How to generate Fibonacci faster

Question

I am a CSE student and preparing myself for programming contest.Now I am working on Fibonacci series. I have a input file of size about some Kilo bytes containing positive integers. Input formate looks like

3 5 6 7 8 0

A zero means the end of file. Output should like

2 
5 
8 
13 
21 

my code is

#include<stdio.h>

int fibonacci(int n) {
  if (n==1 || n==2)
    return 1;
  else
    return fibonacci(n-1) +fibonacci(n-2);
}
int main() {
  int z;
  FILE * fp;    
  fp = fopen ("input.txt","r");    
  while(fscanf(fp,"%d", &z) && z) 
   printf("%d \n",fibonacci(z));
  return 0;
}

The code works fine for sample input and provide accurate result but problem is for my real input set it is taking more time than my time limit. Can anyone help me out.

Answer 1

You could simply use a tail recursion version of a function that returns the two last fibonacci numbers if you have a limit on the memory.

int fib(int n)
{
    int a = 0;
    int b = 1;
    while (n-- > 1) {
        int t = a;
        a = b;
        b += t;
    }
    return b;
}

This is O(n) and needs a constant space.