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For example, for the array of values [−2, 1, −3, 4, −1, 2, 1, −5, 4], the contiguous subarray with the largest sum is [4, −1, 2, 1], with sum 6. Some properties of this problem are: If the array contains all non-negative numbers, then the problem is trivial; a maximum subarray is the entire array.
The dope vector is a complete handle for the array, and is a convenient way to pass arrays as arguments to procedures. Many useful array slicing operations (such as selecting a sub-array, swapping indices, or reversing the direction of the indices) can be performed very efficiently by manipulating the dope vector. [2]
is how one would use Fortran to create arrays from the even and odd entries of an array. Another common use of vectorized indices is a filtering operation. Consider a clipping operation of a sine wave where amplitudes larger than 0.5 are to be set to 0.5. Using S-Lang, this can be done by
More generally, there are d! possible orders for a given array, one for each permutation of dimensions (with row-major and column-order just 2 special cases), although the lists of stride values are not necessarily permutations of each other, e.g., in the 2-by-3 example above, the strides are (3,1) for row-major and (1,2) for column-major.
For example, in the Pascal programming language, the declaration type MyTable = array [1.. 4, 1.. 2] of integer, defines a new array data type called MyTable. The declaration var A: MyTable then defines a variable A of that type, which is an aggregate of eight elements, each being an integer variable identified by two indices.
For "one-dimensional" (single-indexed) arrays – vectors, sequence, strings etc. – the most common slicing operation is extraction of zero or more consecutive elements. Thus, if we have a vector containing elements (2, 5, 7, 3, 8, 6, 4, 1), and we want to create an array slice from the 3rd to the 6th items, we get (7, 3, 8, 6).
In array languages, operations are generalized to apply to both scalars and arrays. Thus, a+b expresses the sum of two scalars if a and b are scalars, or the sum of two arrays if they are arrays. An array language simplifies programming but possibly at a cost known as the abstraction penalty.
In mathematical terms, an associative array is a function with finite domain. [1] It supports 'lookup', 'remove', and 'insert' operations. The dictionary problem is the classic problem of designing efficient data structures that implement associative arrays. [2] The two major solutions to the dictionary problem are hash tables and search trees.