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

NP-complete problems are indeed a subset that represents the intersection between NP (nondeterministic polynomial time) problems and NP-hard problems.

NP problems are those for which a given solution can be verified in polynomial time. This means that if someone provides a proposed solution to an NP problem, it is possible to check whether that solution is correct within a time that grows polynomially with the size of the input.

On the other hand, NP-hard problems are at least as hard as the hardest problems in NP. This implies that if you could solve an NP-hard problem in polynomial time, you could also solve all NP problems in polynomial time, but NP-hard problems do not necessarily belong to NP. In fact, some NP-hard problems may not even have solutions that can be verified in polynomial time.

NP-complete problems are those problems that are in NP and also NP-hard. This means that they are the hardest problems in NP; any NP problem can be transformed into an NP-complete problem in polynomial time. Therefore, if an efficient (polynomial time) algorithm exists for solving any NP-complete problem, it implies that all NP problems can also be solved efficiently.

This relationship makes NP-complete problems a distinct category, showing that they are