test/yosupo/line_add_get_min_LiChaoTree.test.cpp

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Last update: 2023-06-25 16:24:15+09:00
Problem: https://judge.yosupo.jp/problem/line_add_get_min

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Code

#define PROBLEM "https://judge.yosupo.jp/problem/line_add_get_min"
#include "../../data-structure/LiChaoTree.hpp"
#include "../../basic/template.hpp"
int n, q;
lint a[200010], b[200010];
std::vector<std::pair<int, lint>> vec;
std::vector<lint> cord;
int main() {
	scanf("%d%d", &n, &q);
	rep(i, n) scanf("%lld%lld", a + i, b + i);
	rep(i, q) {
		int t;
		scanf("%d", &t);
		if (t == 0) {
			int a;
			lint b;
			scanf("%d%lld", &a, &b);
			vec.emplace_back(a, b);
		} else {
			int p;
			scanf("%d", &p);
			vec.emplace_back(p, LINF);
			cord.emplace_back(p);
		}
	}
	std::sort(all(cord));
	cord.erase(std::unique(all(cord)), cord.end());
	LiChaoTree<true> lct(cord);
	rep(i, n) lct.addLine(a[i], b[i]);
	for (auto i : vec) {
		if (i.second == LINF)
			printf("%lld\n", lct.query(std::lower_bound(all(cord), i.first) -
									   cord.begin())
								 .first);
		else
			lct.addLine(i.first, i.second);
	}
}

#line 1 "test/yosupo/line_add_get_min_LiChaoTree.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/line_add_get_min"
#line 2 "basic/template.hpp"
#define _CRT_SECURE_NO_WARNINGS
#ifndef __clang__
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#endif
#include <string.h>
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cfloat>
#include <chrono>
#include <climits>
#include <cmath>
#include <complex>
#include <ctime>
#include <deque>
#include <fstream>
#include <functional>
#include <iomanip>
#include <iostream>
#include <iterator>
#include <list>
#include <map>
#include <memory>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

#define rep(i, n) for (int i = 0; i < int(n); i++)
#define REP(i, n) for (int i = 1; i <= int(n); i++)
#define all(V) V.begin(), V.end()

using i128 = __int128_t;
using u128 = __uint128_t;
using uint = unsigned int;
using lint = long long;
using ulint = unsigned long long;
using IP = std::pair<int, int>;
using LP = std::pair<lint, lint>;

constexpr int INF = INT_MAX / 2;
constexpr lint LINF = LLONG_MAX / 2;
constexpr double eps = DBL_EPSILON * 10;
constexpr double PI = 3.141592653589793238462643383279;

