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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 problem of computing a longest common subsequence has been well studied in computer science. It can be solved in polynomial time by dynamic programming ; [ 5 ] this basic algorithm has additional speedups for small alphabets (the Method of Four Russians ), [ 6 ] for strings with few differences, [ 7 ] for strings with few matching pairs of ...
Comparison of two revisions of an example file, based on their longest common subsequence (black) A longest common subsequence (LCS) is the longest subsequence common to all sequences in a set of sequences (often just two sequences).
The above algorithm has worst-case time and space complexities of O(mn) (see big O notation), where m is the number of elements in sequence A and n is the number of elements in sequence B. The Hunt–Szymanski algorithm modifies this algorithm to have a worst-case time complexity of O ( mn log m ) and space complexity of O ( mn ) , though it ...
The longest increasing subsequences are studied in the context of various disciplines related to mathematics, including algorithmics, random matrix theory, representation theory, and physics. [ 1 ] [ 2 ] The longest increasing subsequence problem is solvable in time O ( n log n ) , {\displaystyle O(n\log n),} where n {\displaystyle n ...
In computer science, the longest repeated substring problem is the problem of finding the longest substring of a string that occurs at least twice. This problem can be solved in linear time and space Θ ( n ) {\displaystyle \Theta (n)} by building a suffix tree for the string (with a special end-of-string symbol like '$' appended), and finding ...
For example, for the array of values [−2, 1, −3, 4, −1, 2, 1, −5, 4], the contiguous subarray with the largest sum is [4, −1, 2, 1], with sum 6. Some properties of this problem are: If the array contains all non-negative numbers, then the problem is trivial; a maximum subarray is the entire array.
[2] The coverability problem for Petri Nets is EXPSPACE-complete. [3] The reachability problem for Petri nets was known to be EXPSPACE-hard for a long time, [4] but shown to be nonelementary, [5] so probably not in EXPSPACE. In 2022 it was shown to be Ackermann-complete. [6] [7]