:heavy_check_mark: verify/segment-tree/LC_rectangle_add_point_get.dual_segment_tree_2d.test.cpp

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Code

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

#include "template/template.hpp"
#include "segment-tree/dual-segment-tree-2d.hpp"

int main() {
  int n, q;
  in(n, q);
  vector<array<int, 5>> rects(n);
  rep(i, 0, n) {
    int l, d, r, u, w;
    in(l, d, r, u, w);
    rects[i] = {l, d, r, u, w};
  }

  vector<array<int, 6>> qs(q);
  vector<pair<int, int>> points;
  rep(i, 0, q) {
    int t;
    in(t);
    if (t == 0) {
      int l, d, r, u, w;
      in(l, d, r, u, w);
      qs[i] = {0, l, d, r, u, w};
    } else {
      int x, y;
      in(x, y);
      qs[i] = {1, x, y, 0, 0, 0};
      points.push_back({x, y});
    }
  }

  DualSegmentTree2D<AddMonoid<long long>> seg(points);
  for (auto [l, d, r, u, w] : rects) seg.apply(l, r, d, u, w);

  for (auto query : qs) {
    if (query[0] == 0) {
      auto [_, l, d, r, u, w] = query;
      seg.apply(l, r, d, u, w);
    } else {
      auto [_, x, y, __, ___, ____] = query;
      out(seg.get(x, y));
    }
  }
}
#line 1 "verify/segment-tree/LC_rectangle_add_point_get.dual_segment_tree_2d.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/rectangle_add_point_get"

#line 2 "template/template.hpp"
#include <bits/stdc++.h>
using namespace std;

#line 2 "template/macro.hpp"
#define rep(i, a, b) for (int i = (a); i < (int)(b); i++)
#define rrep(i, a, b) for (int i = (int)(b) - 1; i >= (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())
#define YN(b) cout << ((b) ? "YES" : "NO") << "\n";
#define Yn(b) cout << ((b) ? "Yes" : "No") << "\n";
#define yn(b) cout << ((b) ? "yes" : "no") << "\n";
#line 6 "template/template.hpp"

#line 2 "template/util.hpp"
using uint = unsigned int;
using ll = long long int;
using ull = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;
template <class T>
using priority_queue_asc = priority_queue<T, vector<T>, greater<T>>;

template <class T, class S = T>
S SUM(const vector<T>& a) {
  return accumulate(ALL(a), S(0));
}
template <class T1, class T2>
inline bool chmin(T1& a, T2 b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
template <class T1, class T2>
inline bool chmax(T1& a, T2 b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
template <class T1, class T2>
inline bool chmin_opt(optional<T1>& a, T2 b) {
  if (!a || a > b) {
    a = b;
    return true;
  }
  return false;
}
template <class T1, class T2>
inline bool chmax_opt(optional<T1>& a, T2 b) {
  if (!a || a < b) {
    a = b;
    return true;
  }
  return false;
}

template <class T>
int popcnt(T x) {
  return __builtin_popcountll(x);
}
template <class T>
int topbit(T x) {
  return (x == 0 ? -1 : 63 - __builtin_clzll(x));
}
template <class T>
int lowbit(T x) {
  return (x == 0 ? -1 : __builtin_ctzll(x));
}
#line 8 "template/template.hpp"

#line 2 "template/inout.hpp"
struct Fast {
  Fast() {
    cin.tie(nullptr);
    ios_base::sync_with_stdio(false);
    cout << fixed << setprecision(15);
  }
} fast;

