树状数组模板

1. 一维树状数组

   快速求区间和, 功能和线段树相似, 查询和更新的时间复杂度都为o(log(n)).
   

#include <iostream>
#include <cstring>
#include <cstdio>
#include <algorithm>

using namespace std;

typedef long long ll;

const int maxn = 1000002;

ll sum[maxn*2];
ll value[maxn];
int n;

inline int lowbit(int x) {
    return x & -x;
}

void update(int idx, int v) {
    while (idx <= n) {
        sum[idx] += v;
        idx += lowbit(idx);
    }
}

ll query(int x) {
    ll ans = 0;
    while(x > 0) {
        ans += sum[x];
        x -= lowbit(x);
    }
    return ans;
}

1. 二维树状数组

   快速求区间和, 查询和更新的时间复杂度都为o(n^2).
   

#include <iostream>
#include <cstdio>
#include <cstring>
#include <alogorithm>

using namespace std;
typedef long long ll;

const int maxn = 100005;

ll sum[maxn*2][maxn*2];
int value[maxn][maxn];

int nx, ny;

inline int lowbit(int x){
    return -x&x;
}

void update(int x, int y, int v){
    for(int i = x; i <= nx; i += lowbit(i))
        for(int j = y; j <= ny; j += lowbit(j))
            sum[i][j] += v;
}

ll query(int x, int y){
    ll ans = 0;

    for(int i = x; i >= 0; i -= lowbit(i))
        for(int j = y; j >= 0; j -= lowbit(i))
            ans += sum[i][j];
    return ans;
}