Suffix arrays and suffix trees are data structures used to efficiently store and process the suffixes of a given string. Suffixes are the substrings that begin at every possible position in the string and extend to the end of the string.
A suffix array is a sorted array of all the suffixes of a string. Each entry in the suffix array represents the starting position of a suffix in the original string. The suffix array can be constructed in O(n log n) time, where n is the length of the input string, using algorithms like the SA-IS algorithm.
A suffix tree, on the other hand, is a tree-like data structure that represents all the suffixes of a string in a more compact way than a suffix array. The suffix tree can be constructed in linear time, i.e., O(n), using algorithms like the Ukkonen’s algorithm.
Suffix arrays and suffix trees can be used to solve various string-related problems such as substring search, longest common substring, and pattern matching. For example, to find all occurrences of a pattern P in a text T, we can construct the suffix array or suffix tree of T and then search for P in the suffix array or tree using binary search. The starting position of each match can be obtained from the corresponding entry in the suffix array or by traversing the path in the suffix tree corresponding to P. This approach has a time complexity of O(m log n) for a pattern of length m and a text of length n.
Another example is the construction of a Burrows-Wheeler transform (BWT) of a string, which is used in data compression and bioinformatics. The BWT of a string is a permutation of its characters that preserves the order of the substrings starting at each position. The suffix array or suffix tree can be used to efficiently compute the BWT of a string in O(n) time.
In summary, suffix arrays and suffix trees are powerful data structures that enable efficient processing of suffixes of a string and are useful in various string-related problems.