#pragma once
#include "../template.hpp"
#include "./persistent-segtree.hpp"
// https://nyaannyaan.github.io/library/data-structure-2d/rectangle-sum.hpp
// T 座標の型, (S, op, e) モノイド
template <class T, class S, auto op, auto e> struct rectangle_sum {
persistent_segtree<S, op, e> seg;
using pointer = decltype(seg)::node_type *;
vector<T> xs, ys;
vector<S> ws;
vector<pointer> ps;
rectangle_sum(const vector<T> &xs_, const vector<T> &ys_,
const vector<S> &ws_)
: seg(xs_.size()) {
assert(xs_.size() == ys_.size() and xs_.size() == ws_.size());
const int n = xs_.size();
xs.reserve(n);
ys.reserve(n);
ws.reserve(n);
vector<int> ord(n);
iota(begin(ord), end(ord), 0);
ranges::sort(ord, {}, [&xs_](int i) { return xs_[i]; });
for(auto i : ord) {
xs.emplace_back(xs_[i]);
ys.emplace_back(ys_[i]);
ws.emplace_back(ws_[i]);
}
ranges::sort(ord, {}, [&](int i) { return ys[i]; });
ps.reserve(n + 1);
ps.emplace_back(seg.build(vector<S>(n, e())));
for(auto i : ord) {
ps.emplace_back(seg.set(ps.back(), i, ws[i]));
}
ranges::sort(ys);
};
// op([l,r)×[0,u))
S sum(T l, T r, T u) {
l = lower_bound(begin(xs), end(xs), l) - begin(xs);
r = lower_bound(begin(xs), end(xs), r) - begin(xs);
u = lower_bound(begin(ys), end(ys), u) - begin(ys);
return seg.prod(ps[u], l, r);
}
// op([l,r)×[0,u)) - op([l,r)×[0,d))
// opが足し算じゃない場合は引数3つのsum2回取って勝手にやって
S sum(T l, T d, T r, T u) {
l = lower_bound(begin(xs), end(xs), l) - begin(xs);
r = lower_bound(begin(xs), end(xs), r) - begin(xs);
d = lower_bound(begin(ys), end(ys), d) - begin(ys);
u = lower_bound(begin(ys), end(ys), u) - begin(ys);
return seg.prod(ps[u], l, r) - seg.prod(ps[d], l, r);
}
};
#line 2 "other/fastio.hpp"
// ref: https://maspypy.com/library-checker-many-a-b , Nyaanさん
#line 2 "other/type-utils.hpp"
#include <bits/stdc++.h>
using ll = long long;
using u32 = unsigned int;
using u64 = unsigned long long;
using i128 = __int128;
using u128 = unsigned __int128;
using vi = std::vector<int>;
using vii = std::vector<std::vector<int>>;
using pii = std::pair<int, int>;
using vl = std::vector<ll>;
using vll = std::vector<vl>;
using pll = std::pair<ll, ll>;
template <class T>
concept extended_integral =
std::integral<T> || std::same_as<std::remove_cv_t<T>, i128> ||
std::same_as<std::remove_cv_t<T>, u128>;
template <class T>
concept extended_signed_integral =
std::signed_integral<T> || std::same_as<std::remove_cv_t<T>, i128>;
template <class T>
concept extended_unsigned_integral =
std::unsigned_integral<T> || std::same_as<std::remove_cv_t<T>, u128>;
template <class T>
concept Streamable =
requires(std::ostream &os, T &x) { os << x; } || extended_integral<T>;
template <class mint>
concept is_modint = requires(mint &x) {
{ x.val() } -> std::convertible_to<int>;
};
#line 4 "other/fastio.hpp"
namespace fastio {
constexpr int SZ = 1 << 17;
constexpr int offset = 64;
constexpr int mod = 10000;
char in_buf[SZ];
