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

A linear programming problem involves optimizing a linear objective function, subject to linear equality and inequality constraints. The key characteristics of linear programming are that both the objective function and the constraints must be linear.

The Knapsack problem fits this definition because it involves maximizing the total value of items that can be carried in a knapsack, given the constraint of a maximum weight capacity. The relationship between the items' weights and their values allows for a formulation that can be described by linear equations, particularly when working within specific bounds or when using fractional items.

In contrast, the other options represent different types of optimization or graph problems that do not adhere to the linear programming framework. The Shortest Path problem is concerned with finding the least-cost route between nodes in a graph, while the Traveling Salesperson problem involves finding the shortest possible route visiting a set of cities and returning to the origin. The Minimum Spanning Tree problem seeks to connect all nodes in a graph with the minimum total edge weight, utilizing graph-based algorithms rather than linear programming techniques. Thus, the Knapsack problem is uniquely suited to be classified as a linear programming problem among the given options.