任意给出平面上n个点的坐标，试求覆盖这n个点的圆的最小半径。写C语言程序

以下是使用C语言实现Welzl算法求解最小圆覆盖问题的代码：

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

#define MAX_POINTS 1000

struct Point {
    double x, y;
};

struct Circle {
    struct Point center;
    double radius;
};

double distance(struct Point a, struct Point b) {
    double dx = a.x - b.x;
    double dy = a.y - b.y;
    return sqrt(dx*dx + dy*dy);
}

struct Circle circle_from_points(struct Point a, struct Point b) {
    struct Circle circle;
    circle.center.x = (a.x + b.x) / 2;
    circle.center.y = (a.y + b.y) / 2;
    circle.radius = distance(a, b) / 2;
    return circle;
}

struct Circle circle_from_points_3(struct Point a, struct Point b, struct Point c) {
    double A = a.x - b.x;
    double B = a.y - b.y;
    double C = a.x - c.x;
    double D = a.y - c.y;
    double E = A*(a.x + b.x) + B*(a.y + b.y);
    double F = C*(a.x + c.x) + D*(a.y + c.y);
    double G = 2*(A*(c.y - b.y) - B*(c.x - b.x));
    if (G == 0) {
        struct Circle circle = { {0, 0}, INFINITY };
        return circle;
    }
    double center_x = (D*E - B*F) / G;
    double center_y = (A*F - C*E) / G;
    struct Point center = { center_x, center_y };
    double radius = distance(center, a);
    struct Circle circle = { center, radius };
    return circle;
}

struct Circle circle_from_points_bounding(struct Point* points, int n, struct Point p) {
    struct Circle circle = { p, 0 };
    for (int i = 0; i < n; i++) {
        if (distance(circle.center, points[i]) > circle.radius) {
            if (circle.center.x == p.x && circle.center.y == p.y) {
                circle = circle_from_points(points[i], p);
            } else {
                circle = circle_from_points_3(points[i], p, points[(i+1)%n]);
            }
        }
    }
    return circle;
}

struct Circle welzl(struct Point* points, struct Point* boundary, int n, int b) {
    struct Circle circle = { {0, 0}, INFINITY };
    if (b == 3) {
        circle = circle_from_points_3(boundary[0], boundary[1], boundary[2]);
    } else if (n == 0 && b == 2) {
        circle = circle_from_points(boundary[0], boundary[1]);
    } else if (n == 1 && b == 1) {
        circle.center = points[0];
        circle.radius = 0;
    } else if (n == 0 && b == 1) {
        circle.center = boundary[0];
        circle.radius = 0;
    } else {
        n--;
        struct Circle d = welzl(points+1, boundary, n, b);
        if (distance(d.center, points[0]) > d.radius) {
            boundary[b++] = points[0];
            circle = welzl(points+1, boundary, n, b-1);
            b--;
        } else {
            circle = d;
        }
    }
    return circle;
}

struct Circle min_circle(struct Point* points, int n) {
    struct Point boundary[3];
    srand(time(NULL));
    for (int i = 0; i < 3; i++) {
        boundary[i] = points[i];
    }
    return welzl(points+3, boundary, n-3, 3);
}

int main() {
    int n;
    printf("Enter the number of points: ");
    scanf("%d", &n);
    struct Point points[MAX_POINTS];
    printf("Enter the coordinates of the points:\n");
    for (int i = 0; i < n; i++) {
        scanf("%lf %lf", &points[i].x, &points[i].y);
    }
    struct Circle circle = min_circle(points, n);
    printf("Minimum circle: center = (%.2lf, %.2lf), radius = %.2lf\n", circle.center.x, circle.center.y, circle.radius);
    return 0;
}

注意，该程序假设输入的点集中至少有三个点，且不会进行输入校验。