Question

Please write code in C++

using recursive function

Write a program that computes the sequence of Fibonacci numbers. The formula for generating the next Fibonacci number is: Fn = Fn−1 +Fn−2, where F1 = 1 and F2 = 2. For example, F3 = F2 + F1 = 2 + 1 = 3. You will notice that at some point Fibonacci numbers are too large and they do not fit in type int. This is called the integer overflow. When they become negative (or nonincreasing), stop the program. Please use three different functions, one for each type.

• How many Fibonacci numbers fit in type int? What is the value of the largest one?

• How many Fibonacci numbers fit in type long? What is the value of the largest one?

• How many Fibonacci numbers fit in type long long? What is the value of the largest one?

Answer 1

Code For fibonacci using resursion

Normal For Type Int

#include<bits/stdc++.h>

using namespace std;

// This depicts the function calculation for fibonacci series .

// We get series by summing up last two numbers i.e if we want nth fibonaci number which means we add n-1 and n-2 number to get the series .

int fibonacci(int n)

{

    if (n <= 1)

        return n;

int ans= fibonacci(n-1) + fibonacci(n-2);

if(ans <0)

{

return -1;

}

else

{

return ans;

}

}

  int main ()

{

    int n = 9 ,output;

     output=fibonacci(n);

if(output==-1)

{

cout<<"Integer Overflow";

}

else

{

cout<<"Output';

}

    return 0;

}

So the largest number of fibonaaci in 32 unsigned bit integer is 46 we can compute without getting overflow is so fibonacci(46) it goes out of range  after that and start printing negative

For type long

long fibonacci(int n)

{

    if (n <= 1)

        return n;

long ans= fibonacci(n-1) + fibonacci(n-2);

if(ans <0)

{

return -1;

}

else

{

return ans;

}

}

So the largest number of fibonaaci in 32 unsigned bit long is 47 we can compute without getting overflow is fibonacci(47) as it goes out of range after that and start printing negative

For type long long

long long fibonacci(int n)

{

    if (n <= 1)

        return n;

long long ans= fibonacci(n-1) + fibonacci(n-2);

if(ans <0)

{

return -1;

}

else

{

return ans;

}

}

So the largest number of fibonaaci in 32 unsigned bit long long is 93 we can compute without getting overflow is fibonacci(93) as it goes out of range after that and start printing negative .

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