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// ConsoleApplication9.cpp : 定義主控台應用程式的進入點。
//
#include "stdafx.h"
#include <iostream>
#include <iomanip>
#include <math.h>
using namespace std;
class axn {
public:
    axn() {
        //cout << "inside\t" << "建立了一個項" << endl;
    }
    void set(double ina, double inn) {
        a = ina;
        n = inn;
        //cout << "inside\t" << "設定了一個項為" << a << "x^" << n << endl;
    }
    double df(double x) {
        //cout << "inside\t" << "一次微分了" << a << "x^" << n << endl;
        return pow(x, n - 1)*n*a;
    }
    double f(double x) {
        //cout << "inside\t" << "一次微分了" << a << "x^" << n << endl;
        return pow(x, n )*a;
    }
    double getdfa() {
        return a*n;
    }
    double getdfn() {
        return n-1;
    }
    double ddf(double x) {
        return pow(x, n - 2)*n*(n - 1)*a;
    }
    double geta() {
        return a;
    }
    double getn() {
        return n;
    }
private:
    double n;
    double a;
};
class sumaxn {
public:
    int i;
    axn *arr;
    sumaxn(double ai[], double ni[]) {
        int k = 0;
        while (ni[k] != -50) {
            k++;
        }
        i = k;
        //cout << "inside\t\t" << "建立了一個" << i << "項的項之和" << endl;
        arr = new axn[i];
        for (int j = 0; j<i; j++) {
            arr[j].set(ai[j], ni[j]);
        }
    }
    sumaxn getdf() {
        double *dadate = new double[i];
        double *dndate = new double[i];
        for (int j = 0; j < i; j++) {
            dadate[j] = arr[j].getdfa();
            dndate[j] = arr[j].getdfn();
        }
        //cout << "inside\t\t" << "微分多項式" << endl;
        dadate[i] = -50;
        dndate[i] = -50;
        sumaxn df(dadate, dndate);
        //cout << "inside\t\t" << "微分多項式";
        //df.pp();
        return df;
    }
    double getdf(double x) {
        double tot=0;
        for (int j = 0; j < i; j++) {
            tot += arr[j].df(x);
        }
        return tot;
    }
    double getf(double x) {
        double tot = 0;
        for (int j = 0; j < i; j++) {
            tot += arr[j].f(x);
        }
        return tot;
    }
    void pp() {
        for (int j = 0; j<i; j++) {
            cout <<arr[j].geta() << "x^" << arr[j].getn() <<(j==(i-1)?"":"+");
        }
        cout << endl;
    }
};
int main(int argc, char** argv) {
    double adate[] = { 2,1,3,4,4,4,-50};
    double ndate[] = { 5,8,3,2,1,0,-50};
    sumaxn f(adate, ndate);
    cout << "原方程式為:";
    f.pp();
    cout << "一次微分後的方程式為:";
    f.getdf().pp();
    double a = 10;
    for (int i = 0; i < 100; i++) {
        a = a - f.getf(a) / f.getdf().getf(a);
    }
    cout << "牛頓法求y=0的解x為" << setprecision(20) << a;
    system("pause");
    return 0;
}