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

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

モノイド$(M, \circ, e)$上の列を扱う。

• SegmentTree(n)
• operator[](i)
• at(i)
  • $a_i$を返す。
  • Time complexity $O(1)$
• get(l, r)
  • $a_l \circ a_{l+1} \circ \ldots \circ a_{r-1}$を返す。
  • Time complexity $O(\log n)$
• update(i, value)
  • $a_i$をvalueに変更する。
  • Time complexity $O(\log n)$
• init_with_vector(a)
• init(value)

Requirements

• Monoidは結合律を満たす演算opと単位元idをもつ。

Notes

Problems

References

Required by

• Segment tree (On segment tree) (Mylib/DataStructure/SegmentTree/segment_tree_on_segment_tree.cpp)
• Manhattan distance MST (Mylib/Graph/MinimumSpanningTree/manhattan_minimum_spanning_tree.cpp)

Verified with

• test/aoj/0390/main.test.cpp
• test/aoj/2444/main.test.cpp
• test/aoj/3132/main.test.cpp
• test/aoj/DSL_2_A/main.test.cpp
• test/aoj/DSL_2_B/main.test.cpp
• test/yosupo-judge/manhattanmst/main.test.cpp
• test/yosupo-judge/point_add_rectangle_sum/main.test.cpp
• test/yosupo-judge/point_set_range_composite/main.test.cpp
• test/yosupo-judge/rectangle_sum/main.segment_tree.test.cpp
• test/yosupo-judge/vertex_add_path_sum/main.test.cpp
• test/yosupo-judge/vertex_add_subtree_sum/main.euler_tour.test.cpp
• test/yosupo-judge/vertex_add_subtree_sum/main.hld.test.cpp
• test/yukicoder/1030/main.test.cpp
• test/yukicoder/510/main.test.cpp
• test/yukicoder/776/main.test.cpp
• test/yukicoder/875/main.test.cpp

Code

#pragma once
#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 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

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