Depth-First Search: Traversing and Sorting Graphs

This lecture covers the concepts of depth-first search (DFS) and topological sort in graphs. It explains the representation of graphs using adjacency lists and matrices, compares the efficiency of adjacency list and matrix, and details the breadth-first search (BFS) and DFS algorithms. The lecture also delves into the runtime analysis of BFS and DFS, discussing the exploration process, color-coding vertices, and forming depth-first trees. Additionally, it explores the classification of edges in DFS, the parenthesis theorem, and the white-path theorem. Finally, it introduces the application of DFS in topological sorting, providing a real-life example of ordering vertices in a directed acyclic graph.