test/area_of_union_of_rectangles.test.cpp

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• Last update: 2024-08-31 23:11:05+08:00
• Problem: https://judge.yosupo.jp/problem/area_of_union_of_rectangles

Depends on

• actedmonoid/actedMonoid_addMinCnt.cpp
• default/t.cpp
• ds_problem/area_of_union_of_rectangles.cpp
• segtree/lazySegmentTree.cpp
• segtree/ultraLazySegmentTree.cpp

Code

#define PROBLEM "https://judge.yosupo.jp/problem/area_of_union_of_rectangles"

#include "../default/t.cpp"
#include "../segtree/lazySegmentTree.cpp"
#include "../segtree/ultraLazySegmentTree.cpp"
#include "../actedmonoid/actedMonoid_addMinCnt.cpp"
#include "../ds_problem/area_of_union_of_rectangles.cpp"

signed main() {
  ios::sync_with_stdio(false), cin.tie(NULL);

  int n; cin >> n;
  vector<array<int, 4>> rect(n);
  for(auto &[l, d, r, u] : rect)
    cin >> l >> d >> r >> u;

  cout << area_of_union_of_rectangles<int, ll>(rect) << '\n';

  return 0;
}

#line 1 "test/area_of_union_of_rectangles.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/area_of_union_of_rectangles"

#line 1 "default/t.cpp"
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cctype>
#include <cfenv>
#include <cfloat>
#include <chrono>
#include <cinttypes>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdarg>
#include <cstddef>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <fstream>
#include <functional>
#include <initializer_list>
#include <iomanip>
#include <ios>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <streambuf>
#include <string>
#include <tuple>
#include <type_traits>
#include <variant>
#include <bit>
#include <compare>
#include <concepts>
#include <numbers>
#include <ranges>
#include <span>

#define INT128_MAX (__int128)(((unsigned __int128) 1 << ((sizeof(__int128) * __CHAR_BIT__) - 1)) - 1)
#define INT128_MIN (-INT128_MAX - 1)

#define clock chrono::steady_clock::now().time_since_epoch().count()

using namespace std;

template<class T1, class T2>
ostream& operator<<(ostream& os, const pair<T1, T2> pr) {
  return os << pr.first << ' ' << pr.second;
}
template<class T, size_t N>
ostream& operator<<(ostream& os, const array<T, N> &arr) {
  for(size_t i = 0; T x : arr) {
    os << x;
    if (++i != N) os << ' ';
  }
  return os;
}
template<class T>
ostream& operator<<(ostream& os, const vector<T> &vec) {
  for(size_t i = 0; T x : vec) {
    os << x;
    if (++i != size(vec)) os << ' ';
  }
  return os;
}
template<class T>
ostream& operator<<(ostream& os, const set<T> &s) {
  for(size_t i = 0; T x : s) {
    os << x;
    if (++i != size(s)) os << ' ';
  }
  return os;
}
template<class T1, class T2>
ostream& operator<<(ostream& os, const map<T1, T2> &m) {
  for(size_t i = 0; pair<T1, T2> x : m) {
    os << x;
    if (++i != size(m)) os << ' ';
  }
  return os;
}

#ifdef DEBUG
#define dbg(...) cerr << '(', _do(#__VA_ARGS__), cerr << ") = ", _do2(__VA_ARGS__)
template<typename T> void _do(T &&x) { cerr << x; }
template<typename T, typename ...S> void _do(T &&x, S&&...y) { cerr << x << ", "; _do(y...); }
template<typename T> void _do2(T &&x) { cerr << x << endl; }
template<typename T, typename ...S> void _do2(T &&x, S&&...y) { cerr << x << ", "; _do2(y...); }
#else
#define dbg(...)
#endif

using ll = long long;
using ull = unsigned long long;
using ldb = long double;
using pii = pair<int, int>;
using pll = pair<ll, ll>;

template<typename T> using min_heap = priority_queue<T, vector<T>, greater<T>>;
template<typename T> using max_heap = priority_queue<T>;

template<ranges::forward_range rng, class T = ranges::range_value_t<rng>, class OP = plus<T>>
void pSum(rng &v) {
  if (!v.empty())
    for(T p = v[0]; T &x : v | views::drop(1))
      x = p = OP()(p, x);
}
template<ranges::forward_range rng, class T = ranges::range_value_t<rng>, class OP>
void pSum(rng &v, OP op) {
  if (!v.empty())
    for(T p = v[0]; T &x : v | views::drop(1))
      x = p = op(p, x);
}

template<ranges::forward_range rng>
void Unique(rng &v) {
  ranges::sort(v);
  v.resize(unique(v.begin(), v.end()) - v.begin());
}

template<ranges::random_access_range rng>
rng invPerm(rng p) {
  rng ret = p;
  for(int i = 0; i < ssize(p); i++)
    ret[p[i]] = i;
  return ret;
}

