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Prefix sums are trivial to compute in sequential models of computation, by using the formula y i = y i − 1 + x i to compute each output value in sequence order. However, despite their ease of computation, prefix sums are a useful primitive in certain algorithms such as counting sort, [1] [2] and they form the basis of the scan higher-order function in functional programming languages.
In functional programming languages, variadics can be considered complementary to the apply function, which takes a function and a list/sequence/array as arguments, and calls the function with the arguments supplied in that list, thus passing a variable number of arguments to the function.
String, a sequence of characters representing text; Union, a datum which may be one of a set of types; Tagged union (also called a variant, discriminated union or sum type), a union with a tag specifying which type the data is
Kadane's algorithm: finds the contiguous subarray with largest sum in an array of numbers; Longest common substring problem: find the longest string (or strings) that is a substring (or are substrings) of two or more strings; Substring search
For example, to perform an element by element sum of two arrays, a and b to produce a third c, it is only necessary to write c = a + b In addition to support for vectorized arithmetic and relational operations, these languages also vectorize common mathematical functions such as sine. For example, if x is an array, then y = sin (x)
The smallest integer m > 1 such that p n # + m is a prime number, where the primorial p n # is the product of the first n prime numbers. A005235 Semiperfect numbers
Thus a one-dimensional array is a list of data, a two-dimensional array is a rectangle of data, [12] a three-dimensional array a block of data, etc. This should not be confused with the dimension of the set of all matrices with a given domain, that is, the number of elements in the array.
Pairwise summation is the default summation algorithm in NumPy [9] and the Julia technical-computing language, [10] where in both cases it was found to have comparable speed to naive summation (thanks to the use of a large base case).