请用c++代码构造牛顿差值多项式

以下是使用C++构建牛顿差值多项式的代码：

#include <iostream>
#include <vector>

using namespace std;

// 计算差商
double divided_difference(int i, int j, const vector<double>& X, const vector<double>& Y) {
    if (i == j) {
        return Y[i];
    } else {
        return (divided_difference(i+1, j, X, Y) - divided_difference(i, j-1, X, Y)) / (X[j] - X[i]);
    }
}

// 计算牛顿差值多项式
double newton_interpolation(double x, const vector<double>& X, const vector<double>& Y) {
    double result = 0.0;
    int n = X.size();

    for (int i = 0; i < n; i++) {
        double term = divided_difference(0, i, X, Y);
        for (int j = 0; j < i; j++) {
            term *= (x - X[j]);
        }
        result += term;
    }

    return result;
}

int main() {
    vector<double> X = {1, 2, 4, 5};
    vector<double> Y = {3, 5, 7, 10};

    double x = 3;

    cout << "f(" << x << ") = " << newton_interpolation(x, X, Y) << endl;

    return 0;
}