Dynamic Point Add Rectangle Sum (other/dynamic-point-add-rectangle-sum.hpp)

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• Last update: 2024-04-27 01:27:28+09:00
• Include: #include "other/dynamic-point-add-rectangle-sum.hpp"

Depends on

• Static Point Add Rectangle Sum (other/static-point-add-rectangle-sum.hpp)
• Binary-Indexed-Tree(BIT) (structure/others/binary-indexed-tree.hpp)

Verified with

• test/verify/yosupo-point-add-rectangle-sum-3.test.cpp

Code

#include "static-point-add-rectangle-sum.hpp"

/**
 * @brief Dynamic Point Add Rectangle Sum
 */
template <typename T, typename C>
struct DynamicPointAddRectangleSum {
  using StaticRectangleSumSolver = StaticPointAddRectangleSum<T, C>;

  static_assert(is_integral<T>::value,
                "template parameter T must be integral type");

  struct Point {
    T x, y;
    C w;
  };

  struct Query {
    T l, d, r, u;
  };

  vector<variant<Point, Query> > queries;

  DynamicPointAddRectangleSum() = default;

  DynamicPointAddRectangleSum(int q) { queries.reserve(q); }

  void add_point(T x, T y, C w) { queries.emplace_back(Point{x, y, w}); }

  // tatal weight of [l, r) * [d, u) points
  void add_query(T l, T d, T r, T u) {
    queries.emplace_back(Query{l, d, r, u});
  }

  vector<C> calculate_queries() {
    int q = (int)queries.size();
    vector<int> rev(q);
    int sz = 0;
    for (int i = 0; i < q; i++) {
      if (holds_alternative<Query>(queries[i])) {
        rev[i] = sz++;
      }
    }
    vector<C> ans(sz);
    queue<pair<int, int> > range;
    range.emplace(0, q);
    while (not range.empty()) {
      auto [l, r] = range.front();
      range.pop();
      int m = (l + r) >> 1;
      StaticRectangleSumSolver solver;
      for (int k = l; k < m; k++) {
        if (holds_alternative<Point>(queries[k])) {
          auto &point = get<Point>(queries[k]);
          solver.add_point(point.x, point.y, point.w);
        }
      }
      for (int k = m; k < r; k++) {
        if (holds_alternative<Query>(queries[k])) {
          auto &query = get<Query>(queries[k]);
          solver.add_query(query.l, query.d, query.r, query.u);
        }
      }
      auto sub = solver.calculate_queries();
      for (int k = m, t = 0; k < r; k++) {
        if (holds_alternative<Query>(queries[k])) {
          ans[rev[k]] += sub[t++];
        }
      }
      if (l + 1 < m) range.emplace(l, m);
      if (m + 1 < r) range.emplace(m, r);
    }
    return ans;
  }
};

#line 1 "structure/others/binary-indexed-tree.hpp"
/**
 * @brief Binary-Indexed-Tree(BIT)
 *
 */
template <typename T>
struct BinaryIndexedTree {
 private:
  int n;
  vector<T> data;

 public:
  BinaryIndexedTree() = default;

  explicit BinaryIndexedTree(int n) : n(n) { data.assign(n + 1, T()); }

  explicit BinaryIndexedTree(const vector<T> &v)
      : BinaryIndexedTree((int)v.size()) {
    build(v);
  }

  void build(const vector<T> &v) {
    assert(n == (int)v.size());
    for (int i = 1; i <= n; i++) data[i] = v[i - 1];
    for (int i = 1; i <= n; i++) {
      int j = i + (i & -i);
      if (j <= n) data[j] += data[i];
    }
  }

  void apply(int k, const T &x) {
    for (++k; k <= n; k += k & -k) data[k] += x;
  }

  T prod(int r) const {
    T ret = T();
    for (; r > 0; r -= r & -r) ret += data[r];
    return ret;
  }

  T prod(int l, int r) const { return prod(r) - prod(l); }

  int lower_bound(T x) const {
    int i = 0;
    for (int k = 1 << (__lg(n) + 1); k > 0; k >>= 1) {
      if (i + k <= n && data[i + k] < x) {
        x -= data[i + k];
        i += k;
      }
    }
    return i;
  }

  int upper_bound(T x) const {
    int i = 0;
    for (int k = 1 << (__lg(n) + 1); k > 0; k >>= 1) {
      if (i + k <= n && data[i + k] <= x) {
        x -= data[i + k];
        i += k;
      }
    }
    return i;
  }
};
#line 2 "other/static-point-add-rectangle-sum.hpp"

