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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.
* Initialise d & pi* for each vertex v within V( g ) g.d[v] := infinity g.pi[v] := nil g.d[s] := 0; * Set S to empty * S := { 0 } Q := V(g) * While (V-S)
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