Luzhiled's Library

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:heavy_check_mark: test/verify/yosupo-area-of-union-of-rectangles.test.cpp

Depends on

Code

// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/area_of_union_of_rectangles

#include "../../template/template.hpp"

#include "../../other/area-of-union-of-rectangles.hpp"

#include "../../other/scanner.hpp"

int main() {
  Scanner in(stdin);
  int n;
  in.read(n);
  AreaOfUnionOfRectangles<int> sum(n);
  for (int i = 0; i < n; i++) {
    int l, d, r, u;
    in.read(l, d, r, u);
    sum.add_rectangle(l, d, r, u);
  }
  cout << sum.calc<int64>() << endl;
}

#line 1 "test/verify/yosupo-area-of-union-of-rectangles.test.cpp"
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/area_of_union_of_rectangles

#line 1 "template/template.hpp"
#include <bits/stdc++.h>
#if __has_include(<atcoder/all>)
#include <atcoder/all>
#endif

using namespace std;

using int64 = long long;

const int64 infll = (1LL << 62) - 1;
const int inf = (1 << 30) - 1;

struct IoSetup {
  IoSetup() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(10);
    cerr << fixed << setprecision(10);
  }
} iosetup;

template <typename T1, typename T2>
ostream &operator<<(ostream &os, const pair<T1, T2> &p) {
  os << p.first << " " << p.second;
  return os;
}

template <typename T1, typename T2>
istream &operator>>(istream &is, pair<T1, T2> &p) {
  is >> p.first >> p.second;
  return is;
}

template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
  for (int i = 0; i < (int)v.size(); i++) {
    os << v[i] << (i + 1 != v.size() ? " " : "");
  }
  return os;
}

template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
  for (T &in : v) is >> in;
  return is;
}

template <typename T1, typename T2>
inline bool chmax(T1 &a, T2 b) {
  return a < b && (a = b, true);
}

template <typename T1, typename T2>
inline bool chmin(T1 &a, T2 b) {
  return a > b && (a = b, true);
}

template <typename T = int64>
vector<T> make_v(size_t a) {
  return vector<T>(a);
}

template <typename T, typename... Ts>
auto make_v(size_t a, Ts... ts) {
  return vector<decltype(make_v<T>(ts...))>(a, make_v<T>(ts...));
}

template <typename T, typename V>
typename enable_if<is_class<T>::value == 0>::type fill_v(T &t, const V &v) {
  t = v;
}

template <typename T, typename V>
typename enable_if<is_class<T>::value != 0>::type fill_v(T &t, const V &v) {
  for (auto &e : t) fill_v(e, v);
}

template <typename F>
struct FixPoint : F {
  explicit FixPoint(F &&f) : F(std::forward<F>(f)) {}

  template <typename... Args>
  decltype(auto) operator()(Args &&...args) const {
    return F::operator()(*this, std::forward<Args>(args)...);
  }
};

template <typename F>
inline decltype(auto) MFP(F &&f) {
  return FixPoint<F>{std::forward<F>(f)};
}
#line 4 "test/verify/yosupo-area-of-union-of-rectangles.test.cpp"

#line 2 "structure/class/acted-monoid.hpp"

template <typename S2, typename Op, typename E, typename F2, typename Mapping,
          typename Composition, typename Id>
struct LambdaActedMonoid {
  using S = S2;
  using F = F2;

  S op(const S &a, const S &b) const { return _op(a, b); }

  S e() const { return _e(); }

  S mapping(const S &x, const F &f) const { return _mapping(x, f); }

  F composition(const F &f, const F &g) const { return _composition(f, g); }

  F id() const { return _id(); }

  LambdaActedMonoid(Op _op, E _e, Mapping _mapping, Composition _composition,
                    Id _id)
      : _op(_op),
        _e(_e),
        _mapping(_mapping),
        _composition(_composition),
        _id(_id) {}

 private:
  Op _op;

  E _e;

  Mapping _mapping;

  Composition _composition;

  Id _id;
};

template <typename Op, typename E, typename Mapping, typename Composition,
          typename Id>
LambdaActedMonoid(Op _op, E _e, Mapping _mapping, Composition _composition,
                  Id _id)
    -> LambdaActedMonoid<decltype(_e()), Op, E, decltype(_id()), Mapping,
                         Composition, Id>;

