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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.
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 fundamental idea behind array programming is that operations apply at once to an entire set of values. This makes it a high-level programming model as it allows the programmer to think and operate on whole aggregates of data, without having to resort to explicit loops of individual scalar operations.
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) will result in an array y whose elements are sine of the corresponding elements of the array x. Vectorized index operations are also supported.
Arrays in BASIC could contain integers, floating point or string variables. Some dialects of BASIC supported matrices and matrix operations, which can be used to solve sets of simultaneous linear algebraic equations. These dialects would directly support matrix operations such as assignment, addition, multiplication (of compatible matrix types ...
Most BASICs supported the construction of array variables using the DIM keyword, for instance, DIM A(5), B(2,2) defines two arrays, the single-dimension A and two-dimension (matrix) B. In Full BASIC, the lower bound of any array was normally 1, so in this case, the variable A has five "slots", numbered 1 though 5.
Instead, available external libraries provide matrix operations on arrays, in nearly all currently used programming languages. Matrix manipulation was among the earliest numerical applications of computers. [48] The original Dartmouth BASIC had built-in commands for matrix arithmetic on arrays from its second edition implementation in 1964.
The basic idea behind a hash table is that accessing an element of an array via its index is a simple, constant-time operation. Therefore, the average overhead of an operation for a hash table is only the computation of the key's hash, combined with accessing the corresponding bucket within the array.