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An algorithm is a methodical approach for solving a problem.
1) The algorithm to multiply "A" by "B" is to add "A" to itself "B" times.
2) The algorithm to compute the average of "N" number is to add them up and then divide by "N".
A decision problem B is NP complete if
Here size of the input is n (in some encoding), and in the running time of the worst case is O(n power c) for some constant c. Describing the three types issues, i.e
Theorem: if A is NPC ( NP-complete ) and (A Є NP), then ( P = NP ).
Example: If the Spanning_tree degree is 4 that is NP complete
P : the class of problems which can be solved by a deterministic polynomial algorithm. Example of P is shortest path problem
NP: the class of decision problem which can be solved by a non-deterministic polynomial algorithm. Example of NP complete is Vertex cover problem.
NP-hard: the class of problems to which every NP problem reduces. Example of the NP-hard is Turing Halting Problem.
NP-complete (NPC): the class of problems which are NP-hard and belong to NP