(Fibonacci Series) The Fibonacci series 0, 1, 1, 2, 3, 5, 8, 13, 21, ... begins with the terms 0 and 1 and has the property that each succeeding term is the sum of the two preceding terms. (a) Write a nonrecursive function fibonacci(n) that uses type int to calculate the nth Fibonacci number. (b) Determine the largest int Fibonacci number that can be printed on your system. Modify the program of part (a) to use double instead of int to calculate and return Fibo- nacci numbers, and use this modified program to repeat part (b).

Question

What will be an ideal response?

Answer 1

```
// Nonrecursively calculate Fibonacci numbers.
#include
using namespace std;

int fibonacci( int ); // function prototype
int main()
{
// calculate the fibonacci values of 0 through 10
for ( int counter = 0; counter <= 10; counter++ )
cout << "fibonacci( " << counter << " ) = "
<< fibonacci( counter ) << endl;

// display higher fibonacci values
cout << "fibonacci( 20 ) = " << fibonacci( 20 ) << endl;
cout << "fibonacci( 30 ) = " << fibonacci( 30 ) << endl;
cout << "fibonacci( 35 ) = " << fibonacci( 35 ) << endl;
} // end main

// fibonacci nonrecursively calculates nth Fibonacci number
int fibonacci( int n )
{
int fib0 = 0; // after iteration, holds fib(i-1), initially fib(0) = 0
int fib1 = 1; // after iteration, holds fib(i), initially fib(1) = 1
int temp; // temporary holder for updating fib0 and fib1

if ( n == 0 ) // special case if n is 0
return 0;

// loop until nth number reached
for ( int i = 2; i <= n; i++ )
{
// note at this point:
// fib0 = fib(i-2)
// fib1 = fib(i-1)

temp = fib1; // temporarily hold fib(i-1)

// update fib1 to hold fib(i), fib(i) = fib(i-1) + fib(i-2)
fib1 = fib0 + fib1;
fib0 = temp; // update fib0 to hold fib(i-1)

// note at this point:
// fib0 = fib(i-1)
// fib1 = fib(i)
} // end for

return fib1;
} // end function fibonacci
```