LineContainer.cpp

#include <bits/stdc++.h>
#define ll long long
using namespace std;

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

struct LineContainer : multiset<Line, less<>> {
	static const ll inf = LLONG_MAX; // Double: inf = 1/.0, div(a,b) = a/b
	ll div(ll a, ll b) { return a / b - ((a ^ b) < 0 && a % b); } //floored division
	
	bool isect(iterator x, iterator y) {
		if(y == end()) return x->p = inf, 0;
		if(x->k == y->k) x->p = x->m > y->m ? inf : -inf;
		else x->p = div(y->m - x->m, x->k - y->k);
		return x->p >= y->p;
	}
	
	void add_line(ll k, ll m){ // kx + m  //if minimum k*=-1, m*=-1, query*-1
		auto z = insert({k, m, 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) {
		assert(!empty());
		auto l = *lower_bound(x);
		return l.k * x + l.m;
	}
};
/* Credits: kactl (https://github.com/kth-competitive-programming) */