Algorithms Analysis Practice Test 2025 - Free Algorithms Practice Questions and Study Guide

The Traveling Salesperson Problem (TSP) is indeed known to be NP-complete. This problem involves finding the shortest possible route that visits a set of cities and returns to the original city, ensuring that each city is visited exactly once. The complexity of TSP arises from the combinatorial nature of possible routes, which increases factorially based on the number of cities involved.

Because no polynomial-time algorithm is known to solve this problem in all cases, and it is possible to verify a proposed solution (i.e., a specific route and its total distance) in polynomial time, TSP fits the definition of NP-completeness. Many problems in computer science are reducible to TSP, demonstrating its foundational role in the study of computational complexity.

The other options you mentioned deal with problems that can be efficiently solved using algorithms. For instance, sorting a list can be done in polynomial time using algorithms like quicksort or mergesort. Finding the shortest path in a graph (such as Dijkstra's algorithm) also has a polynomial-time solution. The Minimum Spanning Tree problem can be efficiently solved using Prim's or Kruskal’s algorithms, both of which operate within polynomial time complexities. Thus, these problems do not fit the NP-complete