ostream& operator<<(ostream& os, __uint128_t x) {
  char buf[40];
  size_t k = 0;
  while (x > 0) buf[k++] = (char)(x % 10 + '0'), x /= 10;
  if (k == 0) buf[k++] = '0';
  while (k) os << buf[--k];
  return os;
}
ostream& operator<<(ostream& os, __int128_t x) {
  return x < 0 ? (os << '-' << (__uint128_t)(-x)) : (os << (__uint128_t)x);
}
template <class T, size_t N>
ostream& operator<<(ostream& os, const array<T, N>& a);
template <class T1, class T2>
istream& operator>>(istream& is, pair<T1, T2>& p) {
  return is >> p.first >> p.second;
}
template <class T1, class T2>
ostream& operator<<(ostream& os, const pair<T1, T2>& p) {
  return os << p.first << " " << p.second;
}
template <class T>
istream& operator>>(istream& is, vector<T>& a) {
  for (auto& v : a) is >> v;
  return is;
}
template <class T>
ostream& operator<<(ostream& os, const vector<T>& a) {
  for (auto it = a.begin(); it != a.end();) {
    os << *it;
    if (++it != a.end()) os << " ";
  }
  return os;
}
template <class T, size_t N>
ostream& operator<<(ostream& os, const array<T, N>& a) {
  for (auto it = a.begin(); it != a.end();) {
    os << *it;
    if (++it != a.end()) os << " ";
  }
  return os;
}
template <class T>
ostream& operator<<(ostream& os, const set<T>& st) {
  os << "{";
  for (auto it = st.begin(); it != st.end();) {
    os << *it;
    if (++it != st.end()) os << ",";
  }
  os << "}";
  return os;
}
template <class T1, class T2>
ostream& operator<<(ostream& os, const map<T1, T2>& mp) {
  os << "{";
  for (auto it = mp.begin(); it != mp.end();) {
    os << it->first << ":" << it->second;
    if (++it != mp.end()) os << ",";
  }
  os << "}";
  return os;
}

void in() {}
template <typename T, class... U>
void in(T& t, U&... u) {
  cin >> t;
  in(u...);
}
template <class... T>
void in_zip(int n, T&... t) {
  assert(n >= 0 && ((size(t) >= static_cast<size_t>(n)) && ...));
  for (int i = 0; i < n; i++) in(t[i]...);
}
void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T& t, const U&... u) {
  cout << t;
  if (sizeof...(u)) cout << sep;
  out(u...);
}
template <class T, class U>
void out_opt(const optional<T>& opt, const U& fallback, ostream& os = cout) {
  if (opt.has_value())
    os << opt.value();
  else
    os << fallback;
  os << "\n";
}
template <class T, class U>
void out_opt(const vector<optional<T>>& vec, const U& fallback, ostream& os = cout) {
  for (auto it = vec.begin(); it != vec.end();) {
    if ((*it).has_value())
      os << (*it).value();
    else
      os << fallback;
    if (++it != vec.end()) os << " ";
  }
  os << "\n";
}

namespace IO {
template <class T, class... U>
T read(U&&... u) {
  T t = T(forward<U>(u)...);
  in(t);
  return t;
}
namespace Graph {
vector<vector<int>> unweighted(int n, int m, bool directed = false, int offset = 1) {
  vector<vector<int>> g(n);
  for (int i = 0; i < m; i++) {
    int u, v;
    cin >> u >> v;
    u -= offset, v -= offset;
    g[u].push_back(v);
    if (!directed) g[v].push_back(u);
  }
  return g;
}
template <class T>
vector<vector<pair<int, T>>> weighted(int n, int m, bool directed = false, int offset = 1) {
  vector<vector<pair<int, T>>> g(n);
  for (int i = 0; i < m; i++) {
    int u, v;
    T w;
    cin >> u >> v >> w;
    u -= offset, v -= offset;
    g[u].push_back({v, w});
    if (!directed) g[v].push_back({u, w});
  }
  return g;
}
}  // namespace Graph
namespace Tree {
vector<vector<int>> unweighted(int n, bool directed = false, int offset = 1) {
  return Graph::unweighted(n, n - 1, directed, offset);
}
template <class T>
vector<vector<pair<int, T>>> weighted(int n, bool directed = false, int offset = 1) {
  return Graph::weighted<T>(n, n - 1, directed, offset);
}
vector<vector<int>> rooted(int n, bool to_root = true, bool to_leaf = true, int offset = 1) {
  vector<vector<int>> g(n);
  for (int i = 1; i < n; i++) {
    int p;
    cin >> p;
    p -= offset;
    if (to_root) g[i].push_back(p);
    if (to_leaf) g[p].push_back(i);
  }
  return g;
}
}  // namespace Tree
}  // namespace IO
#line 10 "template/template.hpp"

#line 2 "template/debug.hpp"
#ifdef LOCAL
#define debug 1
#define show(...) _show(0, #__VA_ARGS__, __VA_ARGS__)
#else
#define debug 0
#define show(...) true
#endif
template <class T>
void _show(int, T) {
  cerr << '\n';
}
template <class T1, class T2, class... 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...);
}
#line 2 "segment-tree/dual-segment-tree-2d.hpp"

#line 2 "algebraic-structure/util.hpp"
#ifdef __cpp_concepts
#define REQUIRES(...) requires __VA_ARGS__
#else
#define REQUIRES(...)
#endif
#line 3 "algebraic-structure/magma.hpp"

