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  2. Maximum subarray problem - Wikipedia

    en.wikipedia.org/wiki/Maximum_subarray_problem

    Maximum subarray problems arise in many fields, such as genomic sequence analysis and computer vision.. Genomic sequence analysis employs maximum subarray algorithms to identify important biological segments of protein sequences that have unusual properties, by assigning scores to points within the sequence that are positive when a motif to be recognized is present, and negative when it is not ...

  3. Longest common substring - Wikipedia

    en.wikipedia.org/wiki/Longest_common_substring

    This algorithm runs in () time. The array L stores the length of the longest common suffix of the prefixes S[1..i] and T[1..j] which end at position i and j, respectively. The variable z is used to hold the length of the longest common substring found so far. The set ret is used to hold the set of strings which are of length z.

  4. Longest palindromic substring - Wikipedia

    en.wikipedia.org/wiki/Longest_palindromic_substring

    Manacher (1975) invented an ()-time algorithm for listing all the palindromes that appear at the start of a given string of length . However, as observed e.g., by Apostolico, Breslauer & Galil (1995) , the same algorithm can also be used to find all maximal palindromic substrings anywhere within the input string, again in O ( n ) {\displaystyle ...

  5. Longest common subsequence - Wikipedia

    en.wikipedia.org/wiki/Longest_common_subsequence

    Chowdhury and Ramachandran devised a quadratic-time linear-space algorithm [9] [10] for finding the LCS length along with an optimal sequence which runs faster than Hirschberg's algorithm in practice due to its superior cache performance. [9] The algorithm has an asymptotically optimal cache complexity under the Ideal cache model. [11]

  6. Longest increasing subsequence - Wikipedia

    en.wikipedia.org/wiki/Longest_increasing_subsequence

    The length of is more than the length of but it is possible that not all elements in this array are used by the algorithm (in fact, if the longest increasing sequence has length then only [], …, [] are used by the algorithm).

  7. Longest repeated substring problem - Wikipedia

    en.wikipedia.org/wiki/Longest_repeated_substring...

    The string spelled by the edges from the root to such a node is a longest repeated substring. The problem of finding the longest substring with at least k {\displaystyle k} occurrences can be solved by first preprocessing the tree to count the number of leaf descendants for each internal node, and then finding the deepest node with at least k ...

  8. Range minimum query - Wikipedia

    en.wikipedia.org/wiki/Range_minimum_query

    Range minimum query reduced to the lowest common ancestor problem.. Given an array A[1 … n] of n objects taken from a totally ordered set, such as integers, the range minimum query RMQ A (l,r) =arg min A[k] (with 1 ≤ l ≤ k ≤ r ≤ n) returns the position of the minimal element in the specified sub-array A[l …

  9. Range query (computer science) - Wikipedia

    en.wikipedia.org/wiki/Range_query_(computer_science)

    One of the most famous algorithms for finding the majority of an array was proposed by Boyer and Moore [9] which is also known as the Boyer–Moore majority vote algorithm. Boyer and Moore proposed an algorithm to find the majority element of a string (if it has one) in O ( n ) {\displaystyle O(n)} time and using O ( 1 ) {\displaystyle O(1)} space.