Basic usage of tree arrays

1.The usefulness of dendritic array：

1. In a certain position of the array with a number
2. 求某一个前缀和
3. Is the most important of these are dynamically calculated

2.The composition of dendritic array

A tree each element of the array is composed of a range of,例如TR[i]是由（x-lowbit(x),x]构成.（Note left on the right off）

3.Write the core of the dendritic array code

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

//第x个数加上v
int add(int x,int v)
{
    
    //Starting from the current position and,Each interval islowbit(i),Every time I found it on the above number,直到n
    for(int i=x;i<=n;i+=lowbit(i))
        tr[i]+=v;
}

//返回x的前缀和
int query(int x)
{
    
    int res=0;
   //Starting from the current position accumulation,Each interval islowbit(i),一直减到i==0停止
    for(int i=x;i;i-=lowbit(i)) res+=tr[i];
    return res;
}

4.例题：

动态求连续区间和

代码：

// 时间：2022.07.26 18点07分
// 算法：树状数组
#include<iostream>
using namespace std;

const int N=100010;
int a[N],tr[N];
int n,m;
int lowbit(int x)
{
    
    return x & -x;
}
void add(int x,int v)
{
    
    for(int i=x;i<=n;i+=lowbit(i)) tr[i]+=v;
}
int query(int x)
{
    
    int res=0;
    for(int i=x;i;i-=lowbit(i)) res+=tr[i];
    return res;
}
int main ()
{
    
    scanf("%d%d",&n,&m);
    for(int i=1;i<=n;i++) scanf("%d",&a[i]);
    
    for(int i=1;i<=n;i++) add(i,a[i]);
    
    while(m--)
    {
    
        int k,x,y;
        scanf("%d%d%d",&k,&x,&y);
        if(k==0) printf("%d\n",query(y)-query(x-1));
        else add(x,y);
    }
    return 0;
}