P and NP classes
Explore the fundamental concepts of P and NP complexity classes in computational theory. Understand how decision problems are solved or verified in polynomial time, and grasp why some problems have solutions that can be checked quickly but not necessarily found quickly. This lesson clarifies key distinctions important for analyzing algorithm efficiency and prepares you for deeper complexity theory discussions.
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P - Polynomial Time Problems
The P stands for polynomial time. Problems which can be solved in nk, where k is some constant from the set of natural numbers ( 1, 2, 3 ...), lie in the complexity class P. More simply, problems to which we can find solutions in polynomial time belong to the complexity class P. Note that when we say problems we are talking about decision problems. All the problems in P are decision problems. Strictly speaking, algorithms such as sorting, binary search, and tree-travels are algorithms that can be used to solve decision problems. However, we can always find a problem that a given algorithm will solve. For instance, you may pose a decision problem if an array is sorted. You can either scan over it and verify elements appear in ascending order, or you may just run the ...