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In computer science, the longest palindromic substring or longest symmetric factor problem is the problem of finding a maximum-length contiguous substring of a given string that is also a palindrome. For example, the longest palindromic substring of "bananas" is "anana".
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 ...
In computer science a palindrome tree, also called an EerTree, [1] is a type of search tree, that allows for fast access to all palindromes contained in a string.They can be used to solve the longest palindromic substring, the k-factorization problem [2] (can a given string be divided into exactly k palindromes), palindromic length of a string [3] (what is the minimum number of palindromes ...
Compute a longest common subsequence of these two strings, and let , be the random variable whose value is the length of this subsequence. Then the expected value of λ n , k {\displaystyle \lambda _{n,k}} is (up to lower-order terms) proportional to n , and the k th Chvátal–Sankoff constant γ k {\displaystyle \gamma _{k}} is the constant ...
Finding the longest repeated substring; Finding the longest common substring; Finding the longest palindrome in a string; Suffix trees are often used in bioinformatics applications, searching for patterns in DNA or protein sequences (which can be viewed as long strings of characters). The ability to search efficiently with mismatches might be ...
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.
The similarity of two strings and is determined by this formula: twice the number of matching characters divided by the total number of characters of both strings. The matching characters are defined as some longest common substring [3] plus recursively the number of matching characters in the non-matching regions on both sides of the longest common substring: [2] [4]
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]