Fibonacci

Fibonacci Sequence

In mathematics, the Fibonacci numbers are the numbers in the following integer sequence, called the Fibonacci sequence, and characterized by the fact that every number after the first two is the sum of the two preceding ones.

Fibonacci sequence is entirely described by this property:

Fore More Information: Wikipedia - Fibonacci Numbers

C-Implementation of Fibonacci Prgram:

Recursive Implementation:

#include <stdio.h>
int Fib(int n) 
{ 
       // Base condition to break recursion
       if (n <= 1) 
               return n;
       
       // Recursive call of function Fib for
       // 'n-1'th and 'n-2'th element of sequence
       return Fib(n-1) + Fib(n-2); 
}
 
int main() 
{ 
       // Fibonacci sequence size
       int n = 10;
       
       // Print the first n elements of the sequence
       printf("%d", Fib(n-1)); 
       
   return 0; 
}

Dynamic Programing Implementation:

#include <stdio.h>
int main()
{
       // Fibonacci sequence size
       const int n = 10;
       
       // Array to store the Fibonacci series
   int Fib[105];
       // Initializing the first two elements of series
   Fib[0] = 0; Fib[1] = 1;
       
   for(int i = 2; i < n; i++)
               // Calculate the the 'i'th element by 
               // adding 'i-1'th and 'i-2'th elements
               Fib[i] = Fib[i-1] + Fib[i-2];
       
       // Print the first n elements of the Fibonacci sequence
   for(int i = 0; i < n; i++)
       {
               printf("%d : %d", i, Fib[i]);
               printf("\n");
       }
   
   return 0;
}