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A suffix can be seen as a special case of a substring. Example: The string nana is equal to a suffix (and substring and subsequence) of the string banana: banana |||| nana A suffix tree for a string is a trie data structure that represents all of its suffixes. Suffix trees have large numbers of applications in string algorithms.
Each substring is terminated with special character $. The six paths from the root to the leaves (shown as boxes) correspond to the six suffixes A$, NA$, ANA$, NANA$, ANANA$ and BANANA$. The numbers in the leaves give the start position of the corresponding suffix. Suffix links, drawn dashed, are used during construction.
In computer science, the longest repeated substring problem is the problem of finding the longest substring of a string that occurs at least twice. This problem can be solved in linear time and space Θ ( n ) {\displaystyle \Theta (n)} by building a suffix tree for the string (with a special end-of-string symbol like '$' appended), and finding ...
Building the suffix tree takes () time (if the size of the alphabet is constant). If the tree is traversed from the bottom up with a bit vector telling which strings are seen below each node, the k-common substring problem can be solved in Θ ( N K ) {\displaystyle \Theta (NK)} time.
The suffix automaton is closely related to other suffix structures and substring indices. Given a suffix automaton of a specific string one may construct its suffix tree via compacting and recursive traversal in linear time. [ 20 ]
When constructing such a tree, each string should be padded with a unique out-of-alphabet marker symbol (or string) to ensure no suffix is a substring of another, guaranteeing each suffix is represented by a unique leaf node. Algorithms for constructing a GST include Ukkonen's algorithm (1995) and McCreight's algorithm (1976).
The suffix tree, a radix tree of the suffixes of the string, allowing substring search to be performed symbol-by-symbol [1] [3] The suffix automaton, the minimal deterministic finite automaton that recognizes substrings of a given text, closely related to the suffix tree and constructable by variants of the same algorithms. [4]
Deciding if a pattern of length is a substring of a string of length takes () time if only the suffix array is used. By additionally using the LCP information, this bound can be improved to O ( m + log n ) {\displaystyle O(m+\log n)} time. [ 3 ]