差分形式的牛顿插值法c语言代码

以下是差分形式的牛顿插值法的 C 语言代码：

#include <stdio.h>

// 计算阶乘
int factorial(int n) {
    int result = 1;
    for (int i = 1; i <= n; i++) {
        result *= i;
    }
    return result;
}

// 计算组合数
int combination(int n, int k) {
    return factorial(n) / (factorial(k) * factorial(n - k));
}

// 计算差商
double divided_difference(double x[], double y[], int n, int i, int j) {
    if (j == 0) {
        return y[i];
    } else {
        return (divided_difference(x, y, n, i + 1, j - 1) - divided_difference(x, y, n, i, j - 1)) / (x[i + j] - x[i]);
    }
}

// 计算牛顿插值多项式的值
double newton_interpolation(double x[], double y[], int n, double t) {
    double result = 0;
    for (int i = 0; i < n; i++) {
        double term = divided_difference(x, y, n, 0, i);
        for (int j = 0; j < i; j++) {
            term *= (t - x[j]);
        }
        result += term;
    }
    return result;
}

int main() {
    int n;
    printf("请输入数据点个数：");
    scanf("%d", &n);
    double x[n], y[n];
    printf("请输入数据点的 x 坐标和 y 坐标：\n");
    for (int i = 0; i < n; i++) {
        scanf("%lf %lf", &x[i], &y[i]);
    }
    double t;
    printf("请输入要求的插值点的 x 坐标：");
    scanf("%lf", &t);
    double result = newton_interpolation(x, y, n, t);
    printf("在 x = %lf 处的插值结果为：%lf\n", t, result);
    return 0;
}

希望能够帮助到你！