In this lecture P NP NP-Hard NP-Complete problems has been defined with examples in very simple way.
A problem is said to be Polynomial Problem (P) if it can be solved in polynomial time using deterministic algorithm, like O(nk), where K is constant.
Example; linear search, binary search, insertion sort, merge sort
Polynomial problems can be solve and verify in polynomial time
A problem that can not be solved in polynomial time but can be verifiable in polynomial time using non- deterministic algorithm is known as NP (non- deterministic polynomial) problem
Example; TSP, Sudoku problem, scheduling problem
The problems that can not be solved in Polynomial time are called NP hard problems
Example; subset sum problem
If a problem A can be reduced into NP-problem B in polynomial time Then Problem A will be NP-Complete problem.
Example; Graph coloring problem, longest path problem, Hamiltonian path problem etc.
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