template <class T>
class prique : public std::priority_queue<T, std::vector<T>, std::greater<T>> {};
int popcount(uint x) {
#if __cplusplus >= 202002L
	return std::popcount(x);
#else
#ifndef __clang__
	return __builtin_popcount(x);
#endif
#endif
	x = (x & 0x55555555) + (x >> 1 & 0x55555555);
	x = (x & 0x33333333) + (x >> 2 & 0x33333333);
	x = (x & 0x0f0f0f0f) + (x >> 4 & 0x0f0f0f0f);
	x = (x & 0x00ff00ff) + (x >> 8 & 0x00ff00ff);
	return (x & 0x0000ffff) + (x >> 16 & 0x0000ffff);
}
template <class F>
inline constexpr decltype(auto) lambda_fix(F&& f) {
	return [f = std::forward<F>(f)](auto&&... args) {
		return f(f, std::forward<decltype(args)>(args)...);
	};
}
template <class T>
constexpr std::vector<T> make_vec(size_t n) {
	return std::vector<T>(n);
}
template <class T, class... Args>
constexpr auto make_vec(size_t n, Args&&... args) {
	return std::vector<decltype(make_vec<T>(args...))>(n, make_vec<T>(std::forward<Args>(args)...));
}
template <class T, class U, class Stream>
Stream& operator>>(Stream& ist, std::pair<T, U>& x) {
	return ist >> x.first >> x.second;
}
template <class T, class U, class Stream>
Stream& operator<<(Stream& ost, const std::pair<T, U>& x) {
	return ost << x.first << " " << x.second;
}
template <class Container,
		  std::enable_if_t<!std::is_same<Container, std::string>::value, std::nullptr_t> = nullptr>
auto operator>>(std::istream& ist, Container& cont)
	-> decltype(typename Container::iterator(), std::cin)& {
	Container tmp;
	while (true) {
		typename Container::value_type t;
		ist >> t;
		tmp.emplace_back(t);
		if (getchar() == '\n') break;
	}
	cont = Container(std::move(tmp));
	return ist;
}
template <class Container, class Stream,
		  std::enable_if_t<!std::is_same<Container, std::string>::value, std::nullptr_t> = nullptr>
auto operator<<(Stream& ost, const Container& cont)
	-> decltype(typename Container::iterator(), ost)& {
	for (auto it = cont.begin(); it != cont.end(); it++) {
		if (it != cont.begin()) ost << ' ';
		ost << *it;
	}
	return ost;
}
template <class Container>
auto sum(const Container& cont) -> decltype(typename Container::iterator(), 0LL) {
	lint res = 0;
	for (auto it = cont.begin(); it != cont.end(); it++) res += *it;
	return res;
}
template <class T, class U>
constexpr inline bool chmax(T& lhs, const U& rhs) noexcept {
	if (lhs < rhs) {
		lhs = rhs;
		return true;
	}
	return false;
}
template <class T, class U>
constexpr inline bool chmin(T& lhs, const U& rhs) noexcept {
	if (lhs > rhs) {
		lhs = rhs;
		return true;
	}
	return false;
}
constexpr inline lint gcd(lint a, lint b) noexcept {
	while (b) {
		lint c = a;
		a = b;
		b = c % b;
	}
	return a;
}
inline lint lcm(lint a, lint b) noexcept { return a / gcd(a, b) * b; }
constexpr bool isprime(lint n) noexcept {
	if (n == 1) return false;
	for (int i = 2; i * i <= n; i++) {
		if (n % i == 0) return false;
	}
	return true;
}
template <class T>
constexpr T mypow(T a, lint b) noexcept {
	T res(1);
	while (true) {
		if (b & 1) res *= a;
		b >>= 1;
		if (!b) break;
		a *= a;
	}
	return res;
}
constexpr lint modpow(lint a, lint b, lint m) noexcept {
	a %= m;
	lint res(1);
	while (b) {
		if (b & 1) res *= a, res %= m;
		a *= a, a %= m, b >>= 1;
	}
	return res;
}
LP extGcd(lint a, lint b) noexcept {
	if (b == 0) return {1, 0};
	LP s = extGcd(b, a % b);
	std::swap(s.first, s.second);
	s.second -= a / b * s.first;
	return s;
}
LP ChineseRem(const lint& b1, const lint& m1, const lint& b2, const lint& m2) noexcept {
	auto p = extGcd(m1, m2);
	lint g = gcd(m1, m2), l = m1 / g * m2;
	lint tmp = (b2 - b1) / g * p.first % (m2 / g);
	lint r = (b1 + m1 * tmp + l) % l;
	return {r, l};
}
int LCS(const std::string& a, const std::string& b) {
	auto dp = make_vec<int>(a.size() + 1, b.size() + 1);
	rep(i, a.size()) {
		rep(j, b.size()) {
			chmax(dp[i + 1][j], dp[i][j]);
			chmax(dp[i][j + 1], dp[i][j]);
			if (a[i] == b[j]) chmax(dp[i + 1][j + 1], dp[i][j] + 1);
		}
		chmax(dp[i + 1][b.size()], dp[i][b.size()]);
	}
	rep(j, b.size()) chmax(dp[a.size()][j + 1], dp[a.size()][j]);
	return dp[a.size()][b.size()];
}
template <class T, std::enable_if_t<std::is_convertible<int, T>::value, std::nullptr_t> = nullptr>
void compress(std::vector<T>& vec) {
	auto tmp = vec;
	std::sort(all(tmp));
	tmp.erase(std::unique(all(tmp)), tmp.end());
	for (T& i : vec) i = std::lower_bound(all(tmp), i) - tmp.begin();
}
template <class T>
void compress(T* l, T* r) {
	std::vector<T> tmp(l, r);
	std::sort(all(tmp));
	tmp.erase(std::unique(all(tmp)), tmp.end());
	for (auto i = l; i < r; i++) {
		*i = std::lower_bound(all(tmp), *i) - tmp.begin();
	}
}
template <class InputIter>
void compress(InputIter l, InputIter r) {
	std::vector<typename InputIter::value_type> tmp(l, r);
	std::sort(all(tmp));
	tmp.erase(std::unique(all(tmp)), tmp.end());
	for (auto i = l; i < r; i++) {
		*i = std::lower_bound(all(tmp), *i) - tmp.begin();
	}
}
template <class InputIter,
		  std::enable_if_t<std::is_same<typename InputIter::value_type, std::pair<IP, int>>::value,
						   std::nullptr_t> = nullptr>
void mo_sort(InputIter l, InputIter r, int N) {
	const int M = std::max(1.0, std::sqrt(lint(N) * N / std::distance(l, r)));
	std::sort(l, r, [M](const auto& lhs, const auto& rhs) {
		if (lhs.first.first / M < rhs.first.first / M) return true;
		if (lhs.first.first / M == rhs.first.first / M) return lhs.first.second < rhs.first.second;
		return false;
	});
	int before = -1, cnt = 0;
	bool f = false;
	for (InputIter i = l; i != r; i++) {
		if (before != i->first.first / M) {
			if (f) std::reverse(i - cnt, i);
			f ^= true, before = i->first.first / M, cnt = 1;
		} else
			cnt++;
	}
	if (f) std::reverse(r - cnt, r);
}
template <class T>
std::vector<T> xor_bases(const std::vector<T>& vec) {
	std::vector<T> res;
	for (T i : vec) {
		for (T j : res) {
			chmin(i, i ^ j);
		}
		if (i) res.emplace_back(i);
	}
	return res;
}
#line 3 "data-structure/LiChaoTree.hpp"
template <bool isMin>
class LiChaoTree {
	int n, id;
	std::vector<std::tuple<lint, lint, lint>> interval;
	std::vector<std::pair<LP, int>> node;
	std::vector<lint> cord;
	static lint calc(std::pair<LP, int> l, lint x) { return l.first.first * x + l.first.second; }
	void addSegment(std::pair<LP, int>& newLine, lint cnt) {
		lint l = std::get<0>(interval[cnt]), m = std::get<1>(interval[cnt]),
			 r = std::get<2>(interval[cnt]);
		if (n <= cnt) {
			if (calc(node[cnt], l) > calc(newLine, l)) node[cnt] = newLine;
			return;
		}
		if (calc(node[cnt], l) < calc(newLine, l) && calc(node[cnt], r) < calc(newLine, r)) return;
		if (calc(node[cnt], l) > calc(newLine, l) && calc(node[cnt], r) > calc(newLine, r)) {
			node[cnt] = newLine;
			return;
		}
		if (calc(node[cnt], m) > calc(newLine, m)) std::swap(node[cnt], newLine);
		if (calc(node[cnt], l) > calc(newLine, l))
			addSegment(newLine, cnt << 1);
		else
			addSegment(newLine, cnt << 1 | 1);
	}

