Consider the following algorithm.
ALGORITHM: Mystery(A[0..n-1], B[0..n-1], n)
//Input: Two same-sized arrays A[0..n-1], B[0..n-1] of n real numbers, size of A, B
a ← A[n-1]
b ← B[n-1]
for i ← n-2 downto 0 do
if A[i] < a then
a ← A[i]
if B[i] > b then
b ← B[i]
return b – a
a) What does this algorithm compute?
b) Which of the following statements about the output are true and which are false? Explain your answers by providing an argument for true statements and a counterexample for false statements.
i. It will be equal to a value in one of the arrays.
ii. It can be negative.
iii. It will be between 0 and n-1.
c) What is its basic operation?
d) Show and simplify a summation for the number of times the basic operation is executed.
e) What is the Θ time-efficiency class of this algorithm? Prove your result.
f) Suggest an improvement, or a better algorithm altogether, and indicate its efficiency class, or make a convincing argument that no improvement is possible.