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

A problem that can be verified in polynomial time belongs to the class NP (nondeterministic polynomial time). This class is defined by the ability to check the validity of a proposed solution quickly, within polynomial time limits, once the solution is presented.

To understand why NP is the correct classification, consider that NP is the set of decision problems for which, if given a "yes" instance of the problem, there exists a certificate (or solution) that can be verified in polynomial time by a deterministic algorithm. This means that even if we don’t know how to find the solution efficiently, we can still efficiently confirm its correctness once presented.

For instance, consider a simple problem like determining whether a particular subset of numbers adds up to a specific total. If someone provides a subset, we can quickly sum the numbers in that subset to verify whether they equal the specified total, demonstrating that the verification process is efficient.

In contrast, the class P consists of those problems that can be both solved and verified in polynomial time. NP-Hard encompasses problems for which it is at least as hard as the hardest problems in NP, meaning that they might not be verifiable in polynomial time. Exponential describes a type of computational complexity that grows exponentially with the input size