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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 increasing subsequence - Wikipedia

    en.wikipedia.org/wiki/Longest_increasing_subsequence

    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 ...

  4. Longest common subsequence - Wikipedia

    en.wikipedia.org/wiki/Longest_common_subsequence

    A longest common subsequence (LCS) is the longest subsequence common to all sequences in a set of sequences (often just two sequences). It differs from the longest common substring : unlike substrings, subsequences are not required to occupy consecutive positions within the original sequences.

  5. Longest common substring - Wikipedia

    en.wikipedia.org/wiki/Longest_common_substring

    The longest common substrings of a set of strings can be found by building a generalized suffix tree for the strings, and then finding the deepest internal nodes which have leaf nodes from all the strings in the subtree below it. The figure on the right is the suffix tree for the strings "ABAB", "BABA" and "ABBA", padded with unique string ...

  6. 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 …

  7. Hook length formula - Wikipedia

    en.wikipedia.org/wiki/Hook_length_formula

    In combinatorial mathematics, the hook length formula is a formula for the number of standard Young tableaux whose shape is a given Young diagram.It has applications in diverse areas such as representation theory, probability, and algorithm analysis; for example, the problem of longest increasing subsequences.

  8. Longest palindromic substring - Wikipedia

    en.wikipedia.org/wiki/Longest_palindromic_substring

    With that knowledge, everything after the "c" looks like the reflection of everything before the "c". The "a" after the "c" has the same longest palindrome as the "a" before the "c". Similarly, the "b" after the "c" has a longest palindrome that is at least the length of the longest palindrome centered on the "b" before the "c". There are some ...

  9. Longest alternating subsequence - Wikipedia

    en.wikipedia.org/wiki/Longest_Alternating...

    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 ...