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?

$4.$ Consider the following recursive algorithm.