/*
struct ActedMonoid {
  using S = ?;
  using F = ?;
  static constexpr S op(const S& a, const S& b) {}
  static constexpr S e() {}
  static constexpr S mapping(const S &x, const F &f) {}
  static constexpr F composition(const F &f, const F &g) {}
  static constexpr F id() {}
};
*/
#line 2 "structure/segment-tree/lazy-segment-tree.hpp"

template <typename ActedMonoid>
struct LazySegmentTree {
  using S = typename ActedMonoid::S;
  using F = typename ActedMonoid::F;

 private:
  ActedMonoid m;

  int n{}, sz{}, height{};

  vector<S> data;

  vector<F> lazy;

  inline void update(int k) {
    data[k] = m.op(data[2 * k + 0], data[2 * k + 1]);
  }

  inline void all_apply(int k, const F &x) {
    data[k] = m.mapping(data[k], x);
    if (k < sz) lazy[k] = m.composition(lazy[k], x);
  }

  inline void propagate(int k) {
    if (lazy[k] != m.id()) {
      all_apply(2 * k + 0, lazy[k]);
      all_apply(2 * k + 1, lazy[k]);
      lazy[k] = m.id();
    }
  }

 public:
  LazySegmentTree() = default;

  explicit LazySegmentTree(ActedMonoid m, int n) : m(m), n(n) {
    sz = 1;
    height = 0;
    while (sz < n) sz <<= 1, height++;
    data.assign(2 * sz, m.e());
    lazy.assign(2 * sz, m.id());
  }

  explicit LazySegmentTree(ActedMonoid m, const vector<S> &v)
      : LazySegmentTree(m, v.size()) {
    build(v);
  }

  void build(const vector<S> &v) {
    assert(n == (int)v.size());
    for (int k = 0; k < n; k++) data[k + sz] = v[k];
    for (int k = sz - 1; k > 0; k--) update(k);
  }

  void set(int k, const S &x) {
    k += sz;
    for (int i = height; i > 0; i--) propagate(k >> i);
    data[k] = x;
    for (int i = 1; i <= height; i++) update(k >> i);
  }

  S get(int k) {
    k += sz;
    for (int i = height; i > 0; i--) propagate(k >> i);
    return data[k];
  }

  S operator[](int k) { return get(k); }

  S prod(int l, int r) {
    if (l >= r) return m.e();
    l += sz;
    r += sz;
    for (int i = height; i > 0; i--) {
      if (((l >> i) << i) != l) propagate(l >> i);
      if (((r >> i) << i) != r) propagate((r - 1) >> i);
    }
    S L = m.e(), R = m.e();
    for (; l < r; l >>= 1, r >>= 1) {
      if (l & 1) L = m.op(L, data[l++]);
      if (r & 1) R = m.op(data[--r], R);
    }
    return m.op(L, R);
  }

  S all_prod() const { return data[1]; }

  void apply(int k, const F &f) {
    k += sz;
    for (int i = height; i > 0; i--) propagate(k >> i);
    data[k] = m.mapping(data[k], f);
    for (int i = 1; i <= height; i++) update(k >> i);
  }

  void apply(int l, int r, const F &f) {
    if (l >= r) return;
    l += sz;
    r += sz;
    for (int i = height; i > 0; i--) {
      if (((l >> i) << i) != l) propagate(l >> i);
      if (((r >> i) << i) != r) propagate((r - 1) >> i);
    }
    {
      int l2 = l, r2 = r;
      for (; l < r; l >>= 1, r >>= 1) {
        if (l & 1) all_apply(l++, f);
        if (r & 1) all_apply(--r, f);
      }
      l = l2, r = r2;
    }
    for (int i = 1; i <= height; i++) {
      if (((l >> i) << i) != l) update(l >> i);
      if (((r >> i) << i) != r) update((r - 1) >> i);
    }
  }

  template <typename C>
  int find_first(int l, const C &check) {
    if (l >= n) return n;
    l += sz;
    for (int i = height; i > 0; i--) propagate(l >> i);
    S sum = m.e();
    do {
      while ((l & 1) == 0) l >>= 1;
      if (check(m.op(sum, data[l]))) {
        while (l < sz) {
          propagate(l);
          l <<= 1;
          auto nxt = m.op(sum, data[l]);
          if (not check(nxt)) {
            sum = nxt;
            l++;
          }
        }
        return l + 1 - sz;
      }
      sum = m.op(sum, data[l++]);
    } while ((l & -l) != l);
    return n;
  }

