circle minCircle(point P[], int N) { // `1-based`
if (N == 1) return circle(P[1], 0.0);
random_shuffle(P + 1, P + N + 1);
circle O = minCircle(P[1], P[2]);
Rep(i, 1, N) if(!O.inside(P[i])) { O = minCircle(P[1], P[i]);
Foru(j, 1, i) if(!O.inside(P[j])) { O = minCircle(P[i], P[j]);
Foru(k, 1, j) if(!O.inside(P[k])) O = minCircle(P[i], P[j], P[k]);
}
inline static std::pair<std::pair<long double, long double>, long double> findCircle(unsigned int s, unsigned int e)
{
for(unsigned int p = s; p < e; ++ p)
sPoint[p] = point[p];
return minCircle(s, e);
}
inline static std::pair<std::pair<long double, long double>, long double> minCircle(unsigned int s, unsigned int e, int q1, int q2, int q3)
{
std::pair<std::pair<long double, long double>, long double> res;
std::random_shuffle(sPoint + s, sPoint + e);
if(q3 != -1) // GOT A TRIPLE
{
res.first.first = ((sPoint[q2].first * sPoint[q2].first * sPoint[q3].second + sPoint[q2].second * sPoint[q2].second * sPoint[q3].second - sPoint[q1].first * sPoint[q1].first * sPoint[q3].second + sPoint[q1].first * sPoint[q1].first * sPoint[q2].second - sPoint[q1].second * sPoint[q1].second * sPoint[q3].second + sPoint[q1].second * sPoint[q1].second * sPoint[q2].second + sPoint[q1].second * sPoint[q3].first * sPoint[q3].first + sPoint[q1].second * sPoint[q3].second * sPoint[q3].second - sPoint[q1].second * sPoint[q2].first * sPoint[q2].first - sPoint[q1].second * sPoint[q2].second * sPoint[q2].second - sPoint[q2].second * sPoint[q3].first * sPoint[q3].first - sPoint[q2].second * sPoint[q3].second * sPoint[q3].second) / (sPoint[q1].second * sPoint[q3].first - sPoint[q1].second * sPoint[q2].first - sPoint[q2].second * sPoint[q3].first - sPoint[q3].second * sPoint[q1].first + sPoint[q3].second * sPoint[q2].first + sPoint[q2].second * sPoint[q1].first)) / 2;
res.first.second = ((-sPoint[q1].first * sPoint[q3].first * sPoint[q3].first - sPoint[q1].first * sPoint[q3].second * sPoint[q3].second + sPoint[q1].first * sPoint[q2].first * sPoint[q2].first + sPoint[q1].first * sPoint[q2].second * sPoint[q2].second + sPoint[q2].first * sPoint[q3].first * sPoint[q3].first + sPoint[q2].first * sPoint[q3].second * sPoint[q3].second - sPoint[q2].first * sPoint[q2].first * sPoint[q3].first - sPoint[q2].second * sPoint[q2].second * sPoint[q3].first + sPoint[q1].first * sPoint[q1].first * sPoint[q3].first - sPoint[q1].first * sPoint[q1].first * sPoint[q2].first + sPoint[q1].second * sPoint[q1].second * sPoint[q3].first - sPoint[q1].second * sPoint[q1].second * sPoint[q2].first) / (sPoint[q1].second * sPoint[q3].first - sPoint[q1].second * sPoint[q2].first - sPoint[q2].second * sPoint[q3].first - sPoint[q3].second * sPoint[q1].first + sPoint[q3].second * sPoint[q2].first + sPoint[q2].second * sPoint[q1].first)) / 2;
res.second = dist(res.first, sPoint[q2]);
return res;
}
else if(q2 != -1)
{
res.first = std::make_pair(
(sPoint[q1].first + sPoint[q2].first) / 2,
(sPoint[q1].second + sPoint[q2].second) / 2
);
res.second = dist(res.first, sPoint[q1]);
}
else if(q1 != -1)
{
res.first = std::make_pair(
(sPoint[q1].first + sPoint[s].first) / 2,
(sPoint[q1].second + sPoint[s].second) / 2
);
res.second = dist(res.first, sPoint[q1]);
if(e == s + 1)
return res;
}
else if(e == s + 1)
{
res.first = sPoint[s];
res.second = 0;
return res;
}
else
{
res.first = std::make_pair(
(sPoint[s].first + sPoint[s + 1].first) / 2,
(sPoint[s].second + sPoint[s + 1].second) / 2
);
res.second = dist(res.first, sPoint[s]);
}
for(unsigned int p = s; p < e; ++ p)
{
if(inCircle(res, sPoint[p]))
continue;
if(q2 != -1)
res = minCircle(s, p, q1, q2, p);
else if(q1 != -1)
res = minCircle(s, p, q1, p);
else
res = minCircle(s, p, p);
}
return res;
}
