Suffix Array - Summary


https://www.hackerearth.com/practice/notes/trie-suffix-tree-suffix-array/
Suffix array is a very nice array based structure. Basically, it is a lexicographically sorted array of suffixes of a string s. For example, let's consider a string s = abakan. A word abakan has 6 suffixes {abakan , bakan, akan, kan, an, n} and its suffix tree looks like this:
enter image description here
Of course, in order to reduce space, we do not store the exact suffixes. It is sufficient to store their indices.
Suffix arrays, especially combined with LCP table (which stands for Longest Common Prefix of neighboring suffixes table), are very very useful for solving many problems. I recommend reading this nice programming oriented paper about suffix arrays, their applications and related problems by Stanford University.
Suffix arrays can be build easily in O(n * log2n) time, where n is the length of s, using the algorithm proposed in the paper from the previous paragraph. This time can be improved to O(n * log n) using linear time sorting algorithm.
However, there is so extraordinary, cool and simple linear time algorithm for building suffix arrays by Kärkkäinen and Sanders, that reading it is a pure pleasure and you cannot miss it.

Correspondence between suffix tree and suffix array

It is also worth to mention, that a suffix array can be constructed directly from a suffix tree in linear time using DFS traversal. Suffix tree can be also constructed from the suffix array and LCP table as described here

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