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In computer science, a list or sequence is a collection of items that are finite in number and in a particular order. An instance of a list is a computer representation of the mathematical concept of a tuple or finite sequence. A list may contain the same value more than once, and each occurrence is considered a distinct item.
In computer science, arranging in an ordered sequence is called "sorting". Sorting is a common operation in many applications, and efficient algorithms have been developed to perform it. The most common uses of sorted sequences are: making lookup or search efficient; making merging of sequences efficient; enabling processing of data in a ...
The consequences of the theorem include: the order of a group G is a power of a prime p if and only if ord(a) is some power of p for every a in G. [2] If a has infinite order, then all non-zero powers of a have infinite order as well. If a has finite order, we have the following formula for the order of the powers of a: ord(a k) = ord(a) / gcd ...
In mathematics, the lexicographic or lexicographical order (also known as lexical order, or dictionary order) is a generalization of the alphabetical order of the dictionaries to sequences of ordered symbols or, more generally, of elements of a totally ordered set.
One implementation can be described as arranging the data sequence in a two-dimensional array and then sorting the columns of the array using insertion sort. The worst-case time complexity of Shellsort is an open problem and depends on the gap sequence used, with known complexities ranging from O(n 2) to O(n 4/3) and Θ(n log 2 n).
In other implementations, the order of elements with the same priority is undefined. While priority queues are often implemented using heaps , they are conceptually distinct from heaps. A priority queue is an abstract data type like a list or a map ; just as a list can be implemented with a linked list or with an array , a priority queue can be ...
For example, a sequence differs from a set because (among other things) the order of the composed items matters for the former but not the latter. Data structures such as arrays , linked lists , hash tables , and many others can be used to implement either of them.
Flowchart of using successive subtractions to find the greatest common divisor of number r and s. In mathematics and computer science, an algorithm (/ ˈ æ l ɡ ə r ɪ ð əm / ⓘ) is a finite sequence of mathematically rigorous instructions, typically used to solve a class of specific problems or to perform a computation. [1]