How are the classes of P and NP problems related to each other?
NP is set of problems that can be solved by a Non-deterministic Turing Machine in Polynomial time.
P is subset of NP (any problem that can be solved by deterministic machine in polynomial time can also be solved by non-deterministic machine in polynomial time) but Pu226.
- NP
How do you determine whether a problem is NP hard or P?
NP-hard intuitively means those problems which are harder than every problem in NP.
In order to say that a problem (decision) is NP-hard, all you have to do is to check if every NP problem reduces (efficiently) to it..
How NP problems can become P problems?
There are a large number of important problems that are known to be NP-complete (basically, if any these problems are proven to be in P, then all NP problems are proven to be in P).
If P = NP, then all of these problems will be proven to have an efficient (polynomial time) solution.
Most scientists believe that P= NP..
What are the P problems and NP problems?
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.
But the details are more complicated..
What is computational complexity What is an NP-complete problem?
In computational complexity theory, a problem is NP-complete when: It is a decision problem, meaning that for any input to the problem, the output is either "yes" or "no".
When the answer is "yes", this can be demonstrated through the existence of a short (polynomial length) solution..
What is the complexity of NP problems?
tl;dr: In computational complexity theory, NP is a complexity class used to describe certain types of decision problems.
NP is the set of all decision problems for which the answer can be checked by a polynomial-time algorithm, that is, an algorithm that runs in O(nk) time for some constant k..
What is the difference between P class and NP class problem?
P-class problems - Takes polynomial time to solve a problem like n, n^2, n*logn etc. while, NP-class problems - Takes "Non-Deterministic" polynomial time to quickly check a problem.
NP problems are more hard & takes more time than P-class problems..
Why is the P vs NP problem important in the field of computer science?
Now, if P=NP, we could find solutions to search problems as easily as checking whether those solutions are good.
This would essentially solve all the algorithmic challenges that we face today and computers could solve almost any task..
- NP-Hard problems(say X) can be solved if and only if there is a NP-Complete problem(say Y) that can be reducible into X in polynomial time.
NP-Complete problems can be solved by a non-deterministic Algorithm/Turing Machine in polynomial time.
To solve this problem, it do not have to be in NP . - The answer is complexity.
It's much more difficult to quickly find a solution to an NP problem than a P problem.
Computers can easily check solutions to NP problems, but devising an algorithm that can propose solutions to NP problems in a reasonable time is much more difficult. - Yes, NP is commonly only defined for decision problems
In computational complexity theory, NP (nondeterministic polynomial time) is a complexity class used to classify decision problems.
