FenwickTree2D
(src/data_structure/fenwick_tree_2d.hpp)

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• Last update: 2024-11-09 01:34:39+09:00
• Include: #include "src/data_structure/fenwick_tree_2d.hpp"

FenwickTree2D

サイズが $N \times M$ である $2$ 次元配列に対し，

• $1$ 点加算
• 長方形領域の総和の取得

を $O(\log N \log M)$ 時間で処理することができます．

コンストラクタ

FenwickTree2D<T> fw(int n, int m)

• 型が T でサイズが $n \times m$ である$2$ 次元配列 fw を作ります．
  
• 初期値はすべて $0$ です．

計算量

• $O(nm)$

add

void fw.add(int i, int j, T x)

fw[i][j] += x をします．

制約

• $0 \leq i < n$
• $0 \leq j < m$

計算量

• $O(\log n \log m)$

sum

T fw.sum(int li, int lj, int ri, int rj)

長方形領域 $[li, ri) \times [lj, rj)$ における配列 fw の総和を返します．

制約

• $0 \leq li \leq ri \leq n$
• $0 \leq lj \leq rj \leq m$

計算量

• $O(\log n \log m)$

get

T fw.get(int i, int j)

fw[i][j] を返します．

制約

• $0 \leq i < n$
• $0 \leq j < m$

計算量

• $O(\log n \log m)$

Depends on

• template (src/template/template.hpp)

Verified with

• verify/aizu_online_judge/dsl/the_maximum_number_of_overlaps_2.test.cpp

Code

#pragma once
#include "../template/template.hpp"
template <typename T>
struct FenwickTree2D {
    FenwickTree2D(const int H, const int W)
        : h(H), w(W), data(H + 1, vector<T>(W + 1, 0)) {}
    void add(const int i, const int j, const T& z) {
        assert(0 <= i and i < h);
        assert(0 <= j and j < w);
        for(int x = i + 1; x <= h; x += x & -x) {
            for(int y = j + 1; y <= w; y += y & -y) {
                data[x - 1][y - 1] += z;
            }
        }
    }
    T sum(const int li, const int lj, const int ri, const int rj) const {
        assert(0 <= li and li <= ri and ri <= h);
        assert(0 <= lj and lj <= rj and rj <= w);
        return sum(ri, rj) - sum(li, rj) - sum(ri, lj) + sum(li, lj);
    }
    T get(const int i, const int j) const {
        assert(0 <= i and i < h);
        assert(0 <= j and j < w);
        return sum(i + 1, j + 1) - sum(i, j + 1) - sum(i + 1, j) + sum(i, j);
    }

   private:
    int h, w;
    vector<vector<T>> data;
    inline T sum(const int i, const int j) const {
        T s = 0;
        for(int x = i; x > 0; x -= x & -x) {
            for(int y = j; y > 0; y -= y & -y) {
                s += data[x - 1][y - 1];
            }
        }
        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_2d.hpp"
template <typename T>
struct FenwickTree2D {
    FenwickTree2D(const int H, const int W)
        : h(H), w(W), data(H + 1, vector<T>(W + 1, 0)) {}
    void add(const int i, const int j, const T& z) {
        assert(0 <= i and i < h);
        assert(0 <= j and j < w);
        for(int x = i + 1; x <= h; x += x & -x) {
            for(int y = j + 1; y <= w; y += y & -y) {
                data[x - 1][y - 1] += z;
            }
        }
    }
    T sum(const int li, const int lj, const int ri, const int rj) const {
        assert(0 <= li and li <= ri and ri <= h);
        assert(0 <= lj and lj <= rj and rj <= w);
        return sum(ri, rj) - sum(li, rj) - sum(ri, lj) + sum(li, lj);
    }
    T get(const int i, const int j) const {
        assert(0 <= i and i < h);
        assert(0 <= j and j < w);
        return sum(i + 1, j + 1) - sum(i, j + 1) - sum(i + 1, j) + sum(i, j);
    }

   private:
    int h, w;
    vector<vector<T>> data;
    inline T sum(const int i, const int j) const {
        T s = 0;
        for(int x = i; x > 0; x -= x & -x) {
            for(int y = j; y > 0; y -= y & -y) {
                s += data[x - 1][y - 1];
            }
        }
        return s;
    }
};

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