线段树/树状数组初等模版
使用线段树或树状数组维护区间和即可

线段树代码

#include<iostream>
using namespace std;

struct point{
    int l,r;
    long long sum;
    int lc,rc;
};
point po[500001];
int a[500001];
int pcnt=0;//表示点个数,用于建树

int buildtree(int l,int r){
    //申请点 
    int v=++pcnt;
    po[v].l=l;
    po[v].r=r;
    if(l==r){
        po[v].sum=a[l];
        return v;
    }
    int mid=(l+r)/2;
    po[v].lc= buildtree(l,mid);
    po[v].rc= buildtree(mid+1,r);
    po[v].sum=po[po[v].lc].sum+po[po[v].rc].sum;
    return v;
}

void addval(int k,long long val,point &v){
    v.sum+=val;
    if(v.l==v.r) return;
    int mid=(v.l+v.r)/2;
    if(k<=mid) addval(k,val,po[v.lc]);
    else addval(k,val,po[v.rc]);
}

long long getsum(int l,int r,point v){
    if(l==v.l && r==v.r) return v.sum;
    int mid=(v.l+v.r)/2;
    if(r<=mid) return getsum(l,r,po[v.lc]);
    else if(l>mid) return getsum(l,r,po[v.rc]);
    else return getsum(l,mid,po[v.lc])+getsum(mid+1,r,po[v.rc]);
}

int main(){
    //freopen("dynsum1.in","r",stdin); 
    int n,q,i;
    int l,r,x;
    cin>>n>>q;
    for(i=1;i<=n;i++) cin>>a[i];
    buildtree(1,n);
    for(i=1;i<=q;i++){
        cin>>x;
        if(x==1){
            cin>>l>>r;
            r=r-a[l];
            addval(l,(long long)r,po[1]);
            a[l]+=r;
        }else{
            cin>>l>>r;
            cout<<getsum(l,r,po[1])<<endl;
        }
    }
}

树状数组代码

#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
inline int lowbit(int x){
    return x&(-x);
}
#define N 100001
long long arr[N];
long long init[N];
int n,m;
inline void updata(int k,long long val){
    while(k<=n){
        arr[k]+=val;
        k+=lowbit(k);
    }
}
inline long long getsum(int k){//求arr[1-k]的和 
    long long res=0;
    while(k>0){
        res+=arr[k];
        k-=lowbit(k);
    }
    return res;
}
int main(){
    int i,t,p,q;
    memset(arr,0,sizeof(arr));
    memset(init,0,sizeof(init));
    scanf("%d %d",&n,&m);
    for(i=1;i<=n;i++){
        scanf("%lld",init+i);
        updata(i,init[i]);
    }
    for(i=1;i<=m;i++){
        scanf("%d %d %d",&t,&p,&q);
        if(t==1){
            updata(p,q-init[p]);
            init[p]=q;
        }else if(t==2) {
            printf("%lld\n",getsum(q)-getsum(p-1));
        }
    }
    
}