Answer
See the explanation
Work Step by Step
The distinction lies in the complexity classes to which the problems belong.
- A polynomial problem can be solved by a deterministic algorithm in polynomial time, meaning the time it takes to solve the problem grows polynomially with the size of the input.
- A nondeterministic polynomial (NP) problem can be verified in polynomial time, but there's no known deterministic polynomial-time algorithm to solve it. This means, if someone claims to have a solution, it can be verified quickly, but finding the solution itself might take exponential time.
In summary, stating a problem is polynomial means it's efficiently solvable, while stating it's NP means it's efficiently verifiable but potentially hard to solve.
