Consider the following C-program fragment in which i, j and n are integer variables.
for (i = n, j = 0; i > 0; i /= 2, j += i);
let val (j) denote the value stored in the variable j after termination of the for loop. Which one of the following is true?

The time complexity of computing the transitive closure of a binary relation on a set of elements is known to be:

Consider an array multiplier for multiplying two n bit numbers. If each gate in the circuit has a unit delay, the total delay of the multiplier is

Consider the following three claims
I. (n + k)^m = $$\Theta \,({n^m})$$ where k and m are constants
II. 2ⁿ⁺¹ = O(2ⁿ)
III. 2²ⁿ = O(2²ⁿ)
Which of those claims are correct?