int in_left{}, in_right{};
char out_buf[SZ];
char out_tmp[offset];
int out_right{};
struct Pre {
char num[4 * mod]{};
constexpr Pre() {
for(int i = 0; i < mod; ++i) {
for(int n = i, j = 3; j >= 0; --j, n /= 10)
num[4 * i + j] = '0' + n % 10;
}
}
constexpr const char *operator[](int i) const { return &num[4 * i]; }
} constexpr pre;
void load() {
memmove(in_buf, in_buf + in_left, in_right - in_left);
in_right += -in_left + std::fread(in_buf + in_right - in_left, 1,
SZ - (in_right - in_left), stdin);
in_left = 0;
if(in_right < SZ)
in_buf[in_right++] = '\n';
}
void read(char &c) {
do {
if(in_left == in_right)
load();
c = in_buf[in_left++];
} while(isspace(c));
}
void read(std::string &s) {
s.clear();
char c;
do {
if(in_left == in_right)
load();
c = in_buf[in_left++];
} while(isspace(c));
do {
s += c;
if(in_left == in_right)
load();
c = in_buf[in_left++];
} while(!isspace(c));
}
template <extended_integral T> void read(T &x) {
if(in_right - in_left < offset)
load();
char c;
do
c = in_buf[in_left++];
while(c < '-'); // \n:10 space:32 -:45 '0':48
bool minus{};
if constexpr(extended_signed_integral<T>) {
if(c == '-') {
c = in_buf[in_left++];
minus = true;
}
}
x = 0;
while(c >= '0') {
x = 10 * x + (c & 15);
c = in_buf[in_left++];
}
if constexpr(extended_signed_integral<T>) {
if(minus)
x = -x;
}
}
void flush() { fwrite(out_buf, 1, std::exchange(out_right, 0), stdout); }
void write_range(const char *c, int n) {
int pos{};
while(pos < n) {
if(out_right == SZ)
flush();
int len = std::min(n - pos, SZ - out_right);
memcpy(out_buf + out_right, c + pos, len);
out_right += len;
pos += len;
}
}
void write(char c) {
if(SZ == out_right)
flush();
out_buf[out_right++] = c;
}
void write(const char *c) { write_range(c, strlen(c)); }
void write(const std::string &s) { write_range(s.data(), s.size()); }
template <std::floating_point T> void write(T x) {
int n = std::snprintf(out_tmp, sizeof(out_tmp), "%.16g", x);
write_range(out_tmp, n);
}
void write(bool x) { write(x ? '1' : '0'); }
template <extended_integral T> void write(T x) {
if(x == 0) {
write('0');
}
if constexpr(extended_signed_integral<T>) {
if(x < 0) {
write('-');
x = -x;
}
}
if(SZ - out_right < offset)
flush();
int cur = offset;
for(; x >= 1000; x /= mod) {
cur -= 4;
memcpy(out_tmp + cur, pre[x % mod], 4);
}
if(x >= 100) {
cur -= 3;
memcpy(out_tmp + cur, pre[x % mod] + 1, 3);
} else if(x >= 10) {
cur -= 2;
memcpy(out_tmp + cur, pre[x % mod] + 2, 2);
} else if(x >= 1) {
cur -= 1;
memcpy(out_tmp + cur, pre[x % mod] + 3, 1);
}
write_range(out_tmp + cur, offset - cur);
}
struct Dummy {
// プログラム終了時に出力
~Dummy() { flush(); }
} dummy;
} // namespace fastio
using fastio::write;
#line 4 "template.hpp"
// #pragma GCC target("avx2")
// #pragma GCC optimize("O3")
// #pragma GCC optimize("unroll-loops")
#line 8 "template.hpp"
using namespace std;
#ifdef LOCAL
#include <debug.hpp>
#else
#define debug(...)