  template <typename C>
  int find_last(int r, const C &check) {
    if (r <= 0) return -1;
    r += sz;
    for (int i = height; i > 0; i--) propagate((r - 1) >> i);
    S sum = m.e();
    do {
      r--;
      while (r > 1 and (r & 1)) r >>= 1;
      if (check(m.op(data[r], sum))) {
        while (r < sz) {
          propagate(r);
          r = (r << 1) + 1;
          auto nxt = m.op(data[r], sum);
          if (not check(nxt)) {
            sum = nxt;
            r--;
          }
        }
        return r - sz;
      }
      sum = m.op(data[r], sum);
    } while ((r & -r) != r);
    return -1;
  }
};
#line 2 "other/area-of-union-of-rectangles.hpp"

template <typename T>
struct AreaOfUnionOfRectangles {
 private:
  struct Rectangle {
    T l, d, r, u;
  };
  vector<Rectangle> rectangles;

 public:
  AreaOfUnionOfRectangles() = default;
  explicit AreaOfUnionOfRectangles(int n) : rectangles{} {
    rectangles.reserve(n);
  }
  void add_rectangle(T l, T d, T r, T u) {
    assert(l < r and d < u);
    rectangles.emplace_back(Rectangle{l, d, r, u});
  }

  template <typename T2>
  T2 calc() const {
    int n = (int)rectangles.size();
    if (n == 0) return 0;

    vector<T> ys;
    vector<tuple<T, int, int>> xs;
    ys.reserve(n + n);
    xs.reserve(n + n);
    for (int i = 0; i < n; i++) {
      auto &rect = rectangles[i];
      ys.emplace_back(rect.d);
      ys.emplace_back(rect.u);
      xs.emplace_back(rect.l, i, +1);
      xs.emplace_back(rect.r, i, -1);
    }
    sort(ys.begin(), ys.end());
    ys.erase(unique(ys.begin(), ys.end()), ys.end());
    sort(xs.begin(), xs.end());
    vector<int> to_d(n), to_u(n);
    for (int i = 0; i < n; i++) {
      auto &rect = rectangles[i];
      to_d[i] = lower_bound(ys.begin(), ys.end(), rect.d) - ys.begin();
      to_u[i] = lower_bound(ys.begin(), ys.end(), rect.u) - ys.begin();
    }
    using pi = pair<int, T>;
    auto f = [](const pi &a, const pi &b) -> pi {
      if (a.first < b.first) return a;
      if (b.first < a.first) return b;
      return {a.first, a.second + b.second};
    };
    auto e = [&]() -> pi { return {n + 1, 0}; };
    auto g = [](const pi &a, int b) -> pi { return {a.first + b, a.second}; };
    auto h = [](int a, int b) -> int { return a + b; };
    auto id = []() { return 0; };
    vector<pi> vs(ys.size() - 1);
    for (int i = 0; i + 1 < ys.size(); i++) {
      vs[i] = {0, ys[i + 1] - ys[i]};
    }
    LazySegmentTree seg(LambdaActedMonoid(f, e, g, h, id), vs);
    T2 ret = 0;
    T total = ys.back() - ys.front();
    for (int i = 0; i + 1 < n + n; i++) {
      auto &[k, j, d] = xs[i];
      seg.apply(to_d[j], to_u[j], d);
      auto [v, cnt] = seg.all_prod();
      T2 dy = total - (v == 0 ? cnt : 0);
      T2 dx = get<0>(xs[i + 1]) - k;
      ret += dy * dx;
    }
    return ret;
  }
};
#line 6 "test/verify/yosupo-area-of-union-of-rectangles.test.cpp"

#line 1 "other/scanner.hpp"
/**
 * @brief Scanner(高速入力)
 */
struct Scanner {
 public:
  explicit Scanner(FILE *fp) : fp(fp) {}

  template <typename T, typename... E>
  void read(T &t, E &...e) {
    read_single(t);
    read(e...);
  }

 private:
  static constexpr size_t line_size = 1 << 16;
  static constexpr size_t int_digits = 20;
  char line[line_size + 1] = {};
  FILE *fp = nullptr;
  char *st = line;
  char *ed = line;

  void read() {}

  static inline bool is_space(char c) { return c <= ' '; }

  void reread() {
    ptrdiff_t len = ed - st;
    memmove(line, st, len);
    char *tmp = line + len;
    ed = tmp + fread(tmp, 1, line_size - len, fp);
    *ed = 0;
    st = line;
  }

  void skip_space() {
    while (true) {
      if (st == ed) reread();
      while (*st && is_space(*st)) ++st;
      if (st != ed) return;
    }
  }

