DAA 16 (Part 2) – Dijkstra’s Proof & Worked Examples of Dijkstra and Bellman-Ford | CS F364 скачать в хорошем качестве

DAA 16 (Part 2) – Dijkstra’s Proof & Worked Examples of Dijkstra and Bellman-Ford | CS F364

This lecture is DAA 16 (Part 2) in the Design and Analysis of Algorithms (DAA) course (CS F364). It focuses on the correctness proof of Dijkstra’s Algorithm and presents completely worked examples of both Dijkstra’s Algorithm and the Bellman–Ford Algorithm for the Single Source Shortest Paths (SSSP) problem. The lecture begins with a rigorous correctness proof of Dijkstra’s Algorithm. Using the greedy stays-ahead argument, it is shown that when a vertex is added to the explored set, the distance assigned to it is the true shortest-path distance from the source. The lecture then works through a complete example of the Bellman–Ford Algorithm, demonstrating how shortest-path distances are updated iteratively. Next, a fully worked example of Dijkstra’s Algorithm is presented. The algorithm is executed step by step, showing: how tentative distances are updated, how the explored set grows, and how the final shortest-path tree is constructed. By comparing these two worked examples, the lecture clearly highlights the conceptual and algorithmic differences between greedy and dynamic programming approaches to shortest paths, reinforcing when each algorithm should be used in practice. 📌 Topics Covered in This Lecture Correctness proof of Dijkstra’s Algorithm Greedy stays-ahead argument for shortest paths Fully worked example of Bellman–Ford Algorithm Iterative relaxation of edges Step-by-step worked example of Dijkstra’s Algorithm Construction of the shortest-path tree Comparison of Dijkstra and Bellman–Ford approaches 🎯 Who Should Watch Students studying Design and Analysis of Algorithms (DAA) B.Tech / BE / M.Sc. / MCA / GATE aspirants Learners studying shortest-path algorithms Anyone preparing for proofs and worked examples in graph algorithms 🔗 Playlist This video is part of the playlist: Design and Analysis of Algorithms – Complete DAA Course