Question

Is the recursive or the iterative algorithm for finding the sequence in Exercise 32 more efficient?

Short answer

The iterative algorithm is more efficient.

Step-by-step solution

Sequence given in exercise 32

The sequence is given by,${\mathbf{a}}_{\mathbf{0}}\mathbf{=}\mathbf{1}\mathbf{,}{\mathbf{a}}_{\mathbf{1}}\mathbf{=}\mathbf{2}\mathbf{,}{\mathbf{a}}_{\mathbf{2}}\mathbf{=}\mathbf{3}\mathbf{\text{and}}{\mathbf{a}}_{\mathbf{n}}\mathbf{=}{\mathbf{a}}_{\mathbf{n}\mathbf{-}\mathbf{1}}\mathbf{+}{\mathbf{a}}_{\mathbf{n}\mathbf{-}\mathbf{2}}\mathbf{+}{\mathbf{a}}_{\mathbf{n}\mathbf{-}\mathbf{3}}$for n 3,4,5

Finding which iterative algorithm is more efficient.

For the sequence given in step 1,

The loop will execute n times for the iterative algorithm. The recursive algorithm is less efficient because it will repeatedly calculate the value of the same n many times.

For the iterative algorithm, the loop will run n times. Because it will calculate the same value n times, the recursive method is less effective.

Hence, the iterative algorithm is more efficient.