The traveling salesman problem (TSP) is an NP-hard problem that asks for the shortest possible route to visit a set of cities and return to the origin city, visiting each city exactly once. A dynamic programming approach combined with bitmasking is one way to solve TSP for smaller graphs (with a time complexity of O(n^2 * 2^n)). In this approach, the bitmask represents the set of cities that have been visited, while the DP table stores the minimum distance for each subset of cities. To implement TSP in TypeScript, you can create a 2D array where the rows represent the current city and the columns represent the set of visited cities. The goal is to minimize the total cost by exploring all permutations of cities. TSP has practical applications in logistics and routing, such as delivery services, circuit board manufacturing, and travel itinerary planning. By learning how to implement TSP using dynamic programming in TypeScript, you can handle a wide range of optimization problems involving graph traversal and route planning.