#include <iostream>
using namespace std;
//牛顿插值求解多项式
double * xs;   //all input x
double * ys;   //all input y
int n;      //size
//1 2 3 4
//0 -5 -6 3
//1.5
//-2.625
void init()
{
    cout << "please input n " << endl;
    cin >> n;
    xs = new double[n];
    ys = new double[n];
//input x
    cout << "please input the x‘s value !" << endl;
    for(int i=0; i<n; i++)
    {
        cin >> xs[i];
    }
//input y
    cout << "please input the y‘s value !" << endl;
    for(int i=0; i<n; i++)
    {
        cin >> ys[i];
    }
}
double f(int n)
{
    double f=0;
    double temp=0;
    for(int i=0; i<n+1; i++)
    {
        temp=ys[i];
        for(int j=0; j<n+1; j++)
        {
            if(i!=j)
            temp /= (xs[i]-xs[j]);
        }
        f += temp;
    }
    return f;
}
double newton(double x)
{
    double result=0;
    for(int i=0; i<n; i++)
    {
        double temp=1;
        double fi=f(i);
        for(int j=0; j<i; j++)
        {
            temp = temp*(x-xs[j]);
        }
        result += fi*temp;
    }
    return result;
}
int main()
{
    init();
    double x;
    cout << "please input the x‘ value !" << endl;
    cin >> x;
    cout << "the result of the Newton is " << newton(x);
    return 0;
}

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