vpll convex_hull (vpll points) {
i64 xmin = points[0].x_;
int min = 0;
for (int i = 1; i < points.size(); ++i) {
if ((points[i].x_ < xmin) || (xmin == points[i].x_ && points[i].y_ < points[min].y_)) {
xmin = points[i].x_;
min = i;
}
}
//cout << "min" << points[min].x_ << ' ' << points[min].y_ << endl;
swap(points[0], points[min]);
p0 = points[0];
sort(points.begin() + 1, points.end(), &cmp);
for (int i = 0; i < points.size(); ++i) {
cout << points[i].x_ << " " << points[i].y_ << endl;
}
/*
for (int i = 0; i < points.size(); ++i) {
cout << points[i].x_ << " " << points[i].y_ << endl;
}
*/
vpll stack;
stack.pb(points[0]);
stack.pb(points[1]);
stack.pb(points[2]);
for (int i = 3; i < points.size(); ++i) {
int n = stack.size();
//cout << "stack_size: " << n << endl;
while (orientation(stack[n - 2], stack[n - 1], points[i])) {
//cout << "pop\n";
stack.pop_back();
n = stack.size();
}
//cout << "push: " << points[i].x_ << ' ' << points[i].y_ << endl;
stack.pb(points[i]);
}
return stack;
}
bool violates(vpll ar, long long k){
//binary search over inervals
int lo=0, hi = ar.size()-1;
while(lo <=hi){
int mid = lo + (hi - lo )/2;
if(ar[mid].first <= k && k <= ar[mid].second )
return true;
else if(k < ar[mid].first)
hi = mid - 1;
else if(k > ar[mid].second)
lo = mid + 1;
}
return false;
}
inline pll find_max (pll v, vpll &points) {
int l = 0;
int r = points.size() - 1;
int m;
while (l < r) {
m = (l + r)/2;
//cout << "m: " << m << endl;
if (((points[m + 1].x_ - points[m].x_) * v.x_ > - (points[m + 1].y_ - points[m].y_) * v.y_)) {
/*
cout << "1: " << (points[m + 1].x_ - points[m].x_) * v.x_ << endl;
cout << "2: " << (points[m + 1].y_ - points[m].y_) * v.y_ << endl;
cout << " lol " << (points[m + 1].x_ - points[m].x_) * v.x_ + (points[m + 1].y_ - points[m].y_) * v.y_ << endl;
*/
l = m + 1;
// cout << "l: " << l << endl;
} else {
r = m;
}
}
// cout << l << " " << r << endl;
return points[l];
}