Question

Let C(n) = 1³ + 2³ + 3³+…+n³ be the sum of the first n cubes.

a) Write a recursive algorithm to compute C(n).
b) What is the recurrence relation for your algorithm?
c) What is the time complexity of the algorithm you developed?

Answer 1

To compute C(n), you can use a recursive algorithm. The recurrence relation for this algorithm is C(n) = C(n-1) + n³, and the time complexity is O(n).

Step-by-step explanation:

To compute C(n), you can use a recursive algorithm. Here is an example:

1. If n equals 0, return 0 as the base case.
2. Otherwise, recursively compute C(n-1) and add n cubed to it.

The recurrence relation for this algorithm is C(n) = C(n-1) + n³.

The time complexity of this algorithm is O(n), as each recursive call takes constant time.