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Just learnt that a problem in computer science can be divided into the following categories
Polynomial problems NP problems NP hard problems NP complete problems
based on how long it takes to run the program
For example, suppose there is a problem P that can be solved with two algorithms say A1 and A2 where,
A1 is polynomial in nature, A2 is non-polynomial
According to me, if P is solved using A1, then P is a polynomial problem and if P is solved using A2, then it must be an NP problem.
Am I right?
In other words, is it fair enough to say that classification of a problem does also require the algorithm that is being used to solve it?