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#define PROBLEM "https://judge.yosupo.jp/problem/area_of_union_of_rectangles" #include "Template/template.hpp" #include "Utility/fastio.hpp" #include "DataStructure/unionrect.hpp" int main(){ int n; read(n); UnionRect buf; rep(_,0,n){ int L,D,R,U; read(L,D,R,U); buf.add(L,R,D,U); } ll ret=buf.run(); print(ret); return 0; }
#line 1 "Verify/LC_area_of_union_of_rectangles.test.cpp" #define PROBLEM "https://judge.yosupo.jp/problem/area_of_union_of_rectangles" #line 1 "Template/template.hpp" #include <bits/stdc++.h> using namespace std; #define rep(i, a, b) for (int i = (int)(a); i < (int)(b); i++) #define rrep(i, a, b) for (int i = (int)(b-1); i >= (int)(a); i--) #define ALL(v) (v).begin(), (v).end() #define UNIQUE(v) sort(ALL(v)), (v).erase(unique(ALL(v)), (v).end()) #define SZ(v) (int)v.size() #define MIN(v) *min_element(ALL(v)) #define MAX(v) *max_element(ALL(v)) #define LB(v, x) int(lower_bound(ALL(v), (x)) - (v).begin()) #define UB(v, x) int(upper_bound(ALL(v), (x)) - (v).begin()) using uint = unsigned int; using ll = long long int; using ull = unsigned long long; using i128 = __int128_t; using u128 = __uint128_t; const int inf = 0x3fffffff; const ll INF = 0x1fffffffffffffff; template <typename T> inline bool chmax(T &a, T b) { if (a < b) { a = b; return 1; } return 0; } template <typename T> inline bool chmin(T &a, T b) { if (a > b) { a = b; return 1; } return 0; } template <typename T, typename U> T ceil(T x, U y) { assert(y != 0); if (y < 0) x = -x, y = -y; return (x > 0 ? (x + y - 1) / y : x / y); } template <typename T, typename U> T floor(T x, U y) { assert(y != 0); if (y < 0) x = -x, y = -y; return (x > 0 ? x / y : (x - y + 1) / y); } template <typename T> int popcnt(T x) { return __builtin_popcountll(x); } template <typename T> int topbit(T x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); } template <typename T> int lowbit(T x) { return (x == 0 ? -1 : __builtin_ctzll(x)); } #ifdef LOCAL #define show(...) _show(0, #__VA_ARGS__, __VA_ARGS__) #else #define show(...) true #endif template <typename T> void _show(int i, T name) { cerr << '\n'; } template <typename T1, typename T2, typename... T3> void _show(int i, const T1 &a, const T2 &b, const T3 &...c) { for (; a[i] != ',' && a[i] != '\0'; i++) cerr << a[i]; cerr << ":" << b << " "; _show(i + 1, a, c...); } template <class T, class U> ostream &operator<<(ostream &os, const pair<T, U> &p) { os << "P(" << p.first << ", " << p.second << ")"; return os; } template <typename T, template <class> class C> ostream &operator<<(ostream &os, const C<T> &v) { os << "["; for (auto d : v) os << d << ", "; os << "]"; return os; } #line 2 "Utility/fastio.hpp" #include <unistd.h> namespace fastio { static constexpr uint32_t SZ = 1 << 17; char ibuf[SZ]; char obuf[SZ]; char out[100]; // pointer of ibuf, obuf uint32_t pil = 0, pir = 0, por = 0; struct Pre { char num[10000][4]; constexpr Pre() : num() { for (int i = 0; i < 10000; i++) { int n = i; for (int j = 3; j >= 0; j--) { num[i][j] = n % 10 | '0'; n /= 10; } } } } constexpr pre; inline void load() { memmove(ibuf, ibuf + pil, pir - pil); pir = pir - pil + fread(ibuf + pir - pil, 1, SZ - pir + pil, stdin); pil = 0; if (pir < SZ) ibuf[pir++] = '\n'; } inline void flush() { fwrite(obuf, 1, por, stdout); por = 0; } void rd(char &c) { do { if (pil + 1 > pir) load(); c = ibuf[pil++]; } while (isspace(c)); } void rd(string &x) { x.clear(); char c; do { if (pil + 1 > pir) load(); c = ibuf[pil++]; } while (isspace(c)); do { x += c; if (pil == pir) load(); c = ibuf[pil++]; } while (!isspace(c)); } template <typename T> void rd_real(T &x) { string s; rd(s); x = stod(s); } template <typename T> void rd_integer(T &x) { if (pil + 