Segment tree (On segment tree)
(Mylib/DataStructure/SegmentTree/segment_tree_on_segment_tree.cpp)

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• Last update: 2021-04-23 23:44:44+09:00
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Operations

• SegmentTree2D()
• add(x, y)
  • 点(x, y)を追加する。
• build()
• update(x, y, value)
• get(x1, y1, x2, y2)

Requirements

• Monoidは可換性・結合律を満たす演算opと単位元idをもつ。
• add, build, update / getの順で呼び出す。

Notes

Problems

References

Depends on

• Segment tree (Mylib/DataStructure/SegmentTree/segment_tree.cpp)

Verified with

• test/yosupo-judge/point_add_rectangle_sum/main.test.cpp
• test/yosupo-judge/rectangle_sum/main.segment_tree.test.cpp

Code

#pragma once
#include "Mylib/DataStructure/SegmentTree/segment_tree.cpp"
#include <algorithm>
#include <vector>

namespace haar_lib {
  template <typename Monoid>
  class segment_tree_on_segment_tree {
  public:
    using value_type = typename Monoid::value_type;

  private:
    Monoid M_;
    int N_ = 0;
    std::vector<int64_t> xs_, ys_;
    std::vector<int> c_xs_;
    std::vector<std::vector<int>> c_ys_;
    int x_size_;
    std::vector<segment_tree<Monoid>> segs_;

  public:
    segment_tree_on_segment_tree() {}

    void add(int64_t x, int64_t y) {
      xs_.push_back(x);
      ys_.push_back(y);
      ++N_;
    }

    void build() {
      c_xs_.insert(c_xs_.end(), xs_.begin(), xs_.end());

      std::sort(c_xs_.begin(), c_xs_.end());
      c_xs_.erase(std::unique(c_xs_.begin(), c_xs_.end()), c_xs_.end());

      x_size_ = 1;
      while (x_size_ < (int) c_xs_.size()) x_size_ *= 2;
      x_size_ *= 2;

      c_ys_.resize(x_size_);
      segs_.resize(x_size_);

      for (int i = 0; i < N_; ++i) {
        int j = std::lower_bound(c_xs_.begin(), c_xs_.end(), xs_[i]) - c_xs_.begin();
        c_ys_[j + x_size_ / 2].push_back(ys_[i]);
      }

      for (int i = 0; i < x_size_ / 2; ++i) {
        auto &v = c_ys_[i + x_size_ / 2];
        std::sort(v.begin(), v.end());
        v.erase(std::unique(v.begin(), v.end()), v.end());
      }

      for (int i = x_size_ / 2 - 1; i >= 1; --i) {
        const auto &a = c_ys_[i << 1 | 0];
        const auto &b = c_ys_[i << 1 | 1];
        auto &c       = c_ys_[i];
        c.resize(a.size() + b.size());

        std::merge(a.begin(), a.end(), b.begin(), b.end(), c.begin());
        c.erase(std::unique(c.begin(), c.end()), c.end());
      }

      for (int i = 1; i < x_size_; ++i) {
        segs_[i] = segment_tree<Monoid>(c_ys_[i].size());
      }
    }

    void update(std::pair<int64_t, int64_t> p, const value_type &val) {
      const auto [x, y] = p;
      int i             = std::lower_bound(c_xs_.begin(), c_xs_.end(), x) - c_xs_.begin() + x_size_ / 2;

      while (i >= 1) {
        int j = std::lower_bound(c_ys_[i].begin(), c_ys_[i].end(), y) - c_ys_[i].begin();
        segs_[i].update(j, val);

        i >>= 1;
      }
    }

  private:
    value_type get_sub(int i, int64_t y1, int64_t y2) const {
      int l = std::lower_bound(c_ys_[i].begin(), c_ys_[i].end(), y1) - c_ys_[i].begin();
      int r = std::lower_bound(c_ys_[i].begin(), c_ys_[i].end(), y2) - c_ys_[i].begin();

