Bisection method using Recursion

標題：使用遞迴函式計算二分法

使用遞迴
VC++ (recursion.cpp)：

//Chapter 3 - Recursion
#include <iostream>
using namespace std;

const int No = 1000;
const double tolerance = 0.00001;
const double minimal = 0;
const double maximal = 1;

double equation(double);
double determine(double, double, double=equation(minimal), int=0);

int main(void)
{
    cout << "Best: " << scientific << determine(minimal, maximal) << endl;
    system("pause");
    return 0;
}

double determine(double a, double b, double fa, int n) {
    double p = 0, fp = 0;
    p = a+(b-a)/2;
    fp = equation(p);
    //cout << dec << n << '\t' << scientific << p << endl;
    if(( fp==0 || (b-a)/2 < tolerance ) || n >= No)
        return p;
    return (fa*fp>0) ? determine(p, b, fp, n+1) : determine(a, p, fa, n+1);
}

double equation(double x) {
    return x - 1/pow(2.0, x);
}

/*double equation(double x) {
    return pow(x, 4)-2*pow(x, 3)-4*pow(x, 2)-4*x+4;
}*/

不使用遞迴
VC++ (bisectionMethod.cpp)：

//Chapter 3 - Bisection Method
#include <iostream>
using namespace std;

const int No = 1000;
const double tolerance = 0.00001;
const double minimal = 0;
const double maximal = 1;

double equation(double);

int main(void)
{
    int i=0;
    double x=0, y=0, fa=0, fp=0, p=0, a=0, b=0;
    
    a = minimal;
    b = maximal;

    fa = equation(a);

    while(i<No) {
        p = a+(b-a)/2;
        fp = equation(p);
        if(fp==0 || (b-a)/2 < tolerance) {
            break;
        }
        if(fa*fp>0) {
            a = p;
            fa = fp;
        } else {
            b = p;
        }
        i++;
    }

    cout << scientific << p << endl;
    system("pause");
    return 0;
}

/*
double equation(double x) {
    return pow(x, 4)-2*pow(x, 3)-4*pow(x, 2)-4*x+4;
}
*/

double equation(double x) {
    return x - 1/pow(2.0, x);
}

說明：
比較遞迴與不遞迴方式計算二分法。