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It stores the lengths of the longest common prefixes (LCPs) between all pairs of consecutive suffixes in a sorted suffix array. For example, if A := [aab, ab, abaab, b, baab] is a suffix array, the longest common prefix between A[1] = aab and A[2] = ab is a which has length 1, so H[2] = 1 in the LCP array H.
Then, sorting a subset of is equivalent to convert it into an increasing sequence. The lexicographic order on the resulting sequences induces thus an order on the subsets, which is also called the lexicographical order. In this context, one generally prefer to sort first the subsets by cardinality, such as in the shortlex order. Therefore, in ...
It is a lexicographically sorted array of all suffixes of each string in the set . In the array, each suffix is represented by an integer pair ( i , j ) {\displaystyle (i,j)} which denotes the suffix starting from position j {\displaystyle j} in s i {\displaystyle s_{i}} .
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.
In mathematics, lexicographical order is a means of ordering sequences in a manner analogous to that used to produce alphabetical order. [16] Some computer applications use a version of alphabetical order that can be achieved using a very simple algorithm, based purely on the ASCII or Unicode codes for characters. This may have non-standard ...
Sorted arrays are the most space-efficient data structure with the best locality of reference for sequentially stored data. [citation needed]Elements within a sorted array are found using a binary search, in O(log n); thus sorted arrays are suited for cases when one needs to be able to look up elements quickly, e.g. as a set or multiset data structure.
More generally objects can be sorted based on a property. Such a component or property is called a sort key. For example, the items are books, the sort key is the title, subject or author, and the order is alphabetical. A new sort key can be created from two or more sort keys by lexicographical order.
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 ).