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(n1)+nnn a. Set up and solve a recurrence relation for the number of times the algorithm's basic operation is executed. b. How does this algorithm compare with the straightforward nonrecursive algorithm for computing this function? Hints: - This problem is not asking to calculate the sum S(n) (the algorithm does that!). Do not use the summation formulas for cubes in App. A1 ! The problem is asking to calculate only the number of basic operations executed - a much simpler sum. - Take the basic operation to be the multiplication. Write the recursion. Solve by backsubstitution