Implement a recursive function to compute the cube root of a positive real numbe

Question

Implement a recursive function to compute the cube root of a positive real number greater than or equal to 1 using a bisection (i.e., binary search) approach. You may consider the calculated cube root x accurate enough if x3 is within 0.0001 of the original number (You might find the fabs() function useful for that). The main() function should prompt the user for a real number, call the function to compute the cube root, and display the cube root in an appropriate message.

Start with the template program.
What to hand in:

A C++ program named a5q3.cpp containing the C++ program.

Explanation / Answer

#include<iostream>
#include<cmath>
using namespace std;
int a;
inline double f(double x)
{
    return (x*x*x-a);
}
double bisect(double a,double b)
{
double c;
        c=(a+b)/2.0;
if(fabs(f(c))<0.0001)
return c;
        else if(f(a)*f(c)<0.0)
        return bisect(a,c);
else
        return bisect(c,b);
}
int main()
{
cout << " Enter a Positive Real number :";
        cin >> a;
        for( int i=1; i<100; i++)
{
        if((i*i*i < a ) && (a < (i+1)*(i+1)*(i+1)))
{
        cout<<"Root is at : "<<bisect(i,i+1)<<endl;
        break;
  }
}
        return 0;
}

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