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Quicksort is an efficient, general-purpose sorting algorithm. Quicksort was developed by British computer scientist Tony Hoare in 1959 [1] and published in 1961. [2] It is still a commonly used algorithm for sorting. Overall, it is slightly faster than merge sort and heapsort for randomized data, particularly on larger distributions.
e. In mathematics, a continuous function is a function such that a small variation of the argument induces a small variation of the value of the function. This implies there are no abrupt changes in value, known as discontinuities. More precisely, a function is continuous if arbitrarily small changes in its value can be assured by restricting ...
The probability of a success changes on each draw, as each draw decreases the population ( sampling without replacement from a finite population). A random variable follows the hypergeometric distribution if its probability mass function (pmf) is given by [1] where. N is the population size,
The group operation is the composition of functions (performing one rearrangement after the other), which results in another function (rearrangement). The properties of permutations do not depend on the nature of the elements being permuted, only on their number, so one often considers the standard set S = { 1 , 2 , … , n } {\displaystyle S ...
In mathematics, the Weierstrass function is an example of a real-valued function that is continuous everywhere but differentiable nowhere. It is an example of a fractal curve. It is named after its discoverer Karl Weierstrass . The Weierstrass function has historically served the role of a pathological function, being the first published ...
The binomial distribution is the PMF of k successes given n independent events each with a probability p of success. Mathematically, when α = k + 1 and β = n − k + 1, the beta distribution and the binomial distribution are related by [clarification needed] a factor of n + 1 :
Gene duplication. Gene duplication (or chromosomal duplication or gene amplification) is a major mechanism through which new genetic material is generated during molecular evolution. It can be defined as any duplication of a region of DNA that contains a gene. Gene duplications can arise as products of several types of errors in DNA replication ...
Idempotence ( UK: / ˌɪdɛmˈpoʊtəns /, [1] US: / ˈaɪdəm -/) [2] is the property of certain operations in mathematics and computer science whereby they can be applied multiple times without changing the result beyond the initial application. The concept of idempotence arises in a number of places in abstract algebra (in particular, in the ...