100 > pir) load(); char c; do c = ibuf[pil++]; while (c < '-'); bool minus = 0; if constexpr (is_signed<T>::value || is_same_v<T, i128>) { if (c == '-') { minus = 1, c = ibuf[pil++]; } } x = 0; while ('0' <= c) { x = x * 10 + (c & 15), c = ibuf[pil++]; } if constexpr (is_signed<T>::value || is_same_v<T, i128>) { if (minus) x = -x; } } void rd(int &x) { rd_integer(x); } void rd(ll &x) { rd_integer(x); } void rd(i128 &x) { rd_integer(x); } void rd(uint &x) { rd_integer(x); } void rd(ull &x) { rd_integer(x); } void rd(u128 &x) { rd_integer(x); } void rd(double &x) { rd_real(x); } void rd(long double &x) { rd_real(x); } template <class T, class U> void rd(pair<T, U> &p) { return rd(p.first), rd(p.second); } template <size_t N = 0, typename T> void rd_tuple(T &t) { if constexpr (N < std::tuple_size<T>::value) { auto &x = std::get<N>(t); rd(x); rd_tuple<N + 1>(t); } } template <class... T> void rd(tuple<T...> &tpl) { rd_tuple(tpl); } template <size_t N = 0, typename T> void rd(array<T, N> &x) { for (auto &d : x) rd(d); } template <class T> void rd(vector<T> &x) { for (auto &d : x) rd(d); } void read() {} template <class H, class... T> void read(H &h, T &...t) { rd(h), read(t...); } void wt(const char c) { if (por == SZ) flush(); obuf[por++] = c; } void wt(const string s) { for (char c : s) wt(c); } void wt(const char *s) { size_t len = strlen(s); for (size_t i = 0; i < len; i++) wt(s[i]); } template <typename T> void wt_integer(T x) { if (por > SZ - 100) flush(); if (x < 0) { obuf[por++] = '-', x = -x; } int outi; for (outi = 96; x >= 10000; outi -= 4) { memcpy(out + outi, pre.num[x % 10000], 4); x /= 10000; } if (x >= 1000) { memcpy(obuf + por, pre.num[x], 4); por += 4; } else if (x >= 100) { memcpy(obuf + por, pre.num[x] + 1, 3); por += 3; } else if (x >= 10) { int q = (x * 103) >> 10; obuf[por] = q | '0'; obuf[por + 1] = (x - q * 10) | '0'; por += 2; } else obuf[por++] = x | '0'; memcpy(obuf + por, out + outi + 4, 96 - outi); por += 96 - outi; } template <typename T> void wt_real(T x) { ostringstream oss; oss << fixed << setprecision(15) << double(x); string s = oss.str(); wt(s); } void wt(int x) { wt_integer(x); } void wt(ll x) { wt_integer(x); } void wt(i128 x) { wt_integer(x); } void wt(uint x) { wt_integer(x); } void wt(ull x) { wt_integer(x); } void wt(u128 x) { wt_integer(x); } void wt(double x) { wt_real(x); } void wt(long double x) { wt_real(x); } template <class T, class U> void wt(const pair<T, U> val) { wt(val.first); wt(' '); wt(val.second); } template <size_t N = 0, typename T> void wt_tuple(const T t) { if constexpr (N < std::tuple_size<T>::value) { if constexpr (N > 0) { wt(' '); } const auto x = std::get<N>(t); wt(x); wt_tuple<N + 1>(t); } } template <class... T> void wt(tuple<T...> tpl) { wt_tuple(tpl); } template <class T, size_t S> void wt(const array<T, S> val) { auto n = val.size(); for (size_t i = 0; i < n; i++) { if (i) wt(' '); wt(val[i]); } } template <class T> void wt(const vector<T> val) { auto n = val.size(); for (size_t i = 0; i < n; i++) { if (i) wt(' '); wt(val[i]); } } void print() { wt('\n'); } template <class Head, class... Tail> void print(Head &&head, Tail &&...tail) { wt(head); if (sizeof...