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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.
A list containing a single element is, by definition, sorted. Repeatedly merge sublists to create a new sorted sublist until the single list contains all elements. The single list is the sorted list. The merge algorithm is used repeatedly in the merge sort algorithm. An example merge sort is given in the illustration. It starts with an unsorted ...
Timsort is a hybrid, stable sorting algorithm, derived from merge sort and insertion sort, designed to perform well on many kinds of real-world data.It was implemented by Tim Peters in 2002 for use in the Python programming language.
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 ...
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.
Array indices can also be arrays of integers. For example, suppose that I = [0:9] is an array of 10 integers. Then A[I] is equivalent to an array of the first 10 elements of A. A practical example of this is a sorting operation such as:
We then run through the list comparing each element in the first half to the element in the second half. Our second gap ( k ) is 256, which breaks the array into four sections (starting at 0, 256, 512, 768), and we make sure the first items in each section are sorted relative to each other, then the second item in each section, and so on.
In Miranda, this right-fold, from Hughes (1989:5-6), has the same semantics (by example) as the Scheme implementation above, for two arguments. append a b = reduce cons b a Where reduce is Miranda's name for fold, and cons constructs a list from two values or lists. For example,