5 (15 points) Consider the following algorithm Algorithm 1 Algorithm S(n) 1: //Input: A positive integer n 2: //Output: The sum of the first n cubes 3: if n= 1 then 4: 5: else return 1 6: return [S(n -1)+nn*n (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