Fajarv: P Np Problem

P Np Problem

The p versus np problem is the determination of whether all np problems are actually p problems. The class p consists of those problems that are solvable in polynomial time ie.

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It asks whether every problem whose solution can be quickly verified technically verified in polynomial time can also be solved quickly again in polynomial time.

P np problem. P versus np problem in full polynomial versus nondeterministic polynomial problem in computational complexity a subfield of theoretical computer science and mathematics the question of whether all so called np problems are actually p problems. The p versus np problem is a major unsolved problem in computer science. But the details are more complicated.

These problems belong to an interesting class of problems called the np complete problems whose status is unknown. In this context we can categorize the problems as follows p class. But np problems are checkable in polynomial time means that given a solution of a problem we can check that whether the solution is correct or not in polynomial time.

So till now you have got what is np and what is p. Roughly speaking p is a set of relatively easy problems and np is a set that includes what seem to be very very hard problems so p np would imply that the apparently hard problems actually have relatively easy solutions. Np complete problems are studied because the ability to quickly verify solutions to a problem np seems to correlate with the ability to quickly solve problem p.

It is easy to see that the complexity class p all problems solvable deterministically in polynomial time is contained in np problems where solutions can be verified in polynomial time because if a problem is solvable in polynomial time then a solution is also verifiable in polynomial time by simply solving the problem. A p problem is one that can be solved in polynomial time which means. The single problem in np complete is solved quickly.

If p and np are not equivalent then the solution of np problems requires in the worst case an exhaustive search while if they are then asymptotically faster algorithms may exist. P equals np is a hotly debated millennium prize problem one of a set of seven unsolved mathematical problems laid out by the clay mathematical institute each with a 1 million prize for those. This is an example of what computer scientists call an np problem since it is easy to check if a given choice of one hundred students proposed by a coworker is satisfactory ie no pair taken from your coworkers list also appears on the list from the deans office however the task of generating such a list from scratch seems to be so hard as to be completely impractical.

It is found every problem in np is quickly solvedas called the p np. These problems can be solved in time on k in worst case where k is constant.

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