Easy vs. Hard Problems
The standard definition of a tractable problem is one that can be solved in time that is polynomial in the size of the input. Why?
- Very few practical problems require time which is high-degree polynomial
- equivalent on different models of computation
- nice closure properties
This class of problems called P.
NP -- class of problems whose solution can be verified in polynomial time. Framed as “decision problems”.
Many many many many many many many many many many important problems are in NP (in fact, NP-complete.)