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#include "data_structure/cht.hpp"
<typename S, bool MIN> struct cht Convex Hull Trick を用いてクエリを処理するデータ構造本体。
<typename S, bool MIN> struct cht
typename S テンプレート引数として与える構造体。
typename S
using val_t $V$ を表す型。
using val_t
static val_t div(val_t num, val_t den) $V$ 内で $den \times x \leq num$ となる最大の $x$ を返す。整数なら切り捨て除算、実数なら単なる除算に相当する。
static val_t div(val_t num, val_t den)
static val_t inf() $V$ の最大元を返す。
static val_t inf()
using V $V$ を表す型。
using V
void add(V a, V b) 直線 $y=ax+b$ を集合 $L$ に追加する。 $O(\log |L|)$ 時間。
void add(V a, V b)
V get(V c) $x=c$ において $L$ 内の直線がとる $y$ の最小値を答える。 $O(\log |L|)$ 時間。
V get(V c)
#pragma once #include "../template.hpp" template <typename P, bool MIN> struct cht { using V = typename P::V; struct line { mutable V a, b, l, r; bool operator<(const line &o) const { return a < o.a; }; bool operator<(V x) const { return r < x; }; }; set<line, less<>> lines; void add(V a, V b) { if (MIN) a = -a, b = -b; line cur = {a, b, -P::inf(), P::inf()}; auto p = lines.lower_bound(cur); if (p != lines.end() && p->a == a) { if (p->b > b) { return; } else { p = lines.erase(p); } } auto fi = [](const line &s, const line &t) -> V { return P::div(-s.b + t.b, s.a - t.a); }; auto ci = [](const line &s, const line &t) -> V { return -P::div(s.b - t.b, s.a - t.a); }; if (p != lines.begin() && ci(cur, *prev(p)) >= prev(p)->r && p != lines.end() && fi(cur, *p) <= p->l) return; while (p != lines.begin()) { auto pp = prev(p); if (ci(cur, *pp) <= pp->l) { lines.erase(pp); continue; } cur.l = ci(cur, *pp), pp->r = fi(cur, *pp); break; } while (p != lines.end()) { if (fi(cur, *p) >= p->r) { p = lines.erase(p); continue; } cur.r = fi(cur, *p), p->l = ci(cur, *p); break; } lines.insert(cur); } V get(V c) { line l = *lines.lower_bound(c); V ret = l.a * c + l.b; if (MIN) ret = -ret; return ret; } }; struct ll_cht { using V = ll; static V div(V num, V den) { return fdiv(num, den); } static V inf() { return LLONG_MAX; } }; struct double_cht { using V = double; static V div(V num, V den) { return num / den; } static V inf() { return numeric_limits<double>::infinity(); } };
#line 2 "data_structure/cht.hpp" #line 2 "template.hpp" #include <bits/stdc++.h> using namespace std; #define all(a) begin(a), end(a) #define rall(a) rbegin(a), rend(a) #define uniq(a) (a).erase(unique(all(a)), (a).end()) #define t0 first #define t1 second using ll = long long; using ull = unsigned long long; using pll = pair<ll, ll>; using vll = vector<ll>; constexpr double pi = 3.14159265358979323846; constexpr ll dy[9] = {0, 1, 0, -1, 1, 1, -1, -1, 0}; constexpr ll dx[9] = {1, 0, -1, 0, 1, -1, -1, 1, 0}; constexpr ll sign(ll a) { return (a > 0) - (a < 0); } constexpr ll fdiv(ll a, ll b) { return a / b - ((a ^ b) < 0 && a % b); } constexpr ll cdiv(ll a, ll b) { return -fdiv(-a, b); } constexpr ll pw(ll n) { return 1ll << n; } constexpr ll flg(ll n) { return 63 - __builtin_clzll(n); } constexpr ll clg(ll n) { return n == 1 ? 0 : flg(n - 1) + 1; } constexpr ll safemod(ll x, ll mod) { return (x % mod + mod) % mod; } template <typename T> using priority_queue_rev = priority_queue<T, vector<T>, greater<T>>; template <typename T> constexpr T sq(const T &a) { return a * a; } template <typename T, typename U> constexpr bool chmax(T &a, const U &b) { return a < b ? a = b, true : false; } template <typename T, typename U> constexpr bool chmin(T &a, const U &b) { return a > b ? a = b, true : false; } template <typename T, typename U> ostream &operator<<(ostream &os, const pair<T, U> &a) { os << "(" << a.first << ", " << a.second << ")"; return os; } template <typename T, typename U, typename V> ostream &operator<<(ostream &os, const tuple<T, U, V> &a) { os << "(" << get<0>(a) << ", " << get<1>(a) << ", " << get<2>(a) << ")"; return os; } template <typename T> ostream &operator<<(ostream &os, const vector<T> &a) { os << "("; for (auto itr = a.begin(); itr != a.end(); ++itr) os << *itr << (next(itr) != a.end() ? ", " : ""); os << ")"; return os; } template <typename T> ostream &operator<<(ostream &os, const set<T> &a) { os << "("; for (auto itr = a.begin(); itr != a.end(); ++itr) os << *itr << (next(itr) != a.end() ? ", " : ""); os << ")"; return os; } template <typename T> ostream &operator<<(ostream &os, const multiset<T> &a) { os << "("; for (auto itr = a.begin(); itr != a.end(); ++itr) os << *itr << (next(itr) != a.end() ? ", " : ""); os << ")"; return os; } template <typename T, typename U> ostream &operator<<(ostream &os, const map<T, U> &a) { os << "("; for (auto itr = a.begin(); itr != a.end(); ++itr) os << *itr << (next(itr) != a.end() ? ", " : ""); os << ")"; return os; } #ifdef ONLINE_JUDGE #define dump(...) (void(0)) #else void debug() { cerr << endl; } template <typename Head, typename... Tail> void debug(Head &&head, Tail &&... tail) { cerr << head; if (sizeof...(Tail)) cerr << ", "; debug(tail...); } #define dump(...) cerr << __LINE__ << ": " << #__VA_ARGS__ << " = ", debug(__VA_ARGS__) #endif struct rep { struct itr { ll v; itr(ll v) : v(v) {} void operator++() { ++v; } ll operator*() const { return v; } bool operator!=(itr i) const { return v < *i; } }; ll l, r; rep(ll l, ll r) : l(l), r(r) {} rep(ll r) : rep(0, r) {} itr begin() const { return l; }; itr end() const { return r; }; }; struct per { struct itr { ll v; itr(ll v) : v(v) {} void operator++() { --v; } ll operator*() const { return v; } bool operator!=(itr i) const { return v > *i; } }; ll l, r; per(ll l, ll r) : l(l), r(r) {} per(ll r) : per(0, r) {} itr begin() const { return r - 1; }; itr end() const { return l - 1; }; }; struct io_setup { static constexpr int PREC = 20; io_setup() { cout << fixed << setprecision(PREC); cerr << fixed << setprecision(PREC); }; } iOS; #line 4 "data_structure/cht.hpp" template <typename P, bool MIN> struct cht { using V = typename P::V; struct line { mutable V a, b, l, r; bool operator<(const line &o) const { return a < o.a; }; bool operator<(V x) const { return r < x; }; }; set<line, less<>> lines; void add(V a, V b) { if (MIN) a = -a, b = -b; line cur = {a, b, -P::inf(), P::inf()}; auto p = lines.lower_bound(cur); if (p != lines.end() && p->a == a) { if (p->b > b) { return; } else { p = lines.erase(p); } } auto fi = [](const line &s, const line &t) -> V { return P::div(-s.b + t.b, s.a - t.a); }; auto ci = [](const line &s, const line &t) -> V { return -P::div(s.b - t.b, s.a - t.a); }; if (p != lines.begin() && ci(cur, *prev(p)) >= prev(p)->r && p != lines.end() && fi(cur, *p) <= p->l) return; while (p != lines.begin()) { auto pp = prev(p); if (ci(cur, *pp) <= pp->l) { lines.erase(pp); continue; } cur.l = ci(cur, *pp), pp->r = fi(cur, *pp); break; } while (p != lines.end()) { if (fi(cur, *p) >= p->r) { p = lines.erase(p); continue; } cur.r = fi(cur, *p), p->l = ci(cur, *p); break; } lines.insert(cur); } V get(V c) { line l = *lines.lower_bound(c); V ret = l.a * c + l.b; if (MIN) ret = -ret; return ret; } }; struct ll_cht { using V = ll; static V div(V num, V den) { return fdiv(num, den); } static V inf() { return LLONG_MAX; } }; struct double_cht { using V = double; static V div(V num, V den) { return num / den; } static V inf() { return numeric_limits<double>::infinity(); } };