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NP problems have their own significance in programming, but the discussion becomes quite hot when we deal with differences between NP, P , NP-Complete and NP-hard.P and NP- Many of us know the difference between them.P- Polynomial timesolving. Problems which can be solved in polynomial time, which take time like O(n), O(n2), O(n3). Eg: finding maximum element in an array or to check whether a string is palindrome or not. so there are many problems which can be solved in polynomial time.NP- Non deterministic Polynomial time solving. Problem which can’t be solved in polynomial time like TSP( travelling salesman problem) or An easy example of this is subset sum: given a set of numbers, does there exist a subset whose sum is zero?.but NP problems arecheckablein 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.Now we will discuss about NP-Complete and NP-hard.but first we need to know what isreducibility.Take two problems A and B both are NP problems.Reducibility- If we can convert one instance of a problem A into problem B (NP problem) then it means that A is reducible to B.NP-hard– Now suppose we found that A is reducible to B, then it means that B is at least as hard as A.NP-Complete– The group of problems which are both in NP and NP-hard are known as NP-Complete problem.Now suppose we have a NP-Complete problem R and it is reducible to Q then Q is at least as hard as R and since R is an NP-hard problem. therefore Q will also be at least NP-hard , it may be NP-complete also.

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