This course is about advanced 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.
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.
In the first section we are going to talk about the main graph traversal algorithms (BFS, DFS) and its applications of course such as WebCrawler or topological ordering. The next section is about shortest path algorithms: there are several applications which we are going to be familiar with from image processing to FOREX arbitrage. The next chapter is about minimum spanning trees and clustering algorithms. Then, we are going to learn about the maximum flow problem, maybe the most important algorithm in this course. The last chapter is about how to solve NP problems such as the travelling salesman problem with simulated annealing.
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.
We create the helper classes and again, the Graph class. We transpose our directed graph inside this Graph class, because in Kosaraju algorithm we have to do the first DFS (topological ordering) in the transposed graph.
(transposing a graph is just to reverse each edge: startVertex will be targetVertex and targetVertex will be the startVertex)
We create our class in which we will perform the first DFS on the transposed graph
In this video we make sure the our Kosaraju implementation gives the right results
DFS is a robust but not so fast algorithm, so Tarjan algorithm tries to get rid of the DFS.
You can download the slides here!
My name is Balazs Holczer. I am from Budapest, Hungary. I am qualified as a physicist and later on I decided to get a master degree in applied mathematics. At the moment I am working as a simulation engineer at a multinational company. I have been interested in algorithms and data structures and its implementations especially in Java since university. Later on I got acquainted with machine learning techniques, artificial intelligence, numerical methods and recipes such as solving differential equations, linear algebra, interpolation and extrapolation. These things may prove to be very very important in several fields: software engineering, research and development or investment banking. I have a special addiction to quantitative models such as the Black-Scholes model, or the Merton-model. Quantitative analysts use these algorithms and numerical techniques on daily basis so in my opinion these topics are definitely worth learning.
Take a look at my website and join my email list if you are interested in these topics!