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NP complete problem: Big project problem. To finish the big project, you need to finish X...

NP complete problem:

Big project problem. To finish the big project, you need to finish X requirements. However, you only have time to write B < X more classes. Luckily, a single class can satisfy many requirements. Input are list of requirements and list of classes that satisfy each requirement.

a/ Show that the problem is in NP

b/ Show that the problem is in NP-complete by reduction

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Answer #1

A.

NP is set of decision 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).
Informally, NP is set of decision problems which can be solved by a polynomial time via a “Lucky Algorithm”, a magical algorithm that always makes a right guess among the given set of choices .

In the given question the big project problem is solve in certain fix time so from this it is proved that problem is in NP.

B.

To prove that problem is NP compelete first we have to prove it is NP problem which we already proved . As in the question it is stated that single class can satisfy many requirements so for each requirement we dont need separate class which makes our problem NP Compelete

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