CST 370 Week 7

This week I learned about dynamic programming, the Floyd algorithm, and the Warshall algorithm. I was not very familiar with any of these topics before this week, so it was interesting to be introduced to so many new concepts at once. Dynamic programming was especially fascinating because it showed how larger problems can be broken down into smaller subproblems while saving previous results to avoid doing the same work multiple times. I also enjoyed learning about the Floyd algorithm and how it can be used to find the shortest paths between all pairs of vertices in a weighted graph. The Warshall algorithm was interesting as well because it focuses on determining whether a path exists between different vertices. Seeing how similar the Floyd and Warshall algorithms are while still having different purposes helped me understand both of them a little better.

I also learned about spanning trees and Prim's algorithm, which were both new concepts for me. It was interesting to see how a spanning tree can connect all of the vertices in a graph without creating any cycles. Learning about minimum spanning trees made the topic even more fascinating because the goal is to connect every vertex while keeping the total cost as low as possible. Prim's algorithm helped make this easier to understand by showing how a minimum spanning tree can be built step by step by choosing the lowest-cost edge that connects a new vertex. Overall, I was not very familiar with any of this week's topics going into the lessons, but they were all very fascinating to learn. I enjoyed seeing the different ways these algorithms can be used to solve problems involving shortest paths, connectivity, and optimization.