      return segs_[i].fold(l, r);
    }

  public:
    value_type fold(std::pair<int64_t, int64_t> p1, std::pair<int64_t, int64_t> p2) const {
      const auto [x1, y1] = p1;
      const auto [x2, y2] = p2;
      int l               = std::lower_bound(c_xs_.begin(), c_xs_.end(), x1) - c_xs_.begin() + x_size_ / 2;
      int r               = std::lower_bound(c_xs_.begin(), c_xs_.end(), x2) - c_xs_.begin() + x_size_ / 2;

      value_type ret = M_();

      while (l < r) {
        if (r & 1) ret = M_(ret, get_sub(--r, y1, y2));
        if (l & 1) ret = M_(ret, get_sub(l++, y1, y2));
        l >>= 1;
        r >>= 1;
      }

      return ret;
    }
  };
}  // namespace haar_lib

#line 2 "Mylib/DataStructure/SegmentTree/segment_tree.cpp"
#include <algorithm>
#include <cassert>
#include <functional>
#include <vector>

namespace haar_lib {
  template <typename Monoid>
  class segment_tree {
  public:
    using value_type = typename Monoid::value_type;

  private:
    Monoid M_;
    int depth_, size_, hsize_;
    std::vector<value_type> data_;

  public:
    segment_tree() {}
    segment_tree(int n) : depth_(n > 1 ? 32 - __builtin_clz(n - 1) + 1 : 1),
                          size_(1 << depth_),
                          hsize_(size_ / 2),
                          data_(size_, M_()) {}

    auto operator[](int i) const {
      assert(0 <= i and i < hsize_);
      return data_[hsize_ + i];
    }

    auto fold(int l, int r) const {
      assert(0 <= l and l <= r and r <= hsize_);
      value_type ret_left  = M_();
      value_type ret_right = M_();

      int L = l + hsize_, R = r + hsize_;
      while (L < R) {
        if (R & 1) ret_right = M_(data_[--R], ret_right);
        if (L & 1) ret_left = M_(ret_left, data_[L++]);
        L >>= 1, R >>= 1;
      }

      return M_(ret_left, ret_right);
    }

    auto fold_all() const {
      return data_[1];
    }

    void set(int i, const value_type &x) {
      assert(0 <= i and i < hsize_);
      i += hsize_;
      data_[i] = x;
      while (i > 1) i >>= 1, data_[i] = M_(data_[i << 1 | 0], data_[i << 1 | 1]);
    }

    void update(int i, const value_type &x) {
      assert(0 <= i and i < hsize_);
      i += hsize_;
      data_[i] = M_(data_[i], x);
      while (i > 1) i >>= 1, data_[i] = M_(data_[i << 1 | 0], data_[i << 1 | 1]);
    }

    template <typename T>
    void init_with_vector(const std::vector<T> &val) {
      data_.assign(size_, M_());
      for (int i = 0; i < (int) val.size(); ++i) data_[hsize_ + i] = val[i];
      for (int i = hsize_; --i >= 1;) data_[i] = M_(data_[i << 1 | 0], data_[i << 1 | 1]);
    }

    template <typename T>
    void init(const T &val) {
      init_with_vector(std::vector<value_type>(hsize_, val));
    }

  private:
    template <bool Lower, typename F>
    int bound(const int l, const int r, value_type x, F f) const {
      std::vector<int> pl, pr;
      int L = l + hsize_;
      int R = r + hsize_;
      while (L < R) {
        if (R & 1) pr.push_back(--R);
        if (L & 1) pl.push_back(L++);
        L >>= 1, R >>= 1;
      }

      std::reverse(pr.begin(), pr.end());
      pl.insert(pl.end(), pr.begin(), pr.end());

      value_type a = M_();

      for (int i : pl) {
        auto b = M_(a, data_[i]);

        if ((Lower and not f(b, x)) or (not Lower and f(x, b))) {
          while (i < hsize_) {
            const auto c = M_(a, data_[i << 1 | 0]);
            if ((Lower and not f(c, x)) or (not Lower and f(x, c))) {
              i = i << 1 | 0;
            } else {
              a = c;
              i = i << 1 | 1;
            }
          }

          return i - hsize_;
        }

        a = b;
      }

      return r;
    }

  public:
    template <typename F = std::less<value_type>>
    int lower_bound(int l, int r, value_type x, F f = F()) const {
      return bound<true>(l, r, x, f);
    }

