The set of points is given, it is necessary to find the circle of the minimal radius covering them.

Please, help me. My algo is O(n^4) but it very slow.

void min_disk3 (point a, point b, point c, point &circ, double &r)
{
    if (on_line (a, b, c))
    {
        point p1 = minp (minp (a, b), c);
        point p2 = maxp (maxp (a, b), c);

        circ = part (p1, p2, 1, 1);
        r = 0.5 * dist (p1, p2);

        return;
    }

    point mab = part (a, b, 1, 1);
    point mac = part (a, c, 1, 1);
    double a1 = a.x - b.x;
    double b1 = a.y - b.y;
    double c1 = - a1 * mab.x - b1 * mab.y;
    double a2 = a.x - c.x;
    double b2 = a.y - c.y;
    double c2 = - a2 * mac.x - b2 * mac.y;

    double x, y;
    x = (b2 * c1 - b1 * c2) / (a2 * b1 - a1 * b2);
    if (!equald (b1, eps))
        y = - (a1 * x + c1) / b1;
    else
        y = - (a2 * x + c2) / b2;

    circ = point (x, y);
    r = dist (circ, a);
}

void min_disk2 (point p[], int n, point a, point b, point &circ, double &r)
{
    circ = part (a, b, 1, 1);
    r = dist (circ, a);
    for (int i = 0; i < n; ++ i)
        if (lessd (r, dist (p[i], circ)))
            min_disk3 (p[i], a, b, circ, r);
}
void min_disk1 (point p[], int n, point a, point &circ, double &r)
{
    circ = part (p[0], a, 1, 1);
    r = dist (circ, a);
    for (int i = 1; i < n; ++ i)
        if (lessd (r, dist (p[i], circ)))
            min_disk2 (p, i, a, p[i], circ, r);
}
void min_disk (point p[], int n, point &circ, double &r)
{
    circ = part (p[0], p[1], 1, 1);
    r = dist (circ, p[0]);
    for (int i = 2; i < n; ++ i)
        if (lessd (r, dist (p[i], circ)))
            min_disk1 (p, i, p[i], circ, r);
}

O(nlog3n) :-)