Question: Consider the following 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)

Consider the following 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) + n5

a. Which best describes this algorithm: i. Asymptotic ii. Recursive iii. Depth First iv. Iterative v. Insertion Sort

b. Describe what this algorithm computes?

c. What is the basic operation

d. Set up and solve the recurrence relation for the number of times the algorithms basic operation is executed.

e. What is the efficiency class of this algorithm?

f. Compare the efficiency of this algorithm to the iterative algorithm that accomplishes the same result.

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