GATE | GATE CS Mock 2018 | Set 2 | Question 56

The worst-case running time of Merge sort algorithm is described by the following recurrence relation :

                 ⌈ 1               , if n = 1
       T(n)  =   | 2T(n/2)+ n      , otherwise
                 ⌊

Given recurrence equation evaluates to –
(A) 2^k T(n/2^k) + kn
(B) 2^k T(n^k/2) + kn
(C) nk T(n/2^k)
(D) T(n/2^k) + kn

Answer: (A)
Explanation:

T(n) = 2T (n/2) + n
     = 21 T(n/21) + 1.n            [ k = 1]
     = 2k-1 T(n/2k-1) + (k-1)n
     = 2k-1 (2T(n/2k + n/2k-1) + (k-1)n
     = 2k  T(n/2k) + kn

Option (A) is Correct.
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