In computer science, the time complexity of an algorithm quantifies the amount of time taken by an algorithm to run as a function of the size of the input to the problem. The time complexity of an algorithm is commonly expressed using big O notation, which suppresses multiplicative constants and lower order terms. When expressed this way, the time complexity is said to be described asymptotically, i.e. , as the input size goes to infinity.
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Big O notation
In mathematics, big O notation is used to describe the limiting behavior of a function when the argument tends towards a particular value or infinity, usually in terms of simpler functions. It is a member of a larger family of notations that is called Landau notation, Bachmann–Landau notation, or asymptotic notation. In computer science, big O notation is used to classify algorithms by how they respond (e.g. , in their processing time or working space requirements) to changes in input size.
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Asymptotically optimal algorithm
In computer science, an algorithm is said to be asymptotically optimal if, roughly speaking, for large inputs it performs at worst a constant factor (independent of the input size) worse than the best possible algorithm. It is a term commonly encountered in computer science research as a result of widespread use of big-O notation.
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Model of computation
In computability theory and computational complexity theory, a model of computation is the definition of the set of allowable operations used in computation and their respective costs. It is used for measuring the complexity of an algorithm in execution time and or memory space: by assuming a certain model of computation, it is possible to analyze the computational resources required or to discuss the limitations of algorithms or computers.
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Algorithm
In mathematics and computer science, an algorithm Listen/ˈælɡərɪðəm/ (originating from al-Khwārizmī, the famous mathematician Muḥammad ibn Mūsā al-Khwārizmī) is a step-by-step procedure for calculations. Algorithms are used for calculation, data processing, and automated reasoning. More precisely, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function.
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Multiplication
Multiplication (often denoted by the cross symbol "×") is the mathematical operation of scaling one number by another. It is one of the four basic operations in elementary arithmetic.
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Boolean circuit
A Boolean circuit is a mathematical model of computation used in studying computational complexity theory. Boolean circuits are the main object of study in circuit complexity and are a special kind of circuits; a formal language can be decided by a family of Boolean circuits, one circuit for each possible input length. In addition, they are used as a formal model for combinational logic in digital electronics. Boolean circuits are defined in terms of the logic gates they contain.
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Conjecture
A conjecture is a proposition that is unproven but is thought to be true and has not been disproven. Karl Popper pioneered the use of the term "conjecture" in scientific philosophy. Conjecture is contrasted by hypothesis, which is a testable statement based on accepted grounds. In mathematics, a conjecture is an unproven proposition or theorem that appears correct.
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