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The picture shows two strings where the problem has multiple solutions. Although the substring occurrences always overlap, it is impossible to obtain a longer common substring by "uniting" them. The strings "ABABC", "BABCA" and "ABCBA" have only one longest common substring, viz. "ABC" of length 3.
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 ...
Once constructed, several operations can be performed quickly, such as locating a substring in , locating a substring if a certain number of mistakes are allowed, and locating matches for a regular expression pattern. Suffix trees also provided one of the first linear-time solutions for the longest common substring problem. [2]
After computing E(i, j) for all i and j, we can easily find a solution to the original problem: it is the substring for which E(m, j) is minimal (m being the length of the pattern P.) Computing E ( m , j ) is very similar to computing the edit distance between two strings.
Anselm Blumer with a drawing of generalized CDAWG for strings ababc and abcab. The concept of suffix automaton was introduced in 1983 [1] by a group of scientists from University of Denver and University of Colorado Boulder consisting of Anselm Blumer, Janet Blumer, Andrzej Ehrenfeucht, David Haussler and Ross McConnell, although similar concepts had earlier been studied alongside suffix trees ...
For example, the longest palindromic substring of "bananas" is "anana". The longest palindromic substring is not guaranteed to be unique; for example, in the string "abracadabra", there is no palindromic substring with length greater than three, but there are two palindromic substrings with length three, namely, "aca" and "ada".
LCS in particular has overlapping subproblems: the solutions to high-level subproblems often reuse solutions to lower level subproblems. Problems with these two properties are amenable to dynamic programming approaches, in which subproblem solutions are memoized , that is, the solutions of subproblems are saved for reuse.
For example, a digital door lock with a 4-digit code (each digit having 10 possibilities, from 0 to 9) would have B (10, 4) solutions, with length 10 000. Therefore, only at most 10 000 + 3 = 10 003 (as the solutions are cyclic) presses are needed to open the lock, whereas trying all codes separately would require 4 × 10 000 = 40 000 presses.