Which of the following statements describe the base case of a recursive algorithm?
(i) F(0) = 0;
(ii) F(x) = 2 * F(x - 1) ;
(iii) if (x == 0)
F(x) = 5 + x;

A) Only (i)
B) Only (ii)
C) Only (iii)
D) Both (i) and (iii)

The base case of a recursive algorithm is the case where the recursion stops and the function returns a definite result. In (i), F(0) = 0 is a definite result, so it is a valid base case. In (ii), F(x) = 2 * F(x - 1) does not have a definite result for any value of x, so it is not a valid base case. In (iii), if (x==0) F(x) = 5 + x is a definite result, so it is a valid base case. Therefore, the best choice is D, which includes both (i) and (iii) as valid base cases.