Static Rectangle Add Rectangle Sum (other/static-rectangle-add-rectangle-sum.hpp)

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• Last update: 2024-04-24 02:34:04+09:00
• Include: #include "other/static-rectangle-add-rectangle-sum.hpp"

Depends on

• Binary-Indexed-Tree(BIT) (structure/others/binary-indexed-tree.hpp)

Code

#include "../structure/others/binary-indexed-tree.hpp"

/**
 * @brief Static Rectangle Add Rectangle Sum
 */
template< typename T, typename C >
struct StaticRectangleAddRectangleSum {
  struct Hikari : array< C, 4 > {
    using A = array< C, 4 >;

    Hikari &operator+=(const Hikari &p) {
      for(int i = 0; i < 4; i++) {
        this->at(i) += p.at(i);
      }
      return *this;
    }
  };

  using BIT = BinaryIndexedTree< Hikari >;

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

  struct Rectangle {
    T l, d, r, u;
    C w;
  };

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

  vector< Rectangle > rectangles;
  vector< Query > queries;

  StaticRectangleAddRectangleSum() = default;

  StaticRectangleAddRectangleSum(int n, int q) {
    rectangles.reserve(n);
    queries.reserve(q);
  }

  void add_rectangle(T l, T d, T r, T u, C w) {
    rectangles.emplace_back(Rectangle{l, d, r, u, 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) rectangles.size();
    int q = (int) queries.size();
    vector< C > ans(q);
    if(rectangles.empty() or queries.empty()) {
      return ans;
    }
    vector< T > ys;
    ys.reserve(n + n);
    for(Rectangle &p: rectangles) {
      ys.emplace_back(p.d);
      ys.emplace_back(p.u);
    }
    sort(ys.begin(), ys.end());
    ys.erase(unique(ys.begin(), ys.end()), ys.end());

    struct Q {
      T x;
      int d, u;
      bool type;
      int idx;
    };
    vector< Q > rs, qs;
    rs.reserve(n + n);
    qs.reserve(q + q);
    for(int i = 0; i < n; i++) {
      auto &p = rectangles[i];
      int d = lower_bound(ys.begin(), ys.end(), p.d) - ys.begin();
      int u = lower_bound(ys.begin(), ys.end(), p.u) - ys.begin();
      rs.emplace_back(Q{p.l, d, u, false, i});
      rs.emplace_back(Q{p.r, d, u, true, i});
    }
    for(int i = 0; i < q; i++) {
      auto &p = queries[i];
      int d = lower_bound(ys.begin(), ys.end(), p.d) - ys.begin();
      int u = lower_bound(ys.begin(), ys.end(), p.u) - ys.begin();
      qs.emplace_back(Q{p.l, d, u, false, i});
      qs.emplace_back(Q{p.r, d, u, true, i});
    }
    sort(rs.begin(), rs.end(), [](const Q &a, const Q &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 rs[j].x < query.x) {
        auto &p = rectangles[j];
        if(rs[j].type) {
          bit.apply(rs[j].d, {-p.w * p.r * p.d, -p.w, p.d * p.w, p.r * p.w});
          bit.apply(rs[j].u, {p.w * p.r * p.u, p.w, -p.u * p.w, -p.r * p.w});
        } else {
          bit.apply(rs[j].d, {p.w * p.l * p.d, p.w, -p.d * p.w, -p.l * p.w});
          bit.apply(rs[j].u, {-p.w * p.l * p.u, -p.w, p.u * p.w, p.l * p.w});
        }
        ++j;
      }
      auto &p = queries[query.idx];
      auto uret = bit.prod(query.u);
      ans[query.idx] += uret[0];
      ans[query.idx] += uret[1] * query.x * p.u;
      ans[query.idx] += uret[2] * query.x;
      ans[query.idx] += uret[3] * p.u;
      auto dret = bit.prod(query.d);
      ans[query.idx] -= dret[0];
      ans[query.idx] -= dret[1] * query.x * p.d;
      ans[query.idx] -= dret[2] * query.x;
      ans[query.idx] -= dret[3] * p.d;
      if(not query.type) ans[query.idx] *= -1;
    }
    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-rectangle-add-rectangle-sum.hpp"

