Question

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Implement two C++ programs to generate Fibonacci sequence (one using recursion, one using non-recursion structure); analyze their complexity using O notation

Answer 1

Iterative (non-recursive)

#include<iostream>
#include<stdio.h>
using namespace std;
int fibonacciiterative(int n)
{
    if(n==0)
        return 0;
    if(n==1)
        return 1;
    int a = 0;
    int b = 1;
    int c = 0;
    for (int i = 2; i <= n; ++i)
    {
        c = a + b;
        a = b;
        b = c;
    }
    return c;
}
int main(){

cout <<"The seventh fibonacci number is: " << fibonacciiterative(7) << endl;

}
===================================================================================
Recursive Fibonacci

#include <iostream>

using namespace std;

int fibonacciRecursive(int x) {
    if (x == 0)
        return 0;
    else if(x==1)
        return 1;
    else
        return fibonacciRecursive(x-1)+fibonacciRecursive(x-2);

}

int main() {
    cout <<"The seventh fibonacci number is: " << fibonacciRecursive(7) << endl;
}
                                           
===============================================================================
Adding Image and Output:-
                                                                                                                                    



Time Complexity :

For Recursive Implementation: T(n) = T(n-1) + T(N-2) , which tends to exponential time complexity
=> O(2ⁿ)

For Iterative Implementation: Time complexity is Linear => O(n)