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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 ...
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).
Sequential access is a term describing a group of elements (such as data in a memory array or a disk file or on magnetic-tape data storage) being accessed in a predetermined, ordered sequence. It is the opposite of random access, the ability to access an arbitrary element of a sequence as easily and efficiently as any other at any time.
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 ...
Group codes consist of linear block codes which are subgroups of , where is a finite Abelian group. A systematic group code C {\displaystyle C} is a code over G n {\displaystyle G^{n}} of order | G | k {\displaystyle \left|G\right|^{k}} defined by n − k {\displaystyle n-k} homomorphisms which determine the parity check bits.
Informally, a sequence has a limit if the elements of the sequence become closer and closer to some value (called the limit of the sequence), and they become and remain arbitrarily close to , meaning that given a real number greater than zero, all but a finite number of the elements of the sequence have a distance from less than .
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.