#pragma once
#include "../template.hpp"
#include "./compress.hpp"
#include "./lazy-segtree.hpp"
template <class T = int, class ans_type = ll> struct RectangleUnionArea {
private:
using S = pair<T, T>;
static S op(S s, S t) {
if(s.first == t.first)
return S(s.first, s.second + t.second);
return s.first < t.first ? s : t;
}
static S e() {
return S(numeric_limits<T>::max(), 0);
}
using F = T;
static F comp(F f, F g) {
return f + g;
}
static S mapping(F f, S s) {
s.first += f;
return s;
}
static F id() {
return 0;
}
struct Rectangle {
T l, d, r, u;
};
vector<Rectangle> rectangles;
public:
void add_rect(T l, T d, T r, T u) {
assert(l < r and d < u);
rectangles.emplace_back(l, d, r, u);
}
ans_type cul() {
int n = rectangles.size();
if(n == 0)
return 0;
Compress<T> cp;
vector<int> ord(2 * n);
iota(begin(ord), end(ord), -n);
// 下から平面走査 i : d[i]でin, -i-1 : u[i]でout
for(auto [l, d, r, u] : rectangles)
cp.add(l), cp.add(r);
cp.build();
ranges::sort(ord, [&](int i, int j) {
T x = i < 0 ? rectangles[-i - 1].u : rectangles[i].d;
T y = j < 0 ? rectangles[-j - 1].u : rectangles[j].d;
return x < y;
});
lazy_segtree<S, op, e, F, mapping, comp, id> seg(cp.size());
ans_type ans = 0;
for(int i = 0; i + 1 < cp.size(); i++) {
seg.set(i, S(0, cp[i + 1] - cp[i]));
}
seg.set(cp.size() - 1, S(0, 0));
ans_type width = cp[cp.size() - 1] - cp[0];
for(int i = 0; i < 2 * n - 1; i++) {
T x = ord[i] < 0 ? rectangles[-ord[i] - 1].u : rectangles[ord[i]].d;
T y = ord[i + 1] < 0 ? rectangles[-ord[i + 1] - 1].u
: rectangles[ord[i + 1]].d;
if(ord[i] < 0) {
auto &rec = rectangles[-ord[i] - 1];
seg.apply(cp.get(rec.l), cp.get(rec.r), -1);
} else {
auto &rec = rectangles[ord[i]];
seg.apply(cp.get(rec.l), cp.get(rec.r), 1);
}
ans += (y - x) * (width - (seg.all_prod_commute().first == 0
? seg.all_prod_commute().second
: 0));
}
return ans;
}
};
#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/compress.hpp"
// https://ei1333.github.io/library/other/compress.hpp
template <class T> struct Compress {
bool is_built = false;
vector<T> data;
Compress() = default;
explicit Compress(const vector<T> &v) { add(v); }
void add(const T &x) {
is_built = false;
data.emplace_back(x);
}
void add(const vector<T> &v) {
is_built = false;
ranges::copy(v, back_inserter(data));
}
void build() {
is_built = true;
ranges::sort(data);
data.erase(unique(begin(data), end(data)), end(data));
}
// x 以上となる最小のインデックスを返す
int get(const T &x) const {
assert(is_built);
return ranges::lower_bound(data, x) - begin(data);
}
const T &operator[](int t) {
assert(is_built);
return data[t];
}
int size() const { return ssize(data); }
};
#line 3 "data-structure/lazy-segtree.hpp"
template <class S, S (*op)(S, S), S (*e)(), class F, S (*mapping)(F, S),
F (*composition)(F, F), F (*id)()>
// composition(f,g)(x) = f∘g(x) = f(g(x))
// aclと同じ、maspyさん記事と逆
struct lazy_segtree {
int n;
vector<S> v;
vector<F> vf;
explicit lazy_segtree(int n)
: n(n), v(vector<S>(2 * n, e())), vf(vector<F>(2 * n, id())) {};
explicit lazy_segtree(const vector<S> &v_)
: n(v_.size()), v(2 * n, e()), vf(2 * n, id()) {
for(int i = 0; i < n; ++i)
v[i + n] = v_[i];
for(int i = n - 1; i > 0; --i)