template<ranges::random_access_range rng, ranges::random_access_range rng2>
rng Permute(rng v, rng2 p) {
  rng ret = v;
  for(int i = 0; i < ssize(p); i++)
    ret[p[i]] = v[i];
  return ret;
}

template<bool directed>
vector<vector<int>> readGraph(int n, int m, int base) {
  vector<vector<int>> g(n);
  for(int i = 0; i < m; i++) {
    int u, v; cin >> u >> v;
    u -= base, v -= base;
    g[u].emplace_back(v);
    if constexpr (!directed)
      g[v].emplace_back(u);
  }
  return g;
}

template<class T>
void setBit(T &msk, int bit, bool x) {
  msk = (msk & ~(T(1) << bit)) | (T(x) << bit);
}
template<class T> void flipBit(T &msk, int bit) { msk ^= T(1) << bit; }
template<class T> bool getBit(T msk, int bit) { return msk >> bit & T(1); }

template<class T>
T floorDiv(T a, T b) {
  if (b < 0) a *= -1, b *= -1;
  return a >= 0 ? a / b : (a - b + 1) / b;
}
template<class T>
T ceilDiv(T a, T b) {
  if (b < 0) a *= -1, b *= -1;
  return a >= 0 ? (a + b - 1) / b : a / b;
}

template<class T> bool chmin(T &a, T b) { return a > b ? a = b, 1 : 0; }
template<class T> bool chmax(T &a, T b) { return a < b ? a = b, 1 : 0; }
#line 1 "segtree/lazySegmentTree.cpp"
template<class M, M(*Mid)(), M(*Mop)(const M&, const M&), class T, T(*Tid)(), T(*Top)(const T&, const T&), M(*act)(const M&, const T&)>
struct lazySegmentTree {
  int size;
  vector<M> data;
  vector<T> tag;

  lazySegmentTree(int _size) : size(_size), data(2 * size, Mid()), tag(size, Tid()) {}

  lazySegmentTree(vector<M> init) : size(ssize(init)), data(2 * size, Mid()), tag(size, Tid()) {
    ranges::copy(init, data.begin() + size);
    for(int i = size - 1; i > 0; i--)
      data[i] = Mop(data[i << 1], data[i << 1 | 1]);
  }

  void apply(int i, T x) {
    data[i] = act(data[i], x);
    if (i < size) tag[i] = Top(tag[i], x);
  }

  void push(unsigned i) {
    for(int s = (int)bit_width(i) - 1; s > 0; s--) {
      if (tag[i >> s] != Tid()) {
        apply(i >> (s - 1), tag[i >> s]);
        apply(i >> (s - 1) ^ 1, tag[i >> s]);
        tag[i >> s] = Tid();
      }
    }
  }

  void pull(int i) {
    while(i >>= 1) data[i] = Mop(data[i << 1], data[i << 1 | 1]);
  }

  int trunc(unsigned i) { return i >> countr_zero(i); }

  void set(int i, M x) {
    push(i += size);
    data[i] = x;
    pull(i);
  }

  M get(int i) { push(i += size); return data[i]; }

  void modify(int l, int r, T x) {
    if (l >= r or x == Tid()) return;
    push(trunc(l += size)), push(trunc(r += size) - 1);
    int l0 = l, r0 = r;
    for(; l < r; l >>= 1, r >>= 1) {
      if (l & 1) apply(l++, x);
      if (r & 1) apply(--r, x);
    }
    pull(trunc(l0)), pull(trunc(r0) - 1);
  }

  M query(int l, int r) {
    if (l >= r) return Mid();
    M L = Mid(), R = Mid();
    push(trunc(l += size)), push(trunc(r += size) - 1);
    for(; l < r; l >>= 1, r >>= 1) {
      if (l & 1) L = Mop(L, data[l++]);
      if (r & 1) R = Mop(data[--r], R);
    }
    return Mop(L, R);
  }

  int firstTrue(int i, function<bool(const M&)> f) {
    vector<int> idL, idR;
    push(trunc(i + size)), push(trunc(size << 1) - 1);
    for(int l = i + size, r = size << 1; l < r; l >>= 1, r >>= 1) {
      if (l & 1) idL.emplace_back(l++);
      if (r & 1) idR.emplace_back(--r);
    }
    idL.insert(idL.end(), idR.rbegin(), idR.rend());
    M pre = Mid();
    int v = -1;
    for(int j : idL) {
      if (f(Mop(pre, data[j]))) {
        v = j;
        break;
      } else {
        pre = Mop(pre, data[j]);
      }
    }
    if (v == -1) return size;
    while(v < size) {
      if (tag[v] != Tid()) {
        apply(v << 1, tag[v]);
        apply(v << 1 | 1, tag[v]);
        tag[v] = Tid();
      }
      if (f(Mop(pre, data[v << 1])))
        v = v << 1;
      else
        pre = Mop(pre, data[v << 1]), v = v << 1 | 1;
    }
    return v - size;
  }

