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TL;DR This post explores exact algorithms for solving the Traveling Salesman Problem (TSP), including brute force, dynamic programming (Held-Karp), and branch-and-bound. These methods guarantee the shortest path but come with varying levels of comput...

A Timeless Challenge in Optimization Imagine a salesperson who must travel to multiple cities, visiting each one exactly once before returning to their starting point. What’s the shortest route they can take? This seemingly simple question has puzzle...
