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:

• what is a G(V,E) graph

• adjacency matrix representation

• adjacency list representation

Section 2 - Graph Traversal (Breadth-First Search)

• what is breadth-first search?

• how to use BFS for WebCrawling in search engines?

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

• what is a shortest path in a G(V,E) graph

• Dijkstra's shortest path algorithm

Section 7 - Bellman-Ford Shortest Path Algorithm

• Bellman-Ford algorithm

• how to handle negative cycles

• finding arbitrage opportunities on the FOREX

Section 8: - Spanning Trees (Kruskal and Prim's Algorithms)

• what are spanning trees?

• union find data structures

• Kruskal's algorithm

• Prim's algorithm

Section 9 - Strongly Connected Components (SCCs)

• what are strongly connected components

• Kosaraju's algorithm

• Tarjan's algorithm

Section 10 - Maximum Flow Problem

• the famous maximum flow problem

• how to reduce most of the hard problems to maximum flow problem

• Ford-Fulkerson algorithm

• bipartite matching problem

Section 9 - Travelling Salesman Problem and Hamiltonian Cycles:

• travelling salesman problem (TSP)

• how to deal with NP-hard problems

• what are meta-heuristics

Section 10 - Eulerian Paths

• eulerian paths and eulerian cycles

• Hierholzer algorithm and the Chinese Postman Problem

Section 11 - Algorithms Analysis

• how to measure the running time of algorithms

• running time analysis with big O (ordo), big Ω (omega) and big θ (theta) notations

• complexity classes

• polynomial (P)and non-deterministic polynomial (NP)algorithms

• O(1), O(logN), O(N) and several other running time complexities

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!