data_structure/cht.hpp

#pragma once
#include<set>
#include<functional>
#include<climits>
#include<cassert>

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

struct cht : std::multiset<Line, std::less<>> {
	// (for doubles, use inf = 1/.0, div(a,b) = a/b)
	static const long long inf = LLONG_MAX;
	long long div(long long a, long long b) { // floored division
		return a / b - ((a ^ b) < 0 && a % b);
    }
	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(long long k, long long m) {
		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));
	}
	long long query(long long x) {
		assert(!empty());
		auto l = *lower_bound(x);
		return l.k * x + l.m;
	}
};

#line 2 "data_structure/cht.hpp"
#include<set>
#include<functional>
#include<climits>
#include<cassert>

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

struct cht : std::multiset<Line, std::less<>> {
	// (for doubles, use inf = 1/.0, div(a,b) = a/b)
	static const long long inf = LLONG_MAX;
	long long div(long long a, long long b) { // floored division
		return a / b - ((a ^ b) < 0 && a % b);
    }
	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(long long k, long long m) {
		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));
	}
	long long query(long long x) {
		assert(!empty());
		auto l = *lower_bound(x);
		return l.k * x + l.m;
	}
};