/**
 * @brief Static Point Add Rectangle Sum
 */
template <typename T, typename C>
struct StaticPointAddRectangleSum {
  using BIT = BinaryIndexedTree<C>;

  static_assert(is_integral<T>::value,
                "template parameter T must be integral type");

  struct Point {
    T x, y;
    C w;
  };

  struct Query {
    T l, d, r, u;
  };

  vector<Point> points;
  vector<Query> queries;

  StaticPointAddRectangleSum() = default;

  StaticPointAddRectangleSum(int n, int q) {
    points.reserve(n);
    queries.reserve(q);
  }

  void add_point(T x, T y, C w) { points.emplace_back(Point{x, y, w}); }

  // tatal weight of [l, r) * [d, u) points
  void add_query(T l, T d, T r, T u) {
    queries.emplace_back(Query{l, d, r, u});
  }

  vector<C> calculate_queries() {
    int n = (int)points.size();
    int q = (int)queries.size();
    vector<C> ans(q);
    if (points.empty() or queries.empty()) {
      return ans;
    }
    sort(points.begin(), points.end(),
         [](const Point &a, const Point &b) { return a.y < b.y; });
    vector<T> ys;
    ys.reserve(n);
    for (Point &p : points) {
      if (ys.empty() or ys.back() != p.y) ys.emplace_back(p.y);
      p.y = (int)ys.size() - 1;
    }
    ys.shrink_to_fit();

    struct Q {
      T x;
      int d, u;
      bool type;
      int idx;
    };
    vector<Q> qs;
    qs.reserve(q + q);
    for (int i = 0; i < q; i++) {
      auto &query = queries[i];
      int d = lower_bound(ys.begin(), ys.end(), query.d) - ys.begin();
      int u = lower_bound(ys.begin(), ys.end(), query.u) - ys.begin();
      qs.emplace_back(Q{query.l, d, u, false, i});
      qs.emplace_back(Q{query.r, d, u, true, i});
    }
    sort(points.begin(), points.end(),
         [](const Point &a, const Point &b) { return a.x < b.x; });
    sort(qs.begin(), qs.end(),
         [](const Q &a, const Q &b) { return a.x < b.x; });
    int j = 0;
    BIT bit(ys.size());
    for (auto &query : qs) {
      while (j < n and points[j].x < query.x) {
        bit.apply(points[j].y, points[j].w);
        ++j;
      }
      if (query.type)
        ans[query.idx] += bit.prod(query.d, query.u);
      else
        ans[query.idx] -= bit.prod(query.d, query.u);
    }
    return ans;
  }
};
#line 2 "other/dynamic-point-add-rectangle-sum.hpp"

/**
 * @brief Dynamic Point Add Rectangle Sum
 */
template <typename T, typename C>
struct DynamicPointAddRectangleSum {
  using StaticRectangleSumSolver = StaticPointAddRectangleSum<T, C>;

  static_assert(is_integral<T>::value,
                "template parameter T must be integral type");

  struct Point {
    T x, y;
    C w;
  };

  struct Query {
    T l, d, r, u;
  };

  vector<variant<Point, Query> > queries;

  DynamicPointAddRectangleSum() = default;

  DynamicPointAddRectangleSum(int q) { queries.reserve(q); }

  void add_point(T x, T y, C w) { queries.emplace_back(Point{x, y, w}); }

  // tatal weight of [l, r) * [d, u) points
  void add_query(T l, T d, T r, T u) {
    queries.emplace_back(Query{l, d, r, u});
  }

  vector<C> calculate_queries() {
    int q = (int)queries.size();
    vector<int> rev(q);
    int sz = 0;
    for (int i = 0; i < q; i++) {
      if (holds_alternative<Query>(queries[i])) {
        rev[i] = sz++;
      }
    }
    vector<C> ans(sz);
    queue<pair<int, int> > range;
    range.emplace(0, q);
    while (not range.empty()) {
      auto [l, r] = range.front();
      range.pop();
      int m = (l + r) >> 1;
      StaticRectangleSumSolver solver;
      for (int k = l; k < m; k++) {
        if (holds_alternative<Point>(queries[k])) {
          auto &point = get<Point>(queries[k]);
          solver.add_point(point.x, point.y, point.w);
        }
      }
      for (int k = m; k < r; k++) {
        if (holds_alternative<Query>(queries[k])) {
          auto &query = get<Query>(queries[k]);
          solver.add_query(query.l, query.d, query.r, query.u);
        }
      }
      auto sub = solver.calculate_queries();
      for (int k = m, t = 0; k < r; k++) {
        if (holds_alternative<Query>(queries[k])) {
          ans[rev[k]] += sub[t++];
        }
      }
      if (l + 1 < m) range.emplace(l, m);
      if (m + 1 < r) range.emplace(m, r);
    }
    return ans;
  }
};

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