树状数组模板

 这一部分和线段树基础的功能一样

线段树模板的链接
lowbit(x)覆盖长度
c[x]的父节点t[x + lowbit(x)]

单点修改 区间查询

P3374 【模板】树状数组 1

#include <bits/stdc++.h>

using namespace std;
#define int long long
const int maxn = 5e5 + 10;
int n, m, c[maxn];
int lowbit(int x){
    return x & - x;
}

int ask(int i){
    int ans = 0;
    for(;i;i -= lowbit(i))
        ans += c[i];
    return ans;
}
void add(int i,int k){
    for(;i <= n;i += lowbit(i))
        c[i] += k;
}
signed main() {
    //freopen("in", "r", stdin);
    ios::sync_with_stdio(0);
    cin >> n >> m;
    for (int i = 1; i <= n; i++) {
        int t;
        cin >> t;
        add(i,t);
    }
    for (int i = 1; i <= m; i++) {
        int op, x, y;
        cin >> op >> x >> y;
        if (op == 1) add( x, y);
        else cout << ask(y) - ask(x - 1) << endl;
    }
    return 0;
}

区间修改 单点查询

读入的时候，读入到a[]数组里面里面

区间修改：在c[]数组里面改变前缀和的思想，在区间[l,r]上，l + d, r + 1的位置-d;

单点查询:原数组a[x] + (a[x]的增量) ask(x)
P3368 【模板】树状数组 2

#include <bits/stdc++.h>
using namespace std;
#define int long long
const int maxn = 5e5 + 5;
int n,m,c[maxn],a[maxn];
int lowbit(int x){
    return x & -x;
}
int ask(int i){
    int ans = 0;
    for(;i;i -= lowbit(i))
        ans += c[i];
    return ans;
}

void add(int i,int k){
    for(;i <= n; i += lowbit(i))
        c[i] += k;
}

signed main(){
    //freopen("in","r",stdin);
    ios::sync_with_stdio(0);
    cin >> n >> m;
    for(int i = 1; i <= n; i++)
        cin >> a[i];
    while(m--){
        int op,x,y,d;
        cin >> op ;
        if(op == 1) {
            cin >> x >> y >> d;
            add(x,d);
            add(y + 1,-d);
        }
        else {
            cin >> x;
            cout << a[x] + ask(x) << endl;
        }
    }
    return 0;
}