Recursive Fibonacci in C - c

Question

I'm trying to figure out why this code isn't working.
#include <stdio.h>
int main()
{
int num;
puts("what index of the Fibbonaci series do you want?");
scanf("%d", &num);
num = fib(num);
printf("%d", num);
return 0;
}
int fib(int num)
{
if (num == 0)
return 1;
else if (num == 1)
return 1;
else return (fib(num - 1)+fib(num-2));
}
P.S. I'm trying to keep it as simple as possible, and I was told that index's 0 and 1 are equal to 1.

Answer 1

Firstly, your function is not declared before main() and that is why your program does not run1.
Secondly, Fibonacci Sequence is defined as either:
1, 1, 2, 3, 5, 8,...
or
0, 1, 1, 2, 3, 5, 8,...
where the recursive relation describing it is : Fibn = Fibn-1 + Fibn-2
Which converted in C code would look like either something similar with what you got (first definition above), or a bit modified (using the second equally right definition):
int fib(int num)
{
if (num == 0) {
return 0;
} else if (num == 1) {
return 1;
} else {
return fib(num - 1) + fib(num - 2);
}
}
Note:
Both mine and your versions of the function are not very effective as they will make a lot of calls, most of them to calculate overlapping values, i.e. they will calculate a lot of overlapping subproblems. This could be fixed by using memoization.
Here is an example of an implementation, using the above notion of memoization:
// header needed for the container: map
#include <map>
int mem_fact (int i, std::map<int, int>& m) {
// if value with key == i does not exist in m: calculate it
if (m.find(i) == m.end()) {
// the recursive calls are made only if the value doesn't already exist
m[i] = mem_fact (i - 1, m) + mem_fact (i - 2, m);
}
// if value with key == i exists, return the corresponding value
return m[i];
}
int fast_factorial (int i) {
// key (Fibonacci index) - value (Fibbonaci number)
std::map<int, int> memo;
// initialize the first two Fibonacci numbers
memo.insert(std::pair<int,int>(0, 0));
memo.insert(std::pair<int,int>(1, 1));
return mem_fact(i, memo);
}
then in main,if you call both like so:
int slow_fib = fib(10);
int fast_fib = fast_factorial(10);
you will get the same result: slow_fib = fast_fib = 55, however fib() will have to make 177 calls and fast_factorial() only 19 calls.
1. error: 'fib' was not declared in this scope

Answer 2

fib(0) is 0, not 1. Whoever indicated/ordered that fib(0) is 1 is wrong.
Change
if (num == 0)
return 1;
to
if (num == 0)
return 0;

Answer 3

Best thing is to avoid recursive form as possible.
int fib(int index) -- first fibonacci number is at index 0
{
int a = 0;
int b = 1;
int c = 0;
for (int i = 0; i<index; ++i)
{
a = b;
b += c;
c = a;
}
return a; // <<-- value at index
}