  template <typename T, enable_if_t<is_integral<T>::value, int> = 0>
  void read_single(T &s) {
    skip_space();
    if (st + int_digits >= ed) reread();
    bool neg = false;
    if (is_signed<T>::value && *st == '-') {
      neg = true;
      ++st;
    }
    typename make_unsigned<T>::type y = *st++ - '0';
    while (*st >= '0') {
      y = 10 * y + *st++ - '0';
    }
    s = (neg ? -y : y);
  }

  template <typename T, enable_if_t<is_same<T, string>::value, int> = 0>
  void read_single(T &s) {
    s = "";
    skip_space();
    while (true) {
      char *base = st;
      while (*st && !is_space(*st)) ++st;
      s += string(base, st);
      if (st != ed) return;
      reread();
    }
  }

  template <typename T>
  void read_single(vector<T> &s) {
    for (auto &d : s) read(d);
  }
};
#line 8 "test/verify/yosupo-area-of-union-of-rectangles.test.cpp"

int main() {
  Scanner in(stdin);
  int n;
  in.read(n);
  AreaOfUnionOfRectangles<int> sum(n);
  for (int i = 0; i < n; i++) {
    int l, d, r, u;
    in.read(l, d, r, u);
    sum.add_rectangle(l, d, r, u);
  }
  cout << sum.calc<int64>() << endl;
}

Test cases

Env Name Status Elapsed Memory
g++ edge_bound_00 :heavy_check_mark: AC 665 ms 63 MB
g++ edge_bound_01 :heavy_check_mark: AC 675 ms 63 MB
g++ edge_bound_02 :heavy_check_mark: AC 676 ms 63 MB
g++ edge_bound_03 :heavy_check_mark: AC 687 ms 63 MB
g++ edge_bound_04 :heavy_check_mark: AC 650 ms 63 MB
g++ example_00 :heavy_check_mark: AC 5 ms 4 MB
g++ max_random_00 :heavy_check_mark: AC 733 ms 63 MB
g++ max_random_01 :heavy_check_mark: AC 767 ms 63 MB
g++ max_random_02 :heavy_check_mark: AC 781 ms 63 MB
g++ max_random_03 :heavy_check_mark: AC 793 ms 63 MB
g++ max_random_04 :heavy_check_mark: AC 819 ms 63 MB
g++ random_00 :heavy_check_mark: AC 590 ms 55 MB
g++ random_01 :heavy_check_mark: AC 722 ms 60 MB
g++ random_02 :heavy_check_mark: AC 67 ms 10 MB
g++ random_03 :heavy_check_mark: AC 639 ms 58 MB
g++ random_04 :heavy_check_mark: AC 390 ms 47 MB
g++ small_00 :heavy_check_mark: AC 6 ms 4 MB
g++ small_01 :heavy_check_mark: AC 5 ms 4 MB
g++ small_02 :heavy_check_mark: AC 5 ms 4 MB
g++ small_03 :heavy_check_mark: AC 6 ms 4 MB
g++ small_04 :heavy_check_mark: AC 5 ms 4 MB
clang++ edge_bound_00 :heavy_check_mark: AC 622 ms 63 MB
clang++ edge_bound_01 :heavy_check_mark: AC 611 ms 63 MB
clang++ edge_bound_02 :heavy_check_mark: AC 605 ms 63 MB
clang++ edge_bound_03 :heavy_check_mark: AC 605 ms 63 MB
clang++ edge_bound_04 :heavy_check_mark: AC 598 ms 63 MB
clang++ example_00 :heavy_check_mark: AC 5 ms 4 MB
clang++ max_random_00 :heavy_check_mark: AC 694 ms 63 MB
clang++ max_random_01 :heavy_check_mark: AC 686 ms 63 MB
clang++ max_random_02 :heavy_check_mark: AC 687 ms 63 MB
clang++ max_random_03 :heavy_check_mark: AC 713 ms 63 MB
clang++ max_random_04 :heavy_check_mark: AC 695 ms 63 MB
clang++ random_00 :heavy_check_mark: AC 524 ms 55 MB
clang++ random_01 :heavy_check_mark: AC 639 ms 60 MB
clang++ random_02 :heavy_check_mark: AC 62 ms 10 MB
clang++ random_03 :heavy_check_mark: AC 569 ms 58 MB
clang++ random_04 :heavy_check_mark: AC 346 ms 47 MB
clang++ small_00 :heavy_check_mark: AC 6 ms 4 MB
clang++ small_01 :heavy_check_mark: AC 5 ms 4 MB
clang++ small_02 :heavy_check_mark: AC 5 ms 4 MB
clang++ small_03 :heavy_check_mark: AC 6 ms 4 MB
clang++ small_04 :heavy_check_mark: AC 5 ms 4 MB
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