's algorithm. Next time we will talk about Prim's Algorithm.

About Kruskal's Algorithm: Note that when you implement Kruskal's Algorithm, normally you sort the edges by their weights (smallest to largest), then you scan from left to right finding the least-weight edge that connects two clusters. Hence, the need for the union-find disjoint set data structure. I state this during the lecture.

Remark: I think I'm a bit clearer in the notes on what the "clusters" are, as disjoint sets.

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Time Stamps:
0:00 What is a weighted graph?
4:02 Why consider weighted graphs?
6:40 What is a minimum spanning tree (MST)?
9:25 Example of a MST.
11:10 MST Problem, what is an optimization problem?
14:35 Applications of MSTs
20:20 Cut Property of MSTs
35:30 Kruskal's Algorithm

Have a beautiful day!

#Graphs
#ComputerScience
#DataStructures