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The longest alternating subsequence problem has also been studied in the setting of online algorithms, in which the elements of are presented in an online fashion, and a decision maker needs to decide whether to include or exclude each element at the time it is first presented, without any knowledge of the elements that will be presented in the future, and without the possibility of recalling ...
The longest increasing subsequence has also been studied in the setting of online algorithms, in which the elements of a sequence of independent random variables with continuous distribution – or alternatively the elements of a random permutation – are presented one at a time to an algorithm that must decide whether to include or exclude ...
Lexicographically minimal string rotation; Longest alternating subsequence; Longest common subsequence; Longest common substring; Longest increasing subsequence; Longest palindromic substring; Longest repeated substring problem
The second column and second row have been filled in with ε, because when an empty sequence is compared with a non-empty sequence, the longest common subsequence is always an empty sequence. LCS ( R 1 , C 1 ) is determined by comparing the first elements in each sequence.
An f-fold n-ary de Bruijn sequence is an extension of the notion n-ary de Bruijn sequence, such that the sequence of the length contains every possible subsequence of the length n exactly f times. For example, for n = 2 {\displaystyle n=2} the cyclic sequences 11100010 and 11101000 are two-fold binary de Bruijn sequences.
Techniques such as alphabet reduction may alleviate the high space complexity by reinterpreting the original string as a long string over a smaller alphabet i.e. a string of n bytes can alternatively be regarded as a string of 2n four-bit units and stored in a trie with sixteen pointers per node. However, lookups need to visit twice as many ...
Sequence alignment algorithms (6 P) String metrics (14 P) String sorting algorithms (4 P) String collation algorithms (2 P) String matching algorithms (1 C, 16 P)
One application of the algorithm is finding sequence alignments of DNA or protein sequences. It is also a space-efficient way to calculate the longest common subsequence between two sets of data such as with the common diff tool. The Hirschberg algorithm can be derived from the Needleman–Wunsch algorithm by observing that: [3]