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1. A string s is said to be periodic with a period α, if s is αk for some k>2. (Note that αk is the string formed by concatenating k times.) A DNA sequence s is called a tandem repeat if it is periodic. Given a DNA sequence s, determine if it is periodic, and if so, the values for α and k. Note that there could be more than one period for a periodic string. In such a case, you need to report the shortest period.
2. A non-empty string β is called a repeat prefix of a string s if ββ is a prefix of s. Give a linear time algorithm to find the longest repeat prefix of s.
Hint: Think of using lca queries.
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After learning this, you will be able to: understand the concept of algorithm; understand mathematical foundation underlying the analysis of algorithm; to understand se
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