Sqrt(x) Float

Description:

Example:

Note

Idea:

牛顿法。start的数是x/2。 x(n+1) = xn - f(xn)/f'(xn)

x=sqrt(a), f(x) = x*x - a, find root

x=1/2( xn + a/xn )

Code:

#include <iostream>
#include <vector>
#include <algorithm>
#include <cmath>

using namespace std;

double findRoot(double num){
    if(num<0){
        return 0;
    }
    double xn=num/2.0;
    double xn2=1/2.0*(xn+num/xn);

    while(abs(xn2-xn)>10e-10){
        xn=xn2;
        xn2=1/2.0*(xn+num/xn);
    }
    return xn2;
}

int main(){
    cout<<findRoot(5);
}