#ifdef __cpp_concepts
template <class M>
concept Magma = requires(typename M::value_type x, typename M::value_type y) {
  typename M::value_type;
  { M::op(x, y) } -> same_as<typename M::value_type>;
};
#endif

template <class T>
struct AddMagma {
  using value_type = T;
  static T op(T x, T y) { return x + y; }
};
template <class T>
struct MulMagma {
  using value_type = T;
  static T op(T x, T y) { return x * y; }
};
template <class T, T id>
struct MaxMagma {
  using value_type = T;
  static T op(T x, T y) { return x > y ? x : y; }
};
template <class T, T id>
struct MinMagma {
  using value_type = T;
  static T op(T x, T y) { return x < y ? x : y; }
};
#line 3 "algebraic-structure/monoid.hpp"

#ifdef __cpp_concepts
template <class M>
concept Monoid = Magma<M> && requires {
  { M::e() } -> same_as<typename M::value_type>;
};
#endif

template <class T>
struct AddMonoid {
  using value_type = T;
  static T op(T x, T y) { return x + y; }
  static T e() { return T(0); }
};
template <class T>
struct MulMonoid {
  using value_type = T;
  static T op(T x, T y) { return x * y; }
  static T e() { return T(1); }
};
template <class T, T id>
struct MaxMonoid {
  using value_type = T;
  static T op(T x, T y) { return x > y ? x : y; }
  static T e() { return id; }
};
template <class T, T id>
struct MinMonoid {
  using value_type = T;
  static T op(T x, T y) { return x < y ? x : y; }
  static T e() { return id; }
};
#line 3 "segment-tree/dual-segment-tree.hpp"

template <class M>
REQUIRES(Monoid<M>)
struct DualSegmentTree {
  using F = typename M::value_type;

 private:
  int _n, size, log;
  vector<F> lz;

 public:
  DualSegmentTree() : DualSegmentTree(0) {}
  explicit DualSegmentTree(int n) : DualSegmentTree(vector<F>(n, M::e())) {}
  explicit DualSegmentTree(const vector<F> &v) : _n(int(v.size())) {
    size = 1, log = 0;
    while (size < _n) size <<= 1, log++;
    lz = vector<F>(2 * size, M::e());
    for (int i = 0; i < _n; i++) lz[size + i] = v[i];
  }
  void set(int p, F f) {
    assert(0 <= p && p < _n);
    p += size;
    for (int i = log; i > 0; i--) push(p >> i);
    lz[p] = f;
  }
  F get(int p) {
    assert(0 <= p && p < _n);
    p += size;
    for (int i = log; i > 0; i--) push(p >> i);
    return lz[p];
  }
  vector<F> all_get() {
    for (int i = 1; i < size; i++) push(i);
    return vector<F>(lz.begin() + size, lz.begin() + (size + _n));
  }
  void apply(int p, F f) {
    assert(0 <= p && p < _n);
    p += size;
    for (int i = log; i > 0; i--) push(p >> i);
    inner_apply(p, f);
  }
  void apply(int l, int r, F f) {
    if (l >= r) return;
    assert(0 <= l && l <= r && r <= _n);
    l += size, r += size;
    for (int i = log; i > 0; i--) {
      if (((l >> i) << i) != l) push(l >> i);
      if (((r >> i) << i) != r) push((r - 1) >> i);
    }
    while (l < r) {
      if ((l & 1) != 0) inner_apply(l++, f);
      if ((r & 1) != 0) inner_apply(--r, f);
      l >>= 1, r >>= 1;
    }
  }

 private:
  void push(int k) {
    inner_apply(2 * k, lz[k]);
    inner_apply(2 * k + 1, lz[k]);
    lz[k] = M::e();
  }
  void inner_apply(int k, F f) { lz[k] = M::op(f, lz[k]); }
};

/**
 * @brief Dual Segment Tree
 * @docs docs/segment-tree/dual-segment-tree.md
 */
#line 4 "segment-tree/dual-segment-tree-2d.hpp"

// M: commutative monoid
template <class M>
REQUIRES(Monoid<M>)
struct DualSegmentTree2D {
  using F = typename M::value_type;

