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Wikipedia / Longest repeated substring problem

In computer science, the longest repeated substring problem is the problem of finding the longest substring of a string that occurs at least twice.

by building a suffix tree leaf descendants. To avoid overlapping repeats, you can check that the list of suffix lengths has no consecutive elements with less than prefix-length difference.

In the figure with the string "ATCGATCGA$", the longest substring that repeats at least twice is "ATCGA".