Consider the following recursive algorithm for computing the sum of the first n cubes: S(n) = 1 3 + 2 3 + . . . + n 3 ALGORITHM S(n) //Input: A positive integer n //Output: The sum of the first n cubes if n = 1 return 1 else return S(n 1) + n n n a. Set up and solve a recurrence relation for the number of times the algorithms basic operation is executed. b. How does this algorithm compare with the straightforward nonrecursive algorithm for computing this sum?