v[i] = op(v[i << 1], v[i << 1 | 1]);
}
void apply(int l, int r, F f) {
l += n;
r += n;
int l0 = l / (l & -l);
int r0 = r / (r & -r) - 1;
propagate_above(l0);
propagate_above(r0);
while(l < r) {
if(l & 1) {
apply_at(l, f);
l++;
}
if(r & 1) {
r--;
apply_at(r, f);
}
l >>= 1;
r >>= 1;
}
recul_above(l0);
recul_above(r0);
}
S get(int x) {
x += n;
int maxi = (int)bit_width((unsigned)x) - 1;
for(int i = maxi; i > 0; --i)
propagate_at(x >> i);
return v[x];
}
void set(int x, S s) {
x += n;
propagate_above(x);
v[x] = s;
recul_above(x);
}
S prod(int l, int r) {
l += n;
r += n;
int l0 = l / (l & -l);
int r0 = r / (r & -r) - 1;
propagate_above(l0);
propagate_above(r0);
S sl = e(), sr = e();
while(l < r) {
if(l & 1) {
sl = op(sl, v[l]);
l++;
}
if(r & 1) {
r--;
sr = op(v[r], sr);
}
l >>= 1;
r >>= 1;
}
return op(sl, sr);
}
S all_prod_commute() {
// 可換なモノイド専用
// 2冪にすれば非可換でも良さそう
return v[1];
}
private:
void apply_at(int x, F f) {
v[x] = mapping(f, v[x]);
if(x < n)
vf[x] = composition(f, vf[x]);
}
void propagate_at(int x) {
apply_at(x << 1, vf[x]);
apply_at(x << 1 | 1, vf[x]);
vf[x] = id();
}
void propagate_above(int x) {
int maxi = (int)bit_width((unsigned)x) - 1;
for(int i = maxi; i > 0; --i) {
propagate_at(x >> i);
}
return;
}
void recul_above(int x) {
while(x > 1) {
x >>= 1;
v[x] = op(v[x << 1], v[x << 1 | 1]);
}
}
};
#line 5 "data-structure/rectangle-union-area.hpp"
template <class T = int, class ans_type = ll> struct RectangleUnionArea {
private:
using S = pair<T, T>;
static S op(S s, S t) {
if(s.first == t.first)
return S(s.first, s.second + t.second);
return s.first < t.first ? s : t;
}
static S e() {
return S(numeric_limits<T>::max(), 0);
}
using F = T;
static F comp(F f, F g) {
return f + g;
}
static S mapping(F f, S s) {
s.first += f;
return s;
}
static F id() {
return 0;
}
struct Rectangle {
T l, d, r, u;
};
vector<Rectangle> rectangles;
public:
void add_rect(T l, T d, T r, T u) {
assert(l < r and d < u);
rectangles.emplace_back(l, d, r, u);
}
ans_type cul() {
int n = rectangles.size();
if(n == 0)
return 0;
Compress<T> cp;
vector<int> ord(2 * n);
iota(begin(ord), end(ord), -n);
// 下から平面走査 i : d[i]でin, -i-1 : u[i]でout
for(auto [l, d, r, u] : rectangles)
cp.add(l), cp.add(r);
cp.build();
ranges::sort(ord, [&](int i, int j) {
T x = i < 0 ? rectangles[-i - 1].u : rectangles[i].d;
T y = j < 0 ? rectangles[-j - 1].u : rectangles[j].d;
return x < y;
});
lazy_segtree<S, op, e, F, mapping, comp, id> seg(cp.size());
ans_type ans = 0;
for(int i = 0; i + 1 < cp.size(); i++) {
seg.set(i, S(0, cp[i + 1] - cp[i]));
}
seg.set(cp.size() - 1, S(0, 0));
ans_type width = cp[cp.size() - 1] - cp[0];
for(int i = 0; i < 2 * n - 1; i++) {
T x = ord[i] < 0 ? rectangles[-ord[i] - 1].u : rectangles[ord[i]].d;
T y = ord[i + 1] < 0 ? rectangles[-ord[i + 1] - 1].u
: rectangles[ord[i + 1]].d;
if(ord[i] < 0) {
auto &rec = rectangles[-ord[i] - 1];
seg.apply(cp.get(rec.l), cp.get(rec.r), -1);
} else {
auto &rec = rectangles[ord[i]];
seg.apply(cp.get(rec.l), cp.get(rec.r), 1);
}
ans += (y - x) * (width - (seg.all_prod_commute().first == 0
? seg.all_prod_commute().second
: 0));
}
return ans;
}
};
data-structure/rectangle-union-area.hpp