GATE | GATE-IT-2004 | Question 58
Consider a list of recursive algorithms and a list of recurrence relations as shown below. Each recurrence relation corresponds to exactly one algorithm and is used to derive the time complexity of the algorithm.
|Recursive Algorithm||Recurrence Relation|
|P.||Binary search||I.||T(n) = T(n-k) + T(k) + cn|
|Q.||Merge sort||II.||T(n) = 2T(n-1) + 1|
|R.||Quick sort||III.||T(n) = 2T(n/2) + cn|
|S.||Tower of Hanoi||IV.||T(n) = T(n/2) + 1|
(A) P-II, Q-III, R-IV, S-I
(B) P-IV, Q-III, R-I, S-II
(C) P-III, Q-II, R-IV, S-I
(D) P-IV, Q-II, R-I, S-III
Explanation: These are examples of some standard algorithms whose
Merge Sort: T(n) = 2T(n/2) + Θ(n). It falls in case 2 as c is 1 and Logba] is also 1 and the solution is Θ(n Logn) //time complexity can be evaluated using Master Method
Binary Search: T(n) = T(n/2) + Θ(1). It also falls in case 2 as c is 0 and Logba is also 0 and the solution is Θ(Logn) //time complexity can be evaluated using Master Method
Quick Sort : Time taken by QuickSort in general can be written as T(n) = T(k) + T(n-k-1) + (n)
Tower of Hanoi : T(n) = 2T(n-1) + 1
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