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?

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)?

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?

There are n unsorted arrays : A₁, A₂, …, A_n. Assume that n is odd. Each of A₁, A₂, …, A_n 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, …, A_n is :