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What is the time complexity for splitting the string into two new string in the rope data structure?

(a) O (n^2)

(b) O (n!)

(c) O (log n)

(d) O (1)

This intriguing question comes from Binary Trees topic in portion Binary Trees of Data Structures & Algorithms I

I got this question in final exam.

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Correct choice is (c) O (log n)

To explain: In order to perform the splitting on the rope data structure, one can split the given string into two new string S1 and S2 in O (log n) time. So, the time complexity for worst case is O (log n).

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