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What is the time complexity for inserting the string and forming a new string in the rope data structure?

(a) O (log n)

(b) O (n!)

(c) O (n^2)

(d) O (1)

The above asked question is from Binary Trees topic in section Binary Trees of Data Structures & Algorithms I

The question was asked by my school principal while I was bunking the class.

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Right option is (a) O (log n)

For explanation: In order to perform the insertion on the rope data structure, one can insert the given string at any position x to form a new string in O (log n) time. So, the time complexity for worst case is O (log n). This can be done by one split operation and two concatenation operations.

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