/**
 * @brief Static Rectangle Add Rectangle Sum
 */
template< typename T, typename C >
struct StaticRectangleAddRectangleSum {
  struct Hikari : array< C, 4 > {
    using A = array< C, 4 >;

    Hikari &operator+=(const Hikari &p) {
      for(int i = 0; i < 4; i++) {
        this->at(i) += p.at(i);
      }
      return *this;
    }
  };

  using BIT = BinaryIndexedTree< Hikari >;

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

  struct Rectangle {
    T l, d, r, u;
    C w;
  };

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

  vector< Rectangle > rectangles;
  vector< Query > queries;

  StaticRectangleAddRectangleSum() = default;

  StaticRectangleAddRectangleSum(int n, int q) {
    rectangles.reserve(n);
    queries.reserve(q);
  }

  void add_rectangle(T l, T d, T r, T u, C w) {
    rectangles.emplace_back(Rectangle{l, d, r, u, 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) rectangles.size();
    int q = (int) queries.size();
    vector< C > ans(q);
    if(rectangles.empty() or queries.empty()) {
      return ans;
    }
    vector< T > ys;
    ys.reserve(n + n);
    for(Rectangle &p: rectangles) {
      ys.emplace_back(p.d);
      ys.emplace_back(p.u);
    }
    sort(ys.begin(), ys.end());
    ys.erase(unique(ys.begin(), ys.end()), ys.end());

    struct Q {
      T x;
      int d, u;
      bool type;
      int idx;
    };
    vector< Q > rs, qs;
    rs.reserve(n + n);
    qs.reserve(q + q);
    for(int i = 0; i < n; i++) {
      auto &p = rectangles[i];
      int d = lower_bound(ys.begin(), ys.end(), p.d) - ys.begin();
      int u = lower_bound(ys.begin(), ys.end(), p.u) - ys.begin();
      rs.emplace_back(Q{p.l, d, u, false, i});
      rs.emplace_back(Q{p.r, d, u, true, i});
    }
    for(int i = 0; i < q; i++) {
      auto &p = queries[i];
      int d = lower_bound(ys.begin(), ys.end(), p.d) - ys.begin();
      int u = lower_bound(ys.begin(), ys.end(), p.u) - ys.begin();
      qs.emplace_back(Q{p.l, d, u, false, i});
      qs.emplace_back(Q{p.r, d, u, true, i});
    }
    sort(rs.begin(), rs.end(), [](const Q &a, const Q &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 rs[j].x < query.x) {
        auto &p = rectangles[j];
        if(rs[j].type) {
          bit.apply(rs[j].d, {-p.w * p.r * p.d, -p.w, p.d * p.w, p.r * p.w});
          bit.apply(rs[j].u, {p.w * p.r * p.u, p.w, -p.u * p.w, -p.r * p.w});
        } else {
          bit.apply(rs[j].d, {p.w * p.l * p.d, p.w, -p.d * p.w, -p.l * p.w});
          bit.apply(rs[j].u, {-p.w * p.l * p.u, -p.w, p.u * p.w, p.l * p.w});
        }
        ++j;
      }
      auto &p = queries[query.idx];
      auto uret = bit.prod(query.u);
      ans[query.idx] += uret[0];
      ans[query.idx] += uret[1] * query.x * p.u;
      ans[query.idx] += uret[2] * query.x;
      ans[query.idx] += uret[3] * p.u;
      auto dret = bit.prod(query.d);
      ans[query.idx] -= dret[0];
      ans[query.idx] -= dret[1] * query.x * p.d;
      ans[query.idx] -= dret[2] * query.x;
      ans[query.idx] -= dret[3] * p.d;
      if(not query.type) ans[query.idx] *= -1;
    }
    return ans;
  }
};

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