Compare Fibonacci (recursion vs. bottom up)

In this project we will compare the computational time taken by a recursive algorithm to determine the Fibonacci number of an integer n and the time taken by a bottom-up approach (using a loop) to calculate the Fibonacci number of the same integer n.

A Fibonacci number F(n) is determined by the following recurrence function:

F(0) =0; F(1)=1;

F(n)= F(n-1) + F(n-2), for n ≥ 2

Thus the recursive algorithm can be written in C++ as

int FiboR ( int n) // array of size n

{ if (n==0 || n==1)

return (n);

else return (FiboR (n-1) + FiboR(n-2));

}

And the non-recursive algorithm can be written in C++ as

int FiboNR ( int n) // array of size n

{ int F[max];

F[0]=0; F[1]=1;

for (int i =2; i <=n; i++)

{ F[i] = F[i-1] + F[i-2];

}

return (F[n]);

}

While FiboR takes exponential time FiboNR takes n steps

Write an algorithm that computes the time (in seconds using ctime.h header library file that takes to determine Fibonacci (n) using FiboR and the time taken by FiboNR on the same input n.

Try to run both routines using different values of n (n={1,5,10,15,20,25,30,35,40,45,50,55,60…)

You final output should look like:

Fibonacci time analysis (recursive vs. non-recursive)

Integer FiboR (seconds) FiboNR(seconds) Fibo-value

1 XX.XX XX.XX 1

5 XX.XX XX.XX 5

.. .. ..

60 XX.XX XX.XX XXXXXXXXXX

…