Question

What is the general form of the recurrence relation that represents the time complexity of the Merge Sort algorithm?

a) T(n) = 2T(n/2) + Θ(n)
b) T(n) = T(n-1) + Θ(n)
c) T(n) = 2T(n/2) + Θ(1)
d) T(n) = T(n-1) + Θ(1)

Answer 1

The general form of the recurrence relation for the Merge Sort algorithm time complexity is T(n) = 2T(n/2) + Θ(n).

Step-by-step explanation:

The general form of the recurrence relation that represents the time complexity of the Merge Sort algorithm is T(n) = 2T(n/2) + Θ(n). In this relation, 'T(n)' represents the time complexity of the algorithm when sorting an input of size 'n'. The recurrence relation states that to sort an input of size 'n', the algorithm recursively divides the input into two halves of size 'n/2', sorts each half separately, and then merges the two sorted halves together. Additionally, the algorithm has a time complexity of Θ(n), representing the time required to merge the two sorted halves together.