Question

Explain the concepts of P problems, NP problems and NP- complete problems. What is the P versus NP question identified by Stephen Cook in 1971, and why is it so important for Computer Science and Mathematics?

Answer 1

P problems are those set of problems which can be solved in polynomial time eg sorting n numbers

Np problems are those set of problems which cannot be solved in polynomial time e.g. subset sum problem and traveling salesman problem but they can be verified in polynomial time i.e given the solution of the problem we can check whether it is correct or not in polynomial time

NP complete are those set of problems x for which it is possible to reduce any problem y to x in polynomial time e.g. 3-Sat every problem in Np can be reduced to 3-sat problem

Question identified by stephen cook was that It asks whether that every problem whose solution can be verified in polynomial time can also be solved in polynomial time.

P versus np problem is important for computer science because it will help us determine that whether large number prime factorization is possible or not and many other things