Dynamic Programming: Shortest Paths Algorithms

This lecture covers dynamic programming strategies for problem-solving, focusing on algorithms for finding the shortest paths. It starts by tabulating already calculated values, illustrated with Pascal's triangle. Then, it introduces the Floyd algorithm for calculating the shortest path between all train stations in the CFF network. The lecture explains the algorithm step by step, emphasizing the concept of dynamic programming. It also discusses the complexity of the algorithm and its application to networks with n nodes. Additionally, it mentions other algorithms related to finding the shortest paths, such as Dijkstra's algorithm, A*, and Viterbi. The lecture concludes by highlighting the variety of algorithms available based on specific graph conditions.

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Explores graph traversal methods, spanning trees, and shortest paths using BFS and DFS.

Explores Prim's algorithm for minimum spanning trees and introduces the Traveling Salesman Problem.

Introduces unweighted bipartite matching and its solution using linear programming and the simplex method.