Search results
Results from the WOW.Com Content Network
Other properties of the Lehmer code include that the lexicographical order of the encodings of two permutations is the same as that of their sequences (σ 1, ..., σ n), that any value 0 in the code represents a right-to-left minimum in the permutation (i.e., a σ i smaller than any σ j to its right), and a value n − i at position i ...
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 ...
In computer science, the lexicographically minimal string rotation or lexicographically least circular substring is the problem of finding the rotation of a string possessing the lowest lexicographical order of all such rotations. For example, the lexicographically minimal rotation of "bbaaccaadd" would be "aaccaaddbb".
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.
If the alphabet Σ has a total order (cf. alphabetical order) one can define a total order on Σ * called lexicographical order. The lexicographical order is total if the alphabetical order is, but is not well-founded for any nontrivial alphabet, even if the alphabetical order is.
Suffix arrays are closely related to suffix trees: . Suffix arrays can be constructed by performing a depth-first traversal of a suffix tree. The suffix array corresponds to the leaf-labels given in the order in which these are visited during the traversal, if edges are visited in the lexicographical order of their first character.
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.
[5] An alternative construction involves concatenating together, in lexicographic order, all the Lyndon words whose length divides n. [6] An inverse Burrows–Wheeler transform can be used to generate the required Lyndon words in lexicographic order. [7] de Bruijn sequences can also be constructed using shift registers [8] or via finite fields. [9]