Algorithms Analysis 2025 – 400 Free Practice Questions to Pass the Exam

A P problem, or a problem classified within the complexity class P, is defined by its ability to be solved in polynomial time. This means that there exists an algorithm that can solve the problem in a time complexity that can be expressed as a polynomial function of the size of the input. For instance, if the input size is n, the time taken by the algorithm could be represented as n^2, n^3, or any polynomial degree.

This polynomial time characteristic is significant because it generally implies that as the input size grows, the time required to solve the problem increases at a manageable rate, making such problems feasible to solve efficiently, even for relatively large inputs. This contrasts sharply with NP problems, which may not have known efficient solutions, and problems that require exponential time, which grow quickly and become impractical for large inputs.

In summary, the defining characteristic of a P problem is that it can be solved in polynomial time, making it an essential category in computational complexity theory.