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What is the time complexity for deleting the string to form a new string in the rope data structure?

(a) O (n^2)

(b) O (n!)

(c) O (log n)

(d) O (1)

This is a very interesting question from Binary Trees in portion Binary Trees of Data Structures & Algorithms I

This question was posed to me in my homework.

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Correct choice is (c) O (log n)

For explanation: In order to perform the deletion on the rope data structure, one can delete 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 two split operations and one concatenation operation.

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