Last Minute Lecture

Maximum Flow Algorithms — Ford-Fulkerson, Edmonds-Karp & Bipartite Matching | Chapter 24 in Introduction to Algorithms Chapter 24 of Introduction to Algorithms (CLRS) tackles the maximum-flow problem —how to move the greatest possible amount of material through a network from a source to a sink without exceeding edge capacities. This problem has critical applications in transportation, communication networks, and resource allocation. The chapter introduces essential flow concepts, residual networks, augmenting paths, and foundational algorithms like Ford-Fulkerson and Edmonds-Karp . It also explains how flow models apply to bipartite matching and special network structures. 📺 Watch the full chapter summary above, or continue reading for a complete breakdown of every core concept and algorithm covered in Chapter 24. What Is a Flow Network? A flow network is a directed graph where each edge has a nonnegative capacity, and the goal is to determine how much material can ...

Shortest Path Algorithms — Bellman-Ford, Dijkstra & DAG Methods Explained | Chapter 22 in Introduction to Algorithms Chapter 22 of Introduction to Algorithms (CLRS) provides a comprehensive guide to solving the single-source shortest-path problem in weighted, directed graphs. These algorithms are the foundation of many practical applications in computer science, such as GPS navigation, internet routing, and task scheduling. The chapter introduces essential algorithmic tools—including relaxation and optimal substructure—before explaining three powerful solutions: the Bellman-Ford algorithm, DAG shortest paths, and Dijkstra’s algorithm. 📺 Watch the full podcast-style summary above or continue reading for a detailed breakdown of key concepts, methods, and properties that make shortest-path algorithms so essential in graph theory. Understanding the Shortest Path Problem The single-source shortest path problem asks: given a weighted, directed graph and a source vertex s , w...

Graph Algorithms Explained — BFS, DFS, Topological Sort & SCCs | Chapter 20 in Introduction to Algorithms Graph algorithms are at the heart of many critical operations in computer science, from web crawling and pathfinding to task scheduling and dependency resolution. Chapter 20 of Introduction to Algorithms (CLRS) provides a comprehensive overview of graph representations, traversal algorithms like BFS and DFS, and advanced applications such as topological sorting and strongly connected components (SCCs). Whether you're studying for AP Computer Science or brushing up on algorithm fundamentals, this chapter is essential reading. 📺 Watch the full video above for a visual breakdown of each algorithm and its application, or keep reading for an in-depth written explanation. Graph Representations Graphs can be represented in two main ways: adjacency lists and adjacency matrices. Each has trade-offs in space and time complexity depending on the graph’s density. Adja...