An NP-hard problem is one for which no polynomial-time algorithm is known, and solving it quickly would allow us to solve all problems in the complexity class NP efficiently. These problems are at least as hard as the hardest problems in NP, and finding a polynomial-time solution to any NP-hard problem would imply P = NP, a major unsolved question in computer science.

NP-hard Problem

NP-hard problem

A polynomial-time algorithm is an algorithm whose running time grows at a polynomial rate relative to the size of the input, making it efficient and feasible for large inputs. These algorithms are crucial in computer science because they are considered tractable, meaning they can solve problems in a reasonable amount of time compared to exponential-time algorithms.

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