Complexity ClassesDefinition of NP class Problem:  The set of all decisionbased problems came into the division of NP Problems who can't be solved or produced an output within polynomial time but verified in the polynomial time. NP class contains P class as a subset. NP problems being hard to solve. Note:  The term "NP" does not mean "not polynomial." Originally, the term meant "nondeterministic polynomial. It means according to the one input number of output will be produced.Definition of P class Problem:  The set of decisionbased problems come into the division of P Problems who can be solved or produced an output within polynomial time. P problems being easy to solve Definition of Polynomial time:  If we produce an output according to the given input within a specific amount of time such as within a minute, hours. This is known as Polynomial time. Definition of NonPolynomial time:  If we produce an output according to the given input but there are no time constraints is known as NonPolynomial time. But yes output will produce but time is not fixed yet. Definition of Decision Based Problem:  A problem is called a decision problem if its output is a simple "yes" or "no" (or you may need this of this as true/false, 0/1, accept/reject.) We will phrase many optimization problems as decision problems. For example, Greedy method, D.P., given a graph G= (V, E) if there exists any Hamiltonian cycle. Definition of NPhard class:  Here you to satisfy the following points to come into the division of NPhard
Definition of NPcomplete class:  A problem is in NPcomplete, if
Pictorial representation of all NP classes which includes NP, NPhard, and NPcomplete Fig: Complexity Classes
Next TopicPolynomial Time Verification
