Dynamic CHT (Convex Hull Trick).cpp

/**
 * Author: Simon Lindholm
 * Date: 2017-04-20
 * License: CC0
 * Source: own work
 * Description: Container where you can add lines of the form mx+c, and query max values at points x.
                For min query, add line in (-m, -c) format. You will get -ans.
 *  Useful for dynamic programming (``convex hull trick'').
 * Time: O(\log N)
 * Status: stress-tested
 */

struct Line {
    mutable ll m, c, p;
    bool isQuery;
    bool operator<(const Line& o) const {
        if(o.isQuery)
            return p < o.p;
        return m < o.m;
    }
};

struct LineContainer : multiset<Line> {
    // (for doubles, use inf = 1/.0, div(a,b) = a/b)
    const ll inf = LLONG_MAX;
    ll div(ll a, ll b) { // floored division
        return a / b - ((a ^ b) < 0 && a % b); }
    bool isect(iterator x, iterator y) {
        if (y == end()) { x->p = inf; return false; }
        if (x->m == y->m) x->p = x->c > y->c ? inf : -inf;
        else x->p = div(y->c - x->c, x->m - y->m);
        return x->p >= y->p;
    }
    void add(ll m, ll c) {
        auto z = insert({m, c, 0, 0}), y = z++, x = y;
        while (isect(y, z)) z = erase(z);
        if (x != begin() && isect(--x, y)) isect(x, y = erase(y));
        while ((y = x) != begin() && (--x)->p >= y->p)
            isect(x, erase(y));
    }
    ll query(ll x) {
        if(empty()) return inf;
        Line q; q.p = x, q.isQuery = 1;
        auto l = *lower_bound(q);
        return l.m * x + l.c;
    }
};