  DualSegmentTree2D() : n(0), size(1) {}
  explicit DualSegmentTree2D(const vector<pair<int, int>>& points) { build(points); }

  void build(vector<pair<int, int>> points) {
    sort(points.begin(), points.end());
    points.erase(unique(points.begin(), points.end()), points.end());
    ps = points;

    xs.clear();
    xs.reserve(ps.size());
    for (auto [x, _] : ps) xs.push_back(x);
    xs.erase(unique(xs.begin(), xs.end()), xs.end());

    n = xs.size();
    size = 1;
    while (size < n) size <<= 1;
    ys.assign(2 * size, {});
    seg.assign(2 * size, {});

    for (auto [x, y] : ps) {
      int k = lower_bound(xs.begin(), xs.end(), x) - xs.begin();
      for (k += size; k > 0; k >>= 1) ys[k].push_back(y);
    }
    for (int k = 1; k < 2 * size; k++) {
      sort(ys[k].begin(), ys[k].end());
      ys[k].erase(unique(ys[k].begin(), ys[k].end()), ys[k].end());
      seg[k] = DualSegmentTree<M>((int)ys[k].size());
    }
  }

  bool contains(int x, int y) const {
    auto it = lower_bound(ps.begin(), ps.end(), make_pair(x, y));
    return it != ps.end() && *it == make_pair(x, y);
  }

  void apply(int xl, int xr, int yl, int yr, F f) {
    if (xl >= xr || yl >= yr) return;
    int l = lower_bound(xs.begin(), xs.end(), xl) - xs.begin();
    int r = lower_bound(xs.begin(), xs.end(), xr) - xs.begin();
    for (l += size, r += size; l < r; l >>= 1, r >>= 1) {
      if (l & 1) apply_node(l++, yl, yr, f);
      if (r & 1) apply_node(--r, yl, yr, f);
    }
  }

  F get(int x, int y) {
    int k = leaf(x, y);
    F ret = M::e();
    while (k > 0) {
      ret = M::op(get_node(k, y), ret);
      k >>= 1;
    }
    return ret;
  }

  int size_x() const { return n; }
  int size_points() const { return ps.size(); }

 private:
  int n, size;
  vector<pair<int, int>> ps;
  vector<int> xs;
  vector<vector<int>> ys;
  vector<DualSegmentTree<M>> seg;

  int leaf(int x, int y) const {
    auto it = lower_bound(ps.begin(), ps.end(), make_pair(x, y));
    assert(it != ps.end() && *it == make_pair(x, y));
    int k = lower_bound(xs.begin(), xs.end(), x) - xs.begin();
    return k + size;
  }

  void apply_node(int k, int yl, int yr, F f) {
    int l = lower_bound(ys[k].begin(), ys[k].end(), yl) - ys[k].begin();
    int r = lower_bound(ys[k].begin(), ys[k].end(), yr) - ys[k].begin();
    seg[k].apply(l, r, f);
  }

  F get_node(int k, int y) {
    int i = lower_bound(ys[k].begin(), ys[k].end(), y) - ys[k].begin();
    assert(i < (int)ys[k].size() && ys[k][i] == y);
    return seg[k].get(i);
  }
};

/**
 * @brief 2D Dual Segment Tree
 * @docs docs/segment-tree/dual-segment-tree-2d.md
 */
#line 5 "verify/segment-tree/LC_rectangle_add_point_get.dual_segment_tree_2d.test.cpp"

int main() {
  int n, q;
  in(n, q);
  vector<array<int, 5>> rects(n);
  rep(i, 0, n) {
    int l, d, r, u, w;
    in(l, d, r, u, w);
    rects[i] = {l, d, r, u, w};
  }

  vector<array<int, 6>> qs(q);
  vector<pair<int, int>> points;
  rep(i, 0, q) {
    int t;
    in(t);
    if (t == 0) {
      int l, d, r, u, w;
      in(l, d, r, u, w);
      qs[i] = {0, l, d, r, u, w};
    } else {
      int x, y;
      in(x, y);
      qs[i] = {1, x, y, 0, 0, 0};
      points.push_back({x, y});
    }
  }

  DualSegmentTree2D<AddMonoid<long long>> seg(points);
  for (auto [l, d, r, u, w] : rects) seg.apply(l, r, d, u, w);

  for (auto query : qs) {
    if (query[0] == 0) {
      auto [_, l, d, r, u, w] = query;
      seg.apply(l, r, d, u, w);
    } else {
      auto [_, x, y, __, ___, ____] = query;
      out(seg.get(x, y));
    }
  }
}
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