#endif
template <Streamable T> void print_one(const T &value) { fastio::write(value); }
template <is_modint T> void print_one(const T &value) {
print_one(value.val());
}
void print() { print_one('\n'); }
template <class T, class... Ts> void print(const T &a, const Ts &...b) {
print_one(a);
((print_one(' '), print_one(b)), ...);
print();
}
template <ranges::range Iterable>
requires(!Streamable<Iterable>)
void print(const Iterable &v) {
for(auto it = v.begin(); it != v.end(); ++it) {
if(it != v.begin())
print_one(' ');
print_one(*it);
}
print();
}
#define all(v) begin(v), end(v)
template <class T> void UNIQUE(T &v) {
ranges::sort(v);
v.erase(unique(all(v)), end(v));
}
template <typename T> inline bool chmax(T &a, T b) {
return ((a < b) ? (a = b, true) : (false));
}
template <typename T> inline bool chmin(T &a, T b) {
return ((a > b) ? (a = b, true) : (false));
}
// https://trap.jp/post/1224/
template <class... T> constexpr auto min(T... a) {
return min(initializer_list<common_type_t<T...>>{a...});
}
template <class... T> constexpr auto max(T... a) {
return max(initializer_list<common_type_t<T...>>{a...});
}
void input() {}
template <class Head, class... Tail> void input(Head &head, Tail &...tail) {
#ifdef LOCAL
cin >> head;
#else
fastio::read(head);
#endif
input(tail...);
}
template <class T> void input(vector<T> &a) {
for(T &x : a)
input(x);
}
#define INT(...) \
int __VA_ARGS__; \
input(__VA_ARGS__)
#define LL(...) \
long long __VA_ARGS__; \
input(__VA_ARGS__)
#define STR(...) \
string __VA_ARGS__; \
input(__VA_ARGS__)
#define REP1_0(n, c) REP1_1(n, c)
#define REP1_1(n, c) \
for(ll REP_COUNTER_##c = 0; REP_COUNTER_##c < (ll)(n); REP_COUNTER_##c++)
#define REP1(n) REP1_0(n, __COUNTER__)
#define REP2(i, a) for(ll i = 0; i < (ll)(a); i++)
#define REP3(i, a, b) for(ll i = (ll)(a); i < (ll)(b); i++)
#define REP4(i, a, b, c) for(ll i = (ll)(a); i < (ll)(b); i += (ll)(c))
#define overload4(a, b, c, d, e, ...) e
#define rep(...) overload4(__VA_ARGS__, REP4, REP3, REP2, REP1)(__VA_ARGS__)
ll inf = 3e18;
vl dx = {1, -1, 0, 0};
vl dy = {0, 0, 1, -1};
template <class T> constexpr T floor(T x, T y) noexcept {
return x / y - ((x ^ y) < 0 and x % y);
}
template <class T> constexpr T ceil(T x, T y) noexcept {
return x / y + ((x ^ y) >= 0 and x % y);
}
// yの符号に関わらず非負で定義 \bmod:texコマンド
template <class T> constexpr T bmod(T x, T y) noexcept {
T m = x % y;
return (m < 0) ? m + (y > 0 ? y : -y) : m;
}
template <std::signed_integral T> constexpr int bit_width(T x) noexcept {
return std::bit_width((uint64_t)x);
}
template <std::signed_integral T> constexpr int popcount(T x) noexcept {
return std::popcount((uint64_t)x);
}
constexpr bool kth_bit(auto n, auto k) { return (n >> k) & 1; }
#line 3 "data-structure/persistent-segtree.hpp"
/**
* @brief Persistent Segment Tree (永続セグメント木)
* 参考:
* https://ei1333.github.io/library/structure/segment-tree/persistent-segment-tree.hpp.html
* https://37zigen.com/persistent-segment-tree/
*/
template <class S, auto op, auto e> struct persistent_segtree {
private:
int n;
struct Node {
S s;
Node *l{}, *r{};
};
