Dynamic-Convex-Hull.cpp

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;
    }
};