Advanced · Research
NP-completeness
Visual diagram · (in preparation) · Math · (in preparation) · Worked example · 3 difficulty levels.
TL;DR. The hardest problems in NP, where checking a solution is fast, but finding it is generally hard.
Technical Definition
The hardest problems in NP, where checking a solution is fast, but finding it is generally hard.
How it works
NP-completeness identifies problems within the NP class that are the most computationally difficult. These problems have the property that any other problem in NP can be translated into them in polynomial time. While solutions can be verified quickly, finding them is typically a computationally intensive task.
Related Concepts
- NP — A complexity class for decision problems where 'yes' answers can be verified quickly.
- NP-hardness — Problems that are at least as hard as the most difficult problems in the NP complexity class.