Suffix Array notes

These two concepts are frequently seen in string matching issues:

Text: Original

Template (pattern): keyword (equivalent to a substring)

Task: Find pattern in text

Common algorithms:

AC Automata: Multiple pattern

KMP: Known pattern, preprocessing of pattern

Trie: Also known as a prefix tree, often used to find string prefixes

Suffix array: Known text, preprocessing of text

Suffix tree: In fact, the path is compressed version of the trie tree, the tree does not have a forked path compressed

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Sa[i]: suffix array, all suffixes of the pattern are sorted from small to large, and the beginning position of the first suffix (total n suffixes, sa[0..n-1]) is ordered.

Eg: for the word "banana", sa={5,3,1,0,4,2}, respectively, corresponding to the suffix A, ana, Anana, Banana, NA, nana

Rank[i]: Save Sa[i] rank from small to large in all suffixes

Sa[i] and rank[i] reciprocal, namely sa[rank[i]]=i, rank[sa[i]]=i

Defines the longest common prefix length for height[i]=sa[i-1] and Sa[i] (that is, the longest common prefix length for two ranked adjacent suffixes)

Suffix Array notes