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Looking for an efficient algorithm to find the longest substring in a string that has its complementary string as well (bitwise).
That what I mean by saying complementary string bitwise:
100011
011100
Here’s a simple O(n) algorithm that relies on suffix tree construction.
Load the original string s and the complement string s’ into the same suffix tree (O(n) time). Then post-process this tree by setting for each node x two flags f(x) and f'(x) that are true exactly when f(x) (resp. f'(x)) contains a suffix of s (resp. s’). Now simply traverse the tree looking for the deepest node that has both flags set and you have found the longest string in s whose complement also occurs in s. The post-processing also costs only O(n) time so the total running time is O(n).