1
GATE CSE 2021 Set 2
MCQ (Single Correct Answer)
+2
-0.66

For constants a ≥ 1 and b > 1, consider the following recurrence defined on the non-negative integers :

$$T\left( n \right) = a.T\left( {\frac{n}{b}} \right) + f\left( n \right)$$

Which one of the following options is correct about the recurrence T(n)?

A
If f(n) is $$\frac{n}{{{{\log }_2}(n)}}$$, then T(n) is θ(log2(n)).
B
If f(n) is n log2(n), then T(n) is θ(n log2(n)).
C
If f(n) is O(nlogb(a) - ϵ) for some ϵ > 0, then T(n) is θ(nlogb(a)).
D
If f(n) is θ(nlogb(a)), then T(n) is θ(nlogb(a))
2
GATE CSE 2021 Set 1
MCQ (Single Correct Answer)
+2
-0.67

Consider the following recurrence relation.

$$T(n) = \left\{ {\begin{array}{*{20}{c}} {T(n/2) + T(2n/5) + 7n \ \ \ if\ n > 0}\\ {1\ \ \ \ \ \ \ if\ n = 0} \end{array}} \right.$$

Which one of the following option is correct?

A
T(n) = Θ(n log n)
B
T(n) = Θ(n5/2)
C
T(n) = Θ((log n)5/2)
D
T(n) = Θ(n)
3
GATE CSE 2019
MCQ (Single Correct Answer)
+2
-0.67

There are n unsorted arrays : A1, A2, …, An. Assume that n is odd. Each of A1, A2, …, An contains n distinct elements. There are no common elements between any two arrays. The worst-case time complexity of computing the median of the medians of A1, A2, …, An is :

A
$$O\left( n \right)$$
B
$$O\left( {n\log n} \right)$$
C
$$O\left( {{n^2}\log n} \right)$$
D
$$O\left( {{n^2}} \right)$$
4
GATE CSE 2016 Set 2
Numerical
+2
-0
The given diagram shows the flowchart for a recursive function $$A(n).$$ Assume that all statements, except for the recursive calls, have $$O(1)$$ time complexity. If the worst case time complexity of this function is $$O\left( {{n^\alpha }} \right),$$ then the least possible value (accurate up to two decimal positions) of $$\alpha $$ is ____________ . GATE CSE 2016 Set 2 Algorithms - Complexity Analysis and Asymptotic Notations Question 13 English
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