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All decision problems fall in sets of comparable complexity, called as complexity classes.
The complexity class P is the set of decision problems which can be solved through a deterministic machine within polynomial time. This class corresponds to set of difficulty that can be solved effectively in the worst cases. We will consider algorithms associating to this class for analysis of time complexity. Not all of the algorithms in these classes make practical sense as several of them have higher complexity..
The complexity class NP is a set of decision problems which can be solved by a non- deterministic machine within polynomial time. This class contains several problems as Hamiltonian path problem, Boolean satisfiability problem, and the Vertex cover problem.
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