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Problem 47: Suffix Array to the Suffix Tree

The goal of the problem is to transform the Suffix array of a word $x$ into its Suffix tree. Despite the fact that both data structures infer essentially the same types of indexing operations, some come more readily from the Suffix tree structure.

The interest in designing a linear-time algorithm to do it is interesting when the alphabet is linearly sortable. Indeed, with this hypothesis, there are many linear-time algorithms to build the Suffix array of a word, although there is mostly one method to build its Suffix tree in the same time. Moreover, techniques used for the former construction are way easier to develop.

Show how to build the Suffix tree of a word in linear time given its Suffix array.


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