    template <typename F = std::less<value_type>>
    int upper_bound(int l, int r, value_type x, F f = F()) const {
      return bound<false>(l, r, x, f);
    }
  };
}  // namespace haar_lib
#line 5 "Mylib/DataStructure/SegmentTree/segment_tree_on_segment_tree.cpp"

namespace haar_lib {
  template <typename Monoid>
  class segment_tree_on_segment_tree {
  public:
    using value_type = typename Monoid::value_type;

  private:
    Monoid M_;
    int N_ = 0;
    std::vector<int64_t> xs_, ys_;
    std::vector<int> c_xs_;
    std::vector<std::vector<int>> c_ys_;
    int x_size_;
    std::vector<segment_tree<Monoid>> segs_;

  public:
    segment_tree_on_segment_tree() {}

    void add(int64_t x, int64_t y) {
      xs_.push_back(x);
      ys_.push_back(y);
      ++N_;
    }

    void build() {
      c_xs_.insert(c_xs_.end(), xs_.begin(), xs_.end());

      std::sort(c_xs_.begin(), c_xs_.end());
      c_xs_.erase(std::unique(c_xs_.begin(), c_xs_.end()), c_xs_.end());

      x_size_ = 1;
      while (x_size_ < (int) c_xs_.size()) x_size_ *= 2;
      x_size_ *= 2;

      c_ys_.resize(x_size_);
      segs_.resize(x_size_);

      for (int i = 0; i < N_; ++i) {
        int j = std::lower_bound(c_xs_.begin(), c_xs_.end(), xs_[i]) - c_xs_.begin();
        c_ys_[j + x_size_ / 2].push_back(ys_[i]);
      }

      for (int i = 0; i < x_size_ / 2; ++i) {
        auto &v = c_ys_[i + x_size_ / 2];
        std::sort(v.begin(), v.end());
        v.erase(std::unique(v.begin(), v.end()), v.end());
      }

      for (int i = x_size_ / 2 - 1; i >= 1; --i) {
        const auto &a = c_ys_[i << 1 | 0];
        const auto &b = c_ys_[i << 1 | 1];
        auto &c       = c_ys_[i];
        c.resize(a.size() + b.size());

        std::merge(a.begin(), a.end(), b.begin(), b.end(), c.begin());
        c.erase(std::unique(c.begin(), c.end()), c.end());
      }

      for (int i = 1; i < x_size_; ++i) {
        segs_[i] = segment_tree<Monoid>(c_ys_[i].size());
      }
    }

    void update(std::pair<int64_t, int64_t> p, const value_type &val) {
      const auto [x, y] = p;
      int i             = std::lower_bound(c_xs_.begin(), c_xs_.end(), x) - c_xs_.begin() + x_size_ / 2;

      while (i >= 1) {
        int j = std::lower_bound(c_ys_[i].begin(), c_ys_[i].end(), y) - c_ys_[i].begin();
        segs_[i].update(j, val);

        i >>= 1;
      }
    }

  private:
    value_type get_sub(int i, int64_t y1, int64_t y2) const {
      int l = std::lower_bound(c_ys_[i].begin(), c_ys_[i].end(), y1) - c_ys_[i].begin();
      int r = std::lower_bound(c_ys_[i].begin(), c_ys_[i].end(), y2) - c_ys_[i].begin();

      return segs_[i].fold(l, r);
    }

  public:
    value_type fold(std::pair<int64_t, int64_t> p1, std::pair<int64_t, int64_t> p2) const {
      const auto [x1, y1] = p1;
      const auto [x2, y2] = p2;
      int l               = std::lower_bound(c_xs_.begin(), c_xs_.end(), x1) - c_xs_.begin() + x_size_ / 2;
      int r               = std::lower_bound(c_xs_.begin(), c_xs_.end(), x2) - c_xs_.begin() + x_size_ / 2;

      value_type ret = M_();

      while (l < r) {
        if (r & 1) ret = M_(ret, get_sub(--r, y1, y2));
        if (l & 1) ret = M_(ret, get_sub(l++, y1, y2));
        l >>= 1;
        r >>= 1;
      }

      return ret;
    }
  };
}  // namespace haar_lib

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