Explore the complexities of the Traveling Salesman Problem (TSP) in this 30-minute video by Reducible. Dive into the challenges this notorious problem presents for computer scientists and discover clever methods used to solve it. Learn why brute force solutions and exact approaches fail for large instances, then explore heuristic-based approaches like nearest neighbors, greedy algorithms, and Christofides method. Understand how to improve candidate solutions through local search techniques, including 2-opt, random swapping, and 3-opt improvements. Delve into advanced search space analysis methods such as simulated annealing and ant colony optimization. Gain insights into lower bounding TSP and various tour improvement techniques, all explained through engaging animations and clear explanations.