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

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 ____________ .