This course is about advanced algorithms (graph algorithms) focusing on graph traversal, shortest path problems, spanning trees and maximum flow problems and a lots of its applications from Google Web Crawler to taking advantage of stock market arbitrage situations.
Section 1 - Graphs Theory Basics:
Section 2 - Graph Traversal (Breadth-First Search)
Section 3 - Graph Traversal (Depth-First Search)
what is depth-first search?
how to use recursion to implement DFS
applications of DFS such as topological ordering and cycle detection
find way out of a maze with DFS
Section 4 - Topological Ordering
what is topological ordering (topological sort)
directed acyclic graphs (DAGs)
DAG shortest path and longest path
critical path methods and project management
Section 5 - Cycle Detection
what are cycles in a graph?
forward edges and backward edges
cycle detection algorithms (Tarjan's algorithm with DFS)
Section 6 - Dijkstra's Shortest Path Algorithm
Section 7 - Bellman-Ford Shortest Path Algorithm
Section 8: - Spanning Trees (Kruskal and Prim's Algorithms)
Section 9 - Strongly Connected Components (SCCs)
Section 10 - Maximum Flow Problem
the famous maximum flow problem
how to reduce most of the hard problems to maximum flow problem
bipartite matching problem
Section 9 - Travelling Salesman Problem and Hamiltonian Cycles:
Section 10 - Eulerian Paths
The course is going to take approximately 11 hours to completely but I highly suggest you typing these algorithms out several times in order to get a good grasp of it. You can download the source code of the whole course at the last lecture.
You should definitely take this course if you are interested in advanced topics concerning algorithms. There are a bunch of fields where these methods can be used: from software engineering to scientific research.
Thanks for joining the course, let's get started!