vector<unique_ptr<Node>> pool;
Node *make_node_ptr(Node node) {
pool.emplace_back(make_unique<Node>(node));
return pool.back().get();
}
// 区間[l,r)がノードに対応する
// [0,v.size())が根
Node *build(int l, int r, const vector<S> &v) {
if(l + 1 == r) {
return make_node_ptr(Node(v[l]));
}
int m = (l + r) >> 1;
Node *lp = build(l, m, v), *rp = build(m, r, v);
return make_node_ptr(Node(op(lp->s, rp->s), lp, rp));
}
// [a,b) 積を取る区間
// [l,r) pが対応する区間
S prod(int a, int b, Node *p, int l, int r) {
if(r <= a or b <= l)
return e();
if(a <= l and r <= b)
return p->s;
int m = (l + r) >> 1;
return op(prod(a, b, p->l, l, m), prod(a, b, p->r, m, r));
}
Node *merge(Node *lp, Node *rp) {
return make_node_ptr(Node(op(lp->s, rp->s), lp, rp));
}
Node *set(int k, const S &s, Node *p, int l, int r) {
assert(p);
if(k < l or r <= k)
return p;
if(l == k and k + 1 == r) {
return make_node_ptr(Node(s));
}
int m = (l + r) >> 1;
Node *lp = set(k, s, p->l, l, m), *rp = set(k, s, p->r, m, r);
return merge(lp, rp);
}
public:
using node_type = Node;
persistent_segtree(int n) : n(n) {}
Node *build(const vector<S> &v) {
assert(!v.empty());
return build(0, v.size(), v);
}
// [a,b) の総積を計算
S prod(Node *p, int a, int b) { return prod(a, b, p, 0, n); }
Node *set(Node *p, int k, const S &s) { return set(k, s, p, 0, n); }
void dump(Node *p, vector<S> &res) {
assert((p->l == nullptr) == (p->r == nullptr));
if(p->l) {
dump(p->l, res);
dump(p->r, res);
} else {
res.emplace_back(p->s);
}
}
};
#line 4 "data-structure/rectangle-sum.hpp"
// https://nyaannyaan.github.io/library/data-structure-2d/rectangle-sum.hpp
// T 座標の型, (S, op, e) モノイド
template <class T, class S, auto op, auto e> struct rectangle_sum {
persistent_segtree<S, op, e> seg;
using pointer = decltype(seg)::node_type *;
vector<T> xs, ys;
vector<S> ws;
vector<pointer> ps;
rectangle_sum(const vector<T> &xs_, const vector<T> &ys_,
const vector<S> &ws_)
: seg(xs_.size()) {
assert(xs_.size() == ys_.size() and xs_.size() == ws_.size());
const int n = xs_.size();
xs.reserve(n);
ys.reserve(n);
ws.reserve(n);
vector<int> ord(n);
iota(begin(ord), end(ord), 0);
ranges::sort(ord, {}, [&xs_](int i) { return xs_[i]; });
for(auto i : ord) {
xs.emplace_back(xs_[i]);
ys.emplace_back(ys_[i]);
ws.emplace_back(ws_[i]);
}
ranges::sort(ord, {}, [&](int i) { return ys[i]; });
ps.reserve(n + 1);
ps.emplace_back(seg.build(vector<S>(n, e())));
for(auto i : ord) {
ps.emplace_back(seg.set(ps.back(), i, ws[i]));
}
ranges::sort(ys);
};
// op([l,r)×[0,u))
S sum(T l, T r, T u) {
l = lower_bound(begin(xs), end(xs), l) - begin(xs);
r = lower_bound(begin(xs), end(xs), r) - begin(xs);
u = lower_bound(begin(ys), end(ys), u) - begin(ys);
return seg.prod(ps[u], l, r);
}
// op([l,r)×[0,u)) - op([l,r)×[0,d))
// opが足し算じゃない場合は引数3つのsum2回取って勝手にやって
S sum(T l, T d, T r, T u) {
l = lower_bound(begin(xs), end(xs), l) - begin(xs);
r = lower_bound(begin(xs), end(xs), r) - begin(xs);
d = lower_bound(begin(ys), end(ys), d) - begin(ys);
u = lower_bound(begin(ys), end(ys), u) - begin(ys);
return seg.prod(ps[u], l, r) - seg.prod(ps[d], l, r);
}
};
data-structure/rectangle-sum.hpp