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Thus, if the array is seen as a function on a set of possible index combinations, it is the dimension of the space of which its domain is a discrete subset. 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.
In the field of streaming algorithms, Misra–Gries summaries are used to solve the frequent elements problem in the data stream model.That is, given a long stream of input that can only be examined once (and in some arbitrary order), the Misra-Gries algorithm [1] can be used to compute which (if any) value makes up a majority of the stream, or more generally, the set of items that constitute ...
An array data structure can be mathematically modeled as an abstract data structure (an abstract array) with two operations get(A, I): the data stored in the element of the array A whose indices are the integer tuple I. set(A,I,V): the array that results by setting the value of that element to V. These operations are required to satisfy the ...
The most frequently used general-purpose implementation of an associative array is with a hash table: an array combined with a hash function that separates each key into a separate "bucket" of the array. The basic idea behind a hash table is that accessing an element of an array via its index is a simple, constant-time operation.
Array, a sequence of elements of the same type stored contiguously in memory; Record (also called a structure or struct), a collection of fields . Product type (also called a tuple), a record in which the fields are not named
cons (e 1, l 1) = cons (e 2, l 2) if e 1 = e 2 and l 1 = l 2. Note that first (nil ()) and rest (nil ()) are not defined. These axioms are equivalent to those of the abstract stack data type. In type theory, the above definition is more simply regarded as an inductive type defined in terms of constructors: nil and cons.
Matrix multiplication is an example of a 2-rank function, because it operates on 2-dimensional objects (matrices). Collapse operators reduce the dimensionality of an input data array by one or more dimensions. For example, summing over elements collapses the input array by 1 dimension.
In all versions of Python, boolean operators treat zero values or empty values such as "", 0, None, 0.0, [], and {} as false, while in general treating non-empty, non-zero values as true. The boolean values True and False were added to the language in Python 2.2.1 as constants (subclassed from 1 and 0 ) and were changed to be full blown ...