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Lecture# Complexity of Algorithms

Description

This lecture covers the complexity of algorithms, focusing on big-O notation for powers, logarithms, and factorials, as well as the efficiency of algorithms in terms of time and space complexity. It also explains big-Omega and big-Theta notations, with examples and summaries.

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In course

CS-101: Advanced information, computation, communication I

Discrete mathematics is a discipline with applications to almost all areas of study. It provides a set of indispensable tools to computer science in particular. This course reviews (familiar) topics a

Related concepts (36)

Complexity class

In computational complexity theory, a complexity class is a set of computational problems "of related resource-based complexity". The two most commonly analyzed resources are time and memory. In general, a complexity class is defined in terms of a type of computational problem, a model of computation, and a bounded resource like time or memory. In particular, most complexity classes consist of decision problems that are solvable with a Turing machine, and are differentiated by their time or space (memory) requirements.

Computational complexity

In computer science, the computational complexity or simply complexity of an algorithm is the amount of resources required to run it. Particular focus is given to computation time (generally measured by the number of needed elementary operations) and memory storage requirements. The complexity of a problem is the complexity of the best algorithms that allow solving the problem. The study of the complexity of explicitly given algorithms is called analysis of algorithms, while the study of the complexity of problems is called computational complexity theory.

Computational complexity theory

In theoretical computer science and mathematics, computational complexity theory focuses on classifying computational problems according to their resource usage, and relating these classes to each other. A computational problem is a task solved by a computer. A computation problem is solvable by mechanical application of mathematical steps, such as an algorithm. A problem is regarded as inherently difficult if its solution requires significant resources, whatever the algorithm used.

Space complexity

The space complexity of an algorithm or a computer program is the amount of memory space required to solve an instance of the computational problem as a function of characteristics of the input. It is the memory required by an algorithm until it executes completely. This includes the memory space used by its inputs, called input space, and any other (auxiliary) memory it uses during execution, which is called auxiliary space. Similar to time complexity, space complexity is often expressed asymptotically in big O notation, such as etc.

Parameterized complexity

In computer science, parameterized complexity is a branch of computational complexity theory that focuses on classifying computational problems according to their inherent difficulty with respect to multiple parameters of the input or output. The complexity of a problem is then measured as a function of those parameters. This allows the classification of NP-hard problems on a finer scale than in the classical setting, where the complexity of a problem is only measured as a function of the number of bits in the input.

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Algorithmic Complexity: Big-O NotationCS-101: Advanced information, computation, communication I

Introduces Big-O notation for analyzing algorithm efficiency, covering logic, structures, and growth functions.

Complexity of Algorithms: Advanced Big-O FactsCS-101: Advanced information, computation, communication I

Explores advanced big-O facts for powers, logarithms, factorials, and function combinations.

Algorithm Complexity: Search and AnalysisCS-119(c): Information, Computation, Communication

Delves into algorithm complexity, analyzing search efficiency and operation count, with a focus on worst-case scenarios and 'big O' notation.

Elements of computational complexityPHYS-641: Quantum Computing

Covers classical and quantum computational complexity concepts and implications.

Recursive Algorithms: Induction & SortingCS-101: Advanced information, computation, communication I

Explores induction, recursion, and sorting algorithms, including merge sort and the proof of correctness for recursive algorithms.