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?
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?
Consider the following recurrence :
f(1) = 1;
f(2n) = 2f(n) $$-$$ 1, for n $$\ge$$ 1;
f(2n + 1) = 2f(n) + 1, for n $$\ge$$ 1;
Then, which of the following statements is/are TRUE?
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?