样条插值算法c语言实现

根据提供的引用内容，无法回答关于遗传算法和哈密尔顿图的问题。以下是样条插值算法的C语言实现：

样条插值算法是一种数值分析方法，用于在给定一组数据点的情况下，生成一个连续的函数，该函数在每个数据点处都与给定的数据点相等，并且在相邻数据点之间具有平滑的一阶或二阶导数。以下是样条插值算法的C语言实现：

#include <stdio.h>
#include <stdlib.h>
#include <math.h>

#define N 10

double x[N] = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9};
double y[N] = {0, 0.8415, 0.9093, 0.1411, -0.7568, -0.9589, -0.2794, 0.6569, 0.9894, 0.4121};

double h[N], b[N], u[N], v[N], z[N];

void spline()
{
    int i, k;
    double p, qn, sig, un;

    h[0] = x[1] - x[0];
    b[0] = 2.0 * (h[0] + x[2] - x[0]);
    u[0] = 6.0 * ((y[2] - y[1]) / h[0] - (y[1] - y[0]) / h[0]);

    for (i = 1; i < N - 1; i++)
    {
        h[i] = x[i + 1] - x[i];
        b[i] = 2.0 * (h[i] + h[i - 1]);
        u[i] = 6.0 * ((y[i + 1] - y[i]) / h[i] - (y[i] - y[i - 1]) / h[i - 1]);
        z[i] = 0.0;
    }

    qn = 0.0;
    un = 0.0;
    z[0] = un / b[0];

    for (i = 1; i < N - 1; i++)
    {
        sig = h[i - 1] / b[i - 1];
        p = sig * z[i - 1] + 2.0;
        z[i] = (sig - 1.0) / p;
        u[i] = (u[i] - h[i - 1] * u[i - 1] / b[i - 1]) / p;
    }

    qn = (un - h[N - 2] * u[N - 2]) / (h[N - 2] * z[N - 2] + b[N - 2]);

    for (k = N - 2; k >= 0; k--)
    {
        z[k] = z[k] * z[k + 1] + u[k];
    }

    for (i = 0; i < N - 1; i++)
    {
        double xi, xi1, yi, yi1, ai, bi, ci, di;

        xi = x[i];
        xi1 = x[i + 1];
        yi = y[i];
        yi1 = y[i + 1];
        ai = z[i] / (6.0 * h[i]);
        bi = z[i + 1] / (6.0 * h[i]);
        ci = (y[i + 1] / h[i]) - ((z[i + 1] * h[i]) / 6.0);
        di = (y[i] / h[i]) - ((z[i] * h[i]) / 6.0);

        printf("S%d(x) = ", i);
        printf("%.4f(x - %.4f)^3 + ", ai, xi1);
        printf("%.4f(x - %.4f)^3 + ", bi, xi);
        printf("%.4f(x - %.4f) + ", ci, xi1);
        printf("%.4f(x - %.4f)\n", di, xi);
    }
}

int main()
{
    spline();
    return 0;
}