Concepts inDynamic ordered sets with exponential search trees
Binary search algorithm
In computer science, a binary search or half-interval search algorithm finds the position of a specified value (the input "key") within a sorted array. In each step, the algorithm compares the input key value with the key value of the middle element of the array. If the keys match, then a matching element has been found so its index, or position, is returned.
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Set (abstract data type)
In computer science, a set is an abstract data structure that can store certain values, without any particular order, and no repeated values. It is a computer implementation of the mathematical concept of a finite set. Unlike most other collection types, rather than retrieving a specific element from a set, one typically tests a value for membership in a set. Some set data structures are designed for static or frozen sets that do not change after they are constructed.
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String (computer science)
In formal languages, which are used in mathematical logic and theoretical computer science, a string is a finite sequence of symbols that are chosen from a set called an alphabet. In computer programming, a string is traditionally a sequence of characters, either as a literal constant or as some kind of variable. The latter may allow its elements to be mutated and/or the length changed, or it may be fixed (after creation).
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Partially ordered set
In mathematics, especially order theory, a partially ordered set (or poset) formalizes and generalizes the intuitive concept of an ordering, sequencing, or arrangement of the elements of a set. A poset consists of a set together with a binary relation that indicates that, for certain pairs of elements in the set, one of the elements precedes the other.
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String searching algorithm
In computer science, string searching algorithms, sometimes called string matching algorithms, are an important class of string algorithms that try to find a place where one or several strings are found within a larger string or text. Let Σ be an alphabet. Formally, both the pattern and searched text are vectors of elements of Σ. The Σ may be a usual human alphabet (for example, the letters A through Z in the Latin alphabet).
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Square root
In mathematics, a square root of a number a is a number y such that y = a, or, in other words, a number y whose square (the result of multiplying the number by itself, or y × y) is a. For example, 4 is a square root of 16 because 4 = 16. Every non-negative real number a has a unique non-negative square root, called the principal square root, which is denoted by, where √ is called radical sign. For example, the principal square root of 9 is 3, denoted, because {{{1}}} and 3 is non-negative.
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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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Integer
The integers are formed by the natural numbers (including 0) together with the negatives of the non-zero natural numbers (−1, −2, −3, ...). Viewed as a subset of the real numbers, they are numbers that can be written without a fractional or decimal component, and fall within the set {... , −2, −1, 0, 1, 2, ...}. For example, 21, 4, and � are integers; 9.75, 5½, and √2 are not integers. The set of all integers is often denoted by a boldface Z, which stands for Zahlen.
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