COMPUTATIONAL COMPLEXITY THEORY Meaning and
Definition
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Computational complexity theory refers to the study of the resources required to solve computational problems. It is a field within theoretical computer science that investigates the efficiency of algorithms and the inherent difficulty of solving different computational tasks. This branch of study aims to understand the relationship between the input size of a problem and the resources, primarily time and space, required to solve it.
In computational complexity theory, algorithms are classified based on their efficiency in solving problems. The most commonly used measure is time complexity, which estimates the amount of computational time needed for an algorithm to solve a problem as a function of the problem's input size. Space complexity, on the other hand, estimates the amount of memory space required by an algorithm.
Furthermore, computational complexity theory categorizes problems into complexity classes, which group together problems of similar complexity. The most well-known complexity class is P, consisting of decision problems that can be solved in polynomial time. Other prominent complexity classes include NP, representing problems that can be verified in polynomial time, and NP-hard and NP-complete, which are problem classes considered more difficult than P.
Overall, computational complexity theory serves as a framework for analyzing the difficulty of computational problems and offers insights into the inherent limitations of efficient computation. It provides a basis for understanding which problems can be feasibly solved and helps guide the development of efficient algorithms for specific tasks.
