3. Consider the following recursive algorithm for computing the sum of the first n cubes: S(n) = 13 + 23 +...+n3. 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 algo- rithm's basic operation is executed. b. How does this algorithm compare with the straightforward nonrecursive algorithm for computing this sum