FenwickTree
(src/data_structure/fenwick_tree.hpp)

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• Last update: 2024-11-09 01:50:04+09:00
• Include: #include "src/data_structure/fenwick_tree.hpp"

FenwickTree

長さ $N$ の配列に対し，

• 1点加算
• 区間和取得

を $O(\log N)$ 時間で処理することができます．

コンストラクタ

FenwickTree<T> fw(int n)

• 長さ $n$ の配列 $a$ を作ります．初期値はすべて $0$ です．

制約

• $T$ は int / uint / ll / ull / mint

計算量

• $O(n)$

add

void fw.add(int p, T x)

a[p] += x をします．

制約

• $0 \leq p < n$

計算量

• $O(\log n)$

sum

T fw.sum(int l, int r)

a[l] + a[l + 1] + ... + a[r - 1] を返します．

制約

• $0 \leq l \leq r \leq n$

計算量

• $O(\log n)$

get

T fw.get(int x)

a[x] を返します．

制約

• $0 \leq x < n$

計算量

• $O(\log n)$

Depends on

• template (src/template/template.hpp)

Required by

• DynamicRollingHash (src/string/dynamic_rolling_hash.hpp)

Verified with

• verify/aizu_online_judge/grl/range_query_on_a_tree.test.cpp
• verify/library_checker/data_structure/point_add_range_sum.test.cpp
• verify/library_checker/data_structure/static_range_inversions_query.test.cpp
• verify/library_checker/tree/vertex_add_path_sum.test.cpp
• verify/library_checker/tree/vertex_add_subtree_sum.test.cpp
• verify/unit_test/string/dynamic_rolling_hash.test.cpp

Code

#pragma once
#include "../template/template.hpp"
template <typename T>
struct FenwickTree {
    FenwickTree(const int N)
        : n(N), data(N) {}
    void add(int p, const T& x) {
        assert(0 <= p and p < n);
        ++p;
        while(p <= n) {
            data[p - 1] += x;
            p += p & -p;
        }
    }
    T sum(const int l, const int r) const {
        assert(0 <= l and l <= r and r <= n);
        return sum(r) - sum(l);
    }
    T get(const int x) const {
        assert(0 <= x and x < n);
        return sum(x + 1) - sum(x);
    }

   private:
    int n;
    vector<T> data;
    inline T sum(int r) const {
        T s = 0;
        while(r > 0) {
            s += data[r - 1];
            r -= r & -r;
        }
        return s;
    }
};

#line 2 "src/template/template.hpp"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using P = pair<long long, long long>;
#define rep(i, a, b) for(long long i = (a); i < (b); ++i)
#define rrep(i, a, b) for(long long i = (a); i >= (b); --i)
constexpr long long inf = 4e18;
struct SetupIO {
    SetupIO() {
        ios::sync_with_stdio(0);
        cin.tie(0);
        cout << fixed << setprecision(30);
    }
} setup_io;
#line 3 "src/data_structure/fenwick_tree.hpp"
template <typename T>
struct FenwickTree {
    FenwickTree(const int N)
        : n(N), data(N) {}
    void add(int p, const T& x) {
        assert(0 <= p and p < n);
        ++p;
        while(p <= n) {
            data[p - 1] += x;
            p += p & -p;
        }
    }
    T sum(const int l, const int r) const {
        assert(0 <= l and l <= r and r <= n);
        return sum(r) - sum(l);
    }
    T get(const int x) const {
        assert(0 <= x and x < n);
        return sum(x + 1) - sum(x);
    }

   private:
    int n;
    vector<T> data;
    inline T sum(int r) const {
        T s = 0;
        while(r > 0) {
            s += data[r - 1];
            r -= r & -r;
        }
        return s;
    }
};

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