NP-hardness

NP-hardness is a concept in computer science indicating that a problem is at least as challenging as the hardest problems in the class NP (nondeterministic polynomial time). If an NP-hard problem could be solved efficiently (quickly), then every problem in NP could also be solved efficiently, which is considered unlikely. In practical terms, NP-hard problems are difficult to solve exactly within a reasonable time for large instances, often requiring approximation or heuristic methods. Recognizing a problem as NP-hard helps us understand its inherent computational difficulty and guides us in choosing practical solutions.