  int lastTrue(int i, function<bool(const M&)> f) {
    vector<int> idL, idR;
    push(trunc(size)), push(trunc((i + 1) + size) - 1);
    for(int l = size, r = (i + 1) + size; l < r; l >>= 1, r >>= 1) {
      if (l & 1) idL.emplace_back(l++);
      if (r & 1) idR.emplace_back(--r);
    }
    idR.insert(idR.end(), idL.rbegin(), idL.rend());
    M suf = Mid();
    int v = -1;
    for(int j : idR) {
      if (f(Mop(data[j], suf))) {
        v = j;
        break;
      } else {
        suf = Mop(data[j], suf);
      }
    }
    if (v == -1) return -1;
    while(v < size) {
      if (tag[v] != Tid()) {
        apply(v << 1, tag[v]);
        apply(v << 1 | 1, tag[v]);
        tag[v] = Tid();
      }
      if (f(Mop(data[v << 1 | 1], suf)))
        v = v << 1 | 1;
      else
        suf = Mop(data[v << 1 | 1], suf), v = v << 1;
    }
    return v - size;
  }
};
#line 1 "segtree/ultraLazySegmentTree.cpp"
//#include<segtree/lazySegmentTree.cpp>

template<class AM>
struct ultraLazySegmentTree : lazySegmentTree<typename AM::M, AM::Mid, AM::Mop, typename AM::T, AM::Tid, AM::Top, AM::act> {
  using base = lazySegmentTree<typename AM::M, AM::Mid, AM::Mop, typename AM::T, AM::Tid, AM::Top, AM::act>;
  ultraLazySegmentTree(vector<typename AM::M> init) : base(init) {}
  ultraLazySegmentTree(int size) : base(size) {}
};
#line 1 "actedmonoid/actedMonoid_addMinCnt.cpp"
template<class U>
struct actedMonoid_addMinCnt {
  using M = pair<U, int>;
  static M Mid() { return make_pair(numeric_limits<U>::max(), 0); }
  static M Mop(const M &a, const M &b) { return a.first == b.first ? make_pair(a.first, a.second + b.second) : min(a, b); }
  using T = U;
  static T Tid() { return T(0); }
  static T Top(const T &a, const T &b) { return a + b; }
  static M act(const M &a, const T &b) { return make_pair(a.first + b, a.second); }
};
#line 1 "ds_problem/area_of_union_of_rectangles.cpp"
//#include "segtree/lazySegmentTree.cpp"
//#include "segtree/ultraLazySegmentTree.cpp"
//#include "actedMonoid/actedMonoid_addMinCnt.cpp"

template<class coordinate_type, class answer_type>
answer_type area_of_union_of_rectangles(vector<array<coordinate_type, 4>> rect) {
  vector<coordinate_type> xs(2 * size(rect)), ys(2 * size(rect));
  for(int i = 0; auto [a, b, c, d] : rect)
    tie(xs[2 * i], ys[2 * i], xs[2 * i + 1], ys[2 * i + 1]) = make_tuple(a, b, c, d), i++;
  Unique(xs), Unique(ys);

  vector<array<int, 4>> event(2 * size(rect));
  for(int i = 0; i < ssize(rect); i++) {
    event[2 * i] = {rect[i][0], rect[i][1], rect[i][3], 1};
    event[2 * i + 1] = {rect[i][2], rect[i][1], rect[i][3], -1};
  }
  ranges::sort(event, {}, [](auto &x) { return x[0]; });

  using AM = actedMonoid_addMinCnt<coordinate_type>;
  ultraLazySegmentTree<AM> st([&]() {
    vector<typename AM::M> init(ssize(ys) - 1);
    for(int i = 0; i + 1 < ssize(ys); i++)
      init[i] = make_pair(0, ys[i + 1] - ys[i]);
    return init;
  }());

  auto to_id = [&](int y) { return ranges::lower_bound(ys, y) - ys.begin(); };

  answer_type ans = 0;
  for(int i = 0, j = 0; ; i = j) {
    while(j < ssize(event) and event[i][0] == event[j][0]) j++;
    if (j == ssize(event)) break;
    for(int k = i; k < j; k++) {
      auto [_, l, r, d] = event[k];
      st.modify(to_id(l), to_id(r), d);
    }
    auto [mn, cnt] = st.query(0, st.size);
    answer_type w = event[j][0] - event[i][0];
    ans += (ys.back() - ys[0] - (mn == 0 ? cnt : 0)) * w;
  }

  return ans;
}
#line 8 "test/area_of_union_of_rectangles.test.cpp"

signed main() {
  ios::sync_with_stdio(false), cin.tie(NULL);

  int n; cin >> n;
  vector<array<int, 4>> rect(n);
  for(auto &[l, d, r, u] : rect)
    cin >> l >> d >> r >> u;

  cout << area_of_union_of_rectangles<int, ll>(rect) << '\n';

  return 0;
}

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