Algorithms | Sorting | Question 14

In a modified merge sort, the input array is splitted at a position one-third of the length(N) of the array. Which of the following is the tightest upper bound on time complexity of this modified Merge Sort.
(A) N(logN base 3)
(B) N(logN base 2/3)
(C) N(logN base 1/3)
(D) N(logN base 3/2)

Answer: (D)

Explanation: The time complexity is given by:
T(N) = T(N/3) + T(2N/3) + N
Solving the above recurrence relation gives, T(N) = N(logN base 3/2)

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