Fenwick tree
(Mylib/DataStructure/FenwickTree/fenwick_tree.cpp)

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

可換群$(G, +, e)$上の列を扱う。

• FenwickTree(n)
• update(i, v)
  • $a_i \leftarrow a_i + v$に更新する。
  • Time complexity $O(\log n)$
• get(i)
  • $a_0 + a_1 + \ldots + a_{i-1}$を返す。
  • Time complexity $O(\log n)$
• get(l, r)
  • $a_l + a_{l+1} + \ldots + a_{r-1}$を返す。
  • Time complexity $O(\log n)$
• at(i)
  • $a_i$を返す。
  • Time complexity $O(\log n)$

Requirements

• AbelianGroupは可換性・結合性を満たす演算opと単位元idと逆元を与える関数invをもつ。

Notes

Problems

References

Required by

• Fenwick tree (On Fenwick tree) (Mylib/DataStructure/FenwickTree/fenwick_tree_on_fenwick_tree.cpp)

Verified with

• test/aoj/DSL_2_B/main.fenwick_tree.test.cpp
• test/yosupo-judge/rectangle_sum/main.fenwick_tree.test.cpp

Code

#pragma once
#include <cassert>
#include <vector>

namespace haar_lib {
  template <typename AbelianGroup>
  class fenwick_tree {
  public:
    using value_type = typename AbelianGroup::value_type;

  private:
    AbelianGroup G_;
    int size_;
    std::vector<value_type> data_;

  public:
    fenwick_tree() {}
    fenwick_tree(int size) : size_(size), data_(size + 1, G_()) {}

    void update(int i, const value_type &val) {
      assert(0 <= i and i < size_);
      i += 1;  // 1-index

      while (i <= size_) {
        data_[i] = G_(data_[i], val);
        i += i & (-i);
      }
    }

    value_type fold(int i) const {  // [0, i)
      assert(0 <= i and i <= size_);
      value_type ret = G_();

      while (i > 0) {
        ret = G_(ret, data_[i]);
        i -= i & (-i);
      }

      return ret;
    }

    value_type fold(int l, int r) const {  // [l, r)
      assert(0 <= l and l <= r and r <= size_);
      return G_(fold(r), G_.inv(fold(l)));
    }

    value_type operator[](int x) const {
      return fold(x, x + 1);
    }
  };
}  // namespace haar_lib

#line 2 "Mylib/DataStructure/FenwickTree/fenwick_tree.cpp"
#include <cassert>
#include <vector>

namespace haar_lib {
  template <typename AbelianGroup>
  class fenwick_tree {
  public:
    using value_type = typename AbelianGroup::value_type;

  private:
    AbelianGroup G_;
    int size_;
    std::vector<value_type> data_;

  public:
    fenwick_tree() {}
    fenwick_tree(int size) : size_(size), data_(size + 1, G_()) {}

    void update(int i, const value_type &val) {
      assert(0 <= i and i < size_);
      i += 1;  // 1-index

      while (i <= size_) {
        data_[i] = G_(data_[i], val);
        i += i & (-i);
      }
    }

    value_type fold(int i) const {  // [0, i)
      assert(0 <= i and i <= size_);
      value_type ret = G_();

      while (i > 0) {
        ret = G_(ret, data_[i]);
        i -= i & (-i);
      }

      return ret;
    }

    value_type fold(int l, int r) const {  // [l, r)
      assert(0 <= l and l <= r and r <= size_);
      return G_(fold(r), G_.inv(fold(l)));
    }

    value_type operator[](int x) const {
      return fold(x, x + 1);
    }
  };
}  // namespace haar_lib

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