  public:
	LiChaoTree(const std::vector<lint>& vec) { init(vec); }
	LiChaoTree(std::vector<lint>&& vec) { init(std::forward<std::vector<lint>>(vec)); }
	void init(const std::vector<lint>& vec) {
		std::vector<lint> tmp = vec;
		init(std::forward<std::vector<lint>>(tmp));
	}
	void init(std::vector<lint>&& vec) {
		interval.clear();
		node.clear();
		cord.clear();
		n = 1;
		id = 0;
		vec.emplace_back(vec.back() + 1);
		while (n < (int)vec.size()) n *= 2;
		while ((int)vec.size() < n + 1) vec.emplace_back(vec.back() + 1);
		node.assign(2 * n, {{0, LINF}, -1});
		interval.emplace_back(0, 0, 0);
		for (int range = n; range; range >>= 1) {
			for (int i = 0; i < n; i += range) {
				if (range == 1)
					interval.emplace_back(vec[i], 0, vec[i + range]);
				else
					interval.emplace_back(vec[i], vec[i + range / 2], vec[i + range]);
			}
		}
		cord = vec;
	}
	void addLine(lint a, lint b) {
		std::pair<LP, int> newLine = {{a, b}, id++};
		if (!isMin) {
			newLine.first.first *= -1;
			newLine.first.second *= -1;
		}
		addSegment(newLine, 1);
	}
	void addSegment(int l, int r, lint a, lint b) {
		l += n;
		r += n;
		std::pair<LP, int> newLine = {{a, b}, id++};
		if (!isMin) {
			newLine.first.first *= -1;
			newLine.first.second *= -1;
		}
		while (l < r) {
			if (l & 1) {
				auto tmp = newLine;
				addSegment(tmp, l++);
			}
			if (r & 1) {
				auto tmp = newLine;
				addSegment(tmp, --r);
			}
			l >>= 1;
			r >>= 1;
		}
	}
	std::pair<lint, int> query(int idx) const {
		lint x = cord[idx];
		idx += n;
		std::pair<lint, int> res = {LINF, -1};
		while (idx) {
			if (chmin(res.first, calc(node[idx], x))) res.second = node[idx].second;
			idx >>= 1;
		}
		if (!isMin) res.first = -res.first;
		return res;
	}
	void clear() {
		id = 0;
		node.assign(2 * n, {{0, LINF}, -1});
	}
};

/**
 * @title Li Chao Tree
 */
#line 4 "test/yosupo/line_add_get_min_LiChaoTree.test.cpp"
int n, q;
lint a[200010], b[200010];
std::vector<std::pair<int, lint>> vec;
std::vector<lint> cord;
int main() {
	scanf("%d%d", &n, &q);
	rep(i, n) scanf("%lld%lld", a + i, b + i);
	rep(i, q) {
		int t;
		scanf("%d", &t);
		if (t == 0) {
			int a;
			lint b;
			scanf("%d%lld", &a, &b);
			vec.emplace_back(a, b);
		} else {
			int p;
			scanf("%d", &p);
			vec.emplace_back(p, LINF);
			cord.emplace_back(p);
		}
	}
	std::sort(all(cord));
	cord.erase(std::unique(all(cord)), cord.end());
	LiChaoTree<true> lct(cord);
	rep(i, n) lct.addLine(a[i], b[i]);
	for (auto i : vec) {
		if (i.second == LINF)
			printf("%lld\n", lct.query(std::lower_bound(all(cord), i.first) -
									   cord.begin())
								 .first);
		else
			lct.addLine(i.first, i.second);
	}
}