Binary indexed tree / Fenwick tree （BIT・フェニック木）
(segmenttree/binary_indexed_tree.hpp)

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• Last update: 2021-11-06 11:36:55+09:00
• Include: #include "segmenttree/binary_indexed_tree.hpp"

BIT の実装．テンプレート引数として渡すクラス $S$ は加算について結合法則を満たし，また逆元が取れる必要がある．

• BIT<S> bit(n) : コンストラクタ．長さ $n$ の数列 $A$ を $A_0 = \dots = A_{n - 1} = S()$ で初期化．計算量は $O(n)$．
• sum(l, r) : $A_l + \dots + A_{r - 1}$ を計算．計算量は $O(\log n)$．
• sum(k) : sum(0, k) と同じ．計算量は $O(\log n)$．
• add(x, v): $A_x$ に $v$ を加算．計算量は $O(\log n)$．

Example

BIT<int> bit(N);
bit.add(2, 5);

bit.sum(1, 6);

問題例

• AOJ DSL_2_B: Range Sum Query (RSQ)

Required by

• data_structure/range_kth_smallest_offline.hpp
• Static rectangle add rectangle sum （矩形一様加算・矩形総和取得） (data_structure/rectangle_add_rectangle_sum.hpp)
• data_structure/rectangle_sum.hpp

Verified with

• data_structure/test/range_kth_smallest_offline.test.cpp
• data_structure/test/rectangle_add_rectangle_sum.point.test.cpp
• data_structure/test/rectangle_add_rectangle_sum.test.cpp
• data_structure/test/rectangle_sum.test.cpp
• data_structure/test/wavelet_matrix_point_add_rectangle_sum.test.cpp
• segmenttree/test/binary_indexed_tree.test.cpp
• segmenttree/test/point-add-range-sum.test.cpp
• tree/test/vertex-add-subtree-sum.guni.test.cpp

Code

#pragma once
#include <algorithm>
#include <vector>

// CUT begin
// 0-indexed BIT (binary indexed tree / Fenwick tree) (i : [0, len))
template <class T> struct BIT {
    int n;
    std::vector<T> data;
    BIT(int len = 0) : n(len), data(len) {}
    void reset() { std::fill(data.begin(), data.end(), T(0)); }
    void add(int pos, T v) { // a[pos] += v
        pos++;
        while (pos > 0 and pos <= n) data[pos - 1] += v, pos += pos & -pos;
    }
    T sum(int k) const { // a[0] + ... + a[k - 1]
        T res = 0;
        while (k > 0) res += data[k - 1], k -= k & -k;
        return res;
    }

    T sum(int l, int r) const { return sum(r) - sum(l); } // a[l] + ... + a[r - 1]

    template <class OStream> friend OStream &operator<<(OStream &os, const BIT &bit) {
        T prv = 0;
        os << '[';
        for (int i = 1; i <= bit.n; i++) {
            T now = bit.sum(i);
            os << now - prv << ',', prv = now;
        }
        return os << ']';
    }
};

#line 2 "segmenttree/binary_indexed_tree.hpp"
#include <algorithm>
#include <vector>

// CUT begin
// 0-indexed BIT (binary indexed tree / Fenwick tree) (i : [0, len))
template <class T> struct BIT {
    int n;
    std::vector<T> data;
    BIT(int len = 0) : n(len), data(len) {}
    void reset() { std::fill(data.begin(), data.end(), T(0)); }
    void add(int pos, T v) { // a[pos] += v
        pos++;
        while (pos > 0 and pos <= n) data[pos - 1] += v, pos += pos & -pos;
    }
    T sum(int k) const { // a[0] + ... + a[k - 1]
        T res = 0;
        while (k > 0) res += data[k - 1], k -= k & -k;
        return res;
    }

    T sum(int l, int r) const { return sum(r) - sum(l); } // a[l] + ... + a[r - 1]

    template <class OStream> friend OStream &operator<<(OStream &os, const BIT &bit) {
        T prv = 0;
        os << '[';
        for (int i = 1; i <= bit.n; i++) {
            T now = bit.sum(i);
            os << now - prv << ',', prv = now;
        }
        return os << ']';
    }
};

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