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The lexicographical order of two totally ordered sets is thus a linear extension of their product order. One can define similarly the lexicographic order on the Cartesian product of an infinite family of ordered sets, if the family is indexed by the natural numbers, or more generally by a well-ordered set. This generalized lexicographical order ...
The theory of lexicographic codes is closely connected to combinatorial game theory. In particular, the codewords in a binary lexicographic code of distance d encode the winning positions in a variant of Grundy's game , played on a collection of heaps of stones, in which each move consists of replacing any one heap by at most d − 1 smaller ...
In mathematics and in particular in combinatorics, the Lehmer code is a particular way to encode each possible permutation of a sequence of n numbers. It is an instance of a scheme for numbering permutations and is an example of an inversion table. The Lehmer code is named in reference to D. H. Lehmer, [1] but the code had been known since 1888 ...
Merge sort. In computer science, a sorting algorithm is an algorithm that puts elements of a list into an order.The most frequently used orders are numerical order and lexicographical order, and either ascending or descending.
As an example, a term rewriting system for "multiplying out" mathematical expressions could contain a rule x*(y+z) → (x*y) + (x*z). In order to prove termination, a reduction ordering (>) must be found with respect to which the term x*(y+z) is greater than the term (x*y)+(x*z). This is not trivial, since the former term contains both fewer ...
A list containing the string "bencode" and the integer -20 is encoded as l7:bencodei-20ee. Dictionaries are encoded as d<pairs>e. Begins with d and ends with e. Contains key-value pairs. Keys are byte strings and must appear in lexicographical order. Each key is immediately followed by its value, which can be any bencoded type. Examples:
Lexicographic sorting of a set of string keys can be implemented by building a trie for the given keys and traversing the tree in pre-order fashion; [26] this is also a form of radix sort. [27] Tries are also fundamental data structures for burstsort , which is notable for being the fastest string sorting algorithm as of 2007, [ 28 ...
The algorithm is called lexicographic breadth-first search because the order it produces is an ordering that could also have been produced by a breadth-first search, and because if the ordering is used to index the rows and columns of an adjacency matrix of a graph then the algorithm sorts the rows and columns into lexicographical order.