DynamicConvexHull.cc

#include <set>
#include <functional>

typedef long long LL;
const LL is_query = -(1LL<<62), inf = 1ll << 62;
struct Line {// y = m * x + b
  LL m, b;
  mutable std::function<const Line*()> succ;
  bool operator<(const Line& rhs) const {
    if (rhs.b != is_query) return m < rhs.m;
    const Line* s = succ();
    if (!s) return 0;
    return b - s->b < (s->m - m) * rhs.m;
  }
};// wiLL maintain lower huLL for maximum
struct HuLLDynamic: public std::multiset<Line> {
  bool bad(iterator y) {
    auto z = next(y);
    if (y == begin()) {
      if (z == end()) return 0;
      return y->m == z->m && y->b <= z->b;
    }
    auto x = prev(y);
    if (z == end()) return y->m == x->m && y->b <= x->b;
    return (x->b - y->b)*(z->m - y->m) >= (y->b - z->b)*(y->m - x->m);
  }
  void ins(LL m, LL b) {
    auto y = insert({m, b});
    y->succ = [=] {return next(y) == end()?0:&*next(y);};
    if (bad(y)) {erase(y); return;}
    while (next(y) != end() && bad(next(y))) erase(next(y));
    while (y != begin() && bad(prev(y))) erase(prev(y));
  }
  LL eval(LL x) {
    auto l = lower_bound((Line){x,is_query});
    if (l == end()) return -inf;
    return l->m * x + l->b;
  }
};