DAA 12 – Traveling Salesman Problem (TSP) Using Dynamic Programming | CS F364 скачать в хорошем качестве

DAA 12 – Traveling Salesman Problem (TSP) Using Dynamic Programming | CS F364

This lecture is DAA 12 in the Design and Analysis of Algorithms (DAA) course (CS F364). It presents a dynamic programming approach to the Traveling Salesman Problem (TSP), one of the most well-known NP-hard optimization problems. The lecture begins by formally defining the Traveling Salesman Problem for both undirected (two-way traffic) and directed (one-way traffic) graphs, and explains how TSP can be modeled as a weighted complete graph. The concept of optimal substructure is then established, which makes the problem amenable to dynamic programming. A state definition g(i,S) is introduced to represent the minimum-cost tour starting from city i, visiting all cities in subset S, and finally returning to the starting city. Using this formulation, the DP recurrence relation for TSP is derived, and a bottom-up dynamic programming algorithm is presented. The lecture then performs a detailed time complexity analysis, showing that the DP algorithm runs in Θ(n^2.2^n) time, which is significantly better than the brute-force solution with Θ(n!) time complexity. The space complexity Θ(n.2^n) is also derived, and the time–space tradeoff for solving TSP is discussed. Finally, the lecture works through illustrative examples, demonstrates how to reconstruct the optimal tour by tracing back DP decisions, and compares the dynamic programming solution with the brute-force approach. 📌 Topics Covered in This Lecture Traveling Salesman Problem (TSP) formulation Directed vs undirected TSP Graph representation of TSP Optimal substructure of TSP DP state definition g(i,S) DP recurrence relation for TSP Bottom-up dynamic programming algorithm Time complexity: Θ(n²·2ⁿ) Space complexity: Θ(n·2ⁿ) Time–space tradeoff in TSP Worked examples and tour reconstruction Comparison with brute-force TSP 🎯 Who Should Watch Students studying Design and Analysis of Algorithms (DAA) B.Tech / BE / M.Sc. / MCA / GATE aspirants Learners studying Dynamic Programming and NP-hard problems Anyone seeking a rigorous understanding of the DP solution to TSP 🔗 Playlist This video is part of the playlist: Design and Analysis of Algorithms – Complete DAA Course