#include <iostream>
#include <iomanip>
#include <cmath>
#define f(x) ((x) * (x) - a) // 定義方程式 f(x) 

using namespace std;

int main() {
	
	double a;
    cout << "平方根的數值 a= ";
    cin >> a;
    cout << "----------------------------------------"<< endl;
    double c=sqrt(a);
    double left = 0, right = 20; // 設定範圍
    double b = 1e-10; 
    double mid;
    int i = 0;

    while ((right - left) > b) {
        mid = (left + right) / 2.0;
        i++;
        printf("#%d [%f  %f ]\n", i, left, right);

        if (f(mid) == 0.0) {
            cout << "根的近似值為: " << mid << " 且 f(x)= " << f(mid) << endl;
            return 0;
        }

        if (f(left) * f(mid) < 0) {
            right = mid; // 左邊
        } else {
            left = mid; // 右邊
        }
    }
    cout << "-----------------------------------------"<< endl;
    int d=((mid - c) / (c)) * 100 ;
    if(d>0)
      d=d;
    else
      d=-d;
    cout << "sqrt("<< a <<"): " << sqrt(a) << " 誤差值為(%)" << d << endl;
    return 0;
}