Question

The recursive definition of a Fibonacci Number is F(n) = F(n - 1) + F(n - 2), where F(0) = 1 and F(1) = 1. What is the value of Fib(3)?

Answer 1

We have F (n) = F (n - 1) + F (n - 2), where F (0) = 1 and F (1) = 1

Now, we need to find Fib (3) as per the above, F (3) can be written as

   F (3) = F (3 – 1) + F (3 – 2)

• F (2) + F (1)
• F (2) + 1 (since F (1) is 1)
• F (2 – 1) + F (2 – 2) + 1
• F (1) + F (0) + 1
• 1 + 0 + 1 (since F (0) is 0)
• 2

Hence Fib (3) = 2

Program to test:

#include<iostream>
using namespace std;

int RecursiveFib(int);

int main()
{
   int n, i = 0, count;
   int fib=0;

    //read number of terms to be printed in fibonacci series
    cout<<"\nEnter number: ";
    cin>>n;
   
    //call the recursive fibonacci function
    for ( count = 1 ; count <= n ; count++ )
    {
        fib=fib+RecursiveFib(i);
    //cout<<fib<<" ";
    i++;
}
cout<<"\nFib("<<n<<") = "<<fib;

return 0;
}

//this is function that prints fibonacci series using recursive method
int RecursiveFib(int n)
{
   //here n is the number of terms
   //if n is 0 return 0 and if n is 1 return 1
if (n == 0)
return 0;
else if ( n == 1 )
return 1;
else
//else call the function recursively by passing n-1 and n-2 as parameters
return ( RecursiveFib(n-1) + RecursiveFib(n-2) );
}

Output:

C.Users Vicky Desktop\DevC++Programs Fibsum.exe Enter number: 3 Process exited after 1.339 seconds with return value 0 Press any key to continue _