The recurrence equation
T(1) = 1
T(n) = 2T(n - 1)+n, $$n \ge 2$$
Evaluates to

The cube root of a natural number n is defined as the largest natural number m such that $${m^3} \le n$$. The complexity of computing the cube root of n (n is represented in binary notation) is

Consider the following algorithm for searching for a given number x in an unsorted array A[1..n] having n distinct values:
1. Choose an i uniformly at random fro 1..n;
2. If A[i]=x then stop else Goto 1;
Assuming that x is present A, what is the expected number of comparisons made by the algorithm before it terminates?

The running time of the following algorithm Procedure A(n)
If n<=2 return (1) else return (A([$$\sqrt n $$])); is best described by