Solution: 2014 Fall Final - 11

Author: Michiel Smid

Question

Consider the recursive algorithm $\Fib$, which takes as input an integer $n \geq 0$:

$\mathbf{Algorithm}\ \Fib(n)\mathrm{:}$
$\mathbf{if}\ n = 0\ \mathrm{or}\ n = 1$
$\mathbf{then}\ f = n$
$\mathbf{else}\ f = \Fib(n - 1) + \Fib(n - 2)$
$\mathbf{endif};$
$\mathbf{return}\ f$

If we run algorithm $\Fib(20)$, how many calls are there to $\Fib(16)$?

(a)

(b)

(c)

(d)

Solution

We can draw a tree to represent the recursive calls

There are 5 calls to $FIB(16)$