(Tail)) wt(' '); print(forward<Tail>(tail)...); } void __attribute__((destructor)) _d() { flush(); } } // namespace fastio using fastio::flush; using fastio::print; using fastio::read; inline void first(bool i = true) { print(i ? "first" : "second"); } inline void Alice(bool i = true) { print(i ? "Alice" : "Bob"); } inline void yes(bool i = true) { print(i ? "yes" : "no"); } inline void Yes(bool i = true) { print(i ? "Yes" : "No"); } inline void No() { print("No"); } inline void YES(bool i = true) { print(i ? "YES" : "NO"); } inline void NO() { print("NO"); } inline void Yay(bool i = true) { print(i ? "Yay!" : ":("); } inline void Possible(bool i = true) { print(i ? "Possible" : "Impossible"); } inline void POSSIBLE(bool i = true) { print(i ? "POSSIBLE" : "IMPOSSIBLE"); } /** * @brief Fast IO */ #line 5 "Verify/LC_area_of_union_of_rectangles.test.cpp" #line 2 "DataStructure/lazysegtree.hpp" template<typename M,typename N,M (*f)(M,M),M (*g)(M,N),N (*h)(N,N),M (*m1)(),N (*n1)()> class LazySegmentTree{ int sz,height; vector<M> data; vector<N> lazy; void update(int k){data[k]=f(data[k*2],data[k*2+1]);} void apply(int k,N x){ data[k]=g(data[k],x); if(k<sz)lazy[k]=h(lazy[k],x); } void down(int k){ apply(k*2,lazy[k]); apply(k*2+1,lazy[k]); lazy[k]=n1(); } public: LazySegmentTree(int n=0):LazySegmentTree(vector<M>(n,m1())){} LazySegmentTree(const vector<M>& a){ sz=1,height=0; while(sz<(int)a.size())sz<<=1,height++; data.assign(2*sz,m1()); lazy.assign(sz,n1()); rep(i,0,a.size())data[sz+i]=a[i]; for(int i=sz-1;i;i--)update(i); } void set(int k,M x){ k+=sz; for(int i=height;i;i--)down(k>>i); data[k]=x; for(int i=1;i<=height;i++)update(k>>i); } void update(int L,int R,N x){ if(L>=R)return; L+=sz,R+=sz; for(int i=height;i;i--){ if(((L>>i)<<i)!=L)down(L>>i); if(((R>>i)<<i)!=R)down((R-1)>>i); } int lb=L,rb=R; while(L<R){ if(L&1)apply(L++,x); if(R&1)apply(--R,x); L>>=1; R>>=1; } L=lb,R=rb; for(int i=1;i<=height;i++){ if(((L>>i)<<i)!=L)update(L>>i); if(((R>>i)<<i)!=R)update((R-1)>>i); } } M query(int L,int R){ if(L>=R)return m1(); L+=sz,R+=sz; for(int i=height;i;i--){ if(((L>>i)<<i)!=L)down(L>>i); if(((R>>i)<<i)!=R)down((R-1)>>i); } M lb=m1(),rb=m1(); while(L<R){ if(L&1)lb=f(lb,data[L++]); if(R&1)rb=f(data[--R],rb); L>>=1; R>>=1; } return f(lb,rb); } }; /** * @brief Lazy Segment Tree */ #line 3 "DataStructure/unionrect.hpp" struct UnionInterval{ struct M{ ll len,mi,cnt; }; static M f(M a,M b){ if(a.mi<b.mi)return {a.len+b.len,a.mi,a.cnt}; else if(a.mi>b.mi)return {a.len+b.len,b.mi,b.cnt}; else return {a.len+b.len,a.mi,a.cnt+b.cnt}; } static M g(M a,int b){ return M{a.len,min(INF,a.mi+b),a.cnt}; } static int h(int a,int b){ return a+b; } static M m1(){ return M{0,INF,0}; } static int m2(){return 0;} const int n=0; LazySegmentTree<M,int,f,g,h,m1,m2> seg; UnionInterval(){} UnionInterval(vector<int>& xs):n(xs.size()-1){ vector<M> init(n); rep(i,0,n){ init[i]=M{xs[i+1]-xs[i],0,xs[i+1]-xs[i]}; } seg=LazySegmentTree<M,int,f,g,h,m1,m2>(init); } void add(int L,int R){ seg.update(L,R,1); } void erase(int L,int R){ seg.update(L,R,-1); } ll run(){ auto [len,mi,cnt]=seg.query(0,n); if(mi==0)len-=cnt; return len; } }; struct UnionRect{ vector<int> L,R,D,U; UnionRect(){} void add(int lb,int rb,int db,int ub){ L.push_back(lb); R.push_back(rb); D.push_back(db); U.push_back(ub); } ll run(){ int n=L.size(); vector<int> xs=L,ys=D; xs.insert(xs.end(),ALL(R)); ys.insert(ys.end(),ALL(U)); sort(ALL(xs)); xs.erase(unique(ALL(xs)),xs.end()); sort(ALL(ys)); ys.erase(unique(ALL(ys)),ys.end()); UnionInterval buf=UnionInterval(ys); using P=pair<int,int>; vector in(xs.size(),vector<P>()),out(xs.size(),vector<P>()); rep(i,0,n){ L[i]=lower_bound(ALL(xs),L[i])-xs.begin(); R[i]=lower_bound(ALL(xs),R[i])-xs.begin(); D[i]=lower_bound(ALL(ys),D[i])-ys.begin(); U[i]=lower_bound(ALL(ys),U[i])-ys.begin(); in[L[i]].push_back({D[i],U[i]}); out[R[i]].push_back({D[i],U[i]}); } ll ret=0; rep(i,0,xs.size()-1){ for(auto& [d,u]:in[i])buf.add(d,u); for(auto& [d,u]:out[i])buf.erase(d,u); ret+=buf.run()*(xs[i+1]-xs[i]); } return ret; } }; /** * @brief Area of Union of Rectangles */ #line 7 "Verify/LC_area_of_union_of_rectangles.test.cpp" int main(){ int n; read(n); UnionRect buf; rep(_,0,n){ int L,D,R,U; read(L,D,R,U); buf.add(L,R,D,U); } ll ret=buf.run(); print(ret); return 0; }