Luzhiled's Library

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

2 次元平面上に重み付きの点を追加するクエリと、長方形内に含まれる点の重みの総和を求めるいくつかのクエリに答えます。

コンストラクタ

(1) DynamicPointAddRectangleSum< T, C >()
(2) DynamicPointAddRectangleSum< T, C >(int q)

T は座標が収まる型、C は重みの総和が収まる型を指定してください。

(2) でクエリの個数 $q$ を指定した場合、領域を reserve するので少しだけ効率的です。

add_point

void add_point(T x, T y, C w)

$(x, y)$ に重み $w$ の点を追加するクエリを追加します。

計算量

add_query

void add_query(T l, T d, T r, T u)

$\lbrace (x,y):l \leq x \lt r, d \leq y \lt u\rbrace$ で表される長方形内にある点の重みの総和を求めるクエリを追加します。

制約

計算量

calculate_queries

vector<C> calculate_queries() const

それぞれのクエリの答えを返します。$i$ 番目の要素は $i$ 番目に追加したクエリの答えが格納されます。

計算量

Depends on

Verified with

Code

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

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"
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"

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}); }

  // total 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"

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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