Advanced Algorithms (Graph Algorithms) in Java

• Learn about the applications of data structures
• Learn about the fundamental basics of graphs and graph theory
• Implement advanced algorithms (graph algorithms) efficiently
• Learn graph traversing such as breadth-first search and depth-first search
• Learn about topological ordering and cycle detection
• Learn about shortest path algorithms (Dijkstra’s and Bellman-Ford algorithms)
• Learn about spanning trees
• Learn about strongly connected components
• Learn about Hamiltonian cycles and Eulerian cycles 

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

Section 4 – Dijkstra’s Shortest Path Algorithm

• what is a shortest path in a G(V,E) graph
• Dijkstra’s shortest path algorithm

Section 5 – Bellman-Ford Shortest Path Algorithm

• Bellman-Ford algorithm

Section 6: – Spanning Trees (Kruskal and Prim’s Algorithms)

• what are spanning trees
• union find data structures
• Kruskal’s algorithm
• Prim’s algorithm

Section 7 – Strongly Connected Components (SCCs)

• what are strongly connected components
• Kosaraju’s algorithm
• Tarjan’s algorithm

Section 8 – 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