Dynamic Line Container (Convex Hull Trick)
(data-structure/dynamic_hull.hpp)

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• Last update: 2023-07-25 00:50:50+07:00
• Include: #include "data-structure/dynamic_hull.hpp"

Code

struct Line {
  ll m, b;
  mutable function<const Line*()> succ;
  bool operator<(const Line& rhs) const {
    if (rhs.b != -INF) return m < rhs.m;
    const Line* s = succ();
    if (!s) return 0;
    ll x = rhs.m;
    return b - s->b < (s->m - m) * x;
  }
};

struct dynamic_hull
    : public multiset<Line> {  // will maintain upper hull for maximum
  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 1.0 * (x->b - y->b) * (z->m - y->m) >=
           1.0 * (y->b - z->b) * (y->m - x->m);
  }
  void insert_line(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, -INF});
    return l.m * x + l.b;
  }
};

#line 1 "data-structure/dynamic_hull.hpp"
struct Line {
  ll m, b;
  mutable function<const Line*()> succ;
  bool operator<(const Line& rhs) const {
    if (rhs.b != -INF) return m < rhs.m;
    const Line* s = succ();
    if (!s) return 0;
    ll x = rhs.m;
    return b - s->b < (s->m - m) * x;
  }
};

struct dynamic_hull
    : public multiset<Line> {  // will maintain upper hull for maximum
  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 1.0 * (x->b - y->b) * (z->m - y->m) >=
           1.0 * (y->b - z->b) * (y->m - x->m);
  }
  void insert_line(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, -INF});
    return l.m * x + l.b;
  }
};

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