1
GATE CSE 2024 Set 1
+2
-0.66

Consider the following recurrence relation:

$$T(n) = \begin{cases} \sqrt{n} T(\sqrt{n}) + n & \text{for } n \ge 1, \\ 1 & \text{for } n = 1. \end{cases}$$

Which one of the following options is CORRECT?

A

$$T(n) = \Theta(n \log \log n)$$

B

$$T(n) = \Theta(n \log n)$$

C

$$T(n) = \Theta(n^2 \log n)$$

D

$$T(n) = \Theta(n^2 \log \log n)$$

2
GATE CSE 2023
MCQ (More than One Correct Answer)
+2
-0.67

Consider functions Function_1 and Function_2 expressed in pseudocode as follows:

Function 1
while n > 1 do
for i = 1 to n do
x = x + 1;
end for
n = n/2;
end while

Function 2
for i = 1 to 100 ∗ n do
x = x + 1;
end for

Let $$f_1(n)$$ and $$f_2(n)$$ denote the number of times the statement "$$x=x+1$$" is executed in Function_1 and Function_2, respectively.

Which of the following statements is/are TRUE?

A
$${f_1}(n) \in \Theta ({f_2}(n))$$
B
$${f_1}(n) \in o({f_2}(n))$$
C
$${f_1}(n) \in \omega ({f_2}(n))$$
D
$${f_1}(n) \in O(n)$$
3
GATE CSE 2021 Set 1
+2
-0.67

Consider the following three functions.

f1 = 10n, f2 = nlogn, f3 = n√n

Which one of the following options arranges the functions in the increasing order of asymptotic growth rate?

A
f1 , f2, f3
B
f2, f1, f3
C
f3, f2, f1
D
f2, f3, f1
4
GATE CSE 2021 Set 1
+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)
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