Algorithms Analysis Practice Test 2025 – All-in-One Mastery Guide to Exam Success

The focus of the question is on identifying which of the listed problems does not fall under the category of optimization problems.

Topological sorting is a process used in graph theory and specifically pertains to ordering the vertices of a directed acyclic graph (DAG) such that for every directed edge from vertex A to vertex B, A comes before B in the ordering. This is fundamentally about organization rather than optimization; it doesn't involve finding the best solution among many possible solutions, which is a key characteristic of optimization problems.

In contrast, the Traveling Salesperson Problem involves finding the shortest possible route that visits a set of cities and returns to the origin city, which is clearly about optimizing distance. The Minimum Spanning Tree focuses on finding a subset of edges that connect all vertices with the minimum total edge weight. The Knapsack Problem seeks to maximize the total value of items in a knapsack, subject to a weight constraint. Each of these examples hinges on the idea of finding the best solution under given constraints, defining them as optimization problems.