[tem]树状数组

通过差分可以玩区间：

bi＝ai－a(i-1)

查询时考虑位置对答案的贡献 推导一下

#include<iostream>
#include<cstdio>
#include<algorithm>
#include<cstring>
using namespace std;
typedef long long ll;
const int N=1e5;

ll n,a[N],b[N],c1[N],c2[N];

//basic
inline int lowbit(int x){return x&-x;}
ll sum(ll *c,int x){
    ll ret=0;
    for(;x>0;x-=lowbit(x)) ret+=c[x];
    return ret;
}
ll query(ll *c,int l,int r){
    return sum(c,r)-sum(c,l-1);
}
void addPoint(ll *c,int x,ll v){
    for(;x<=n;x+=lowbit(x)) c[x]+=v;
}
void build(ll *c,ll *a,ll n){
    for(int i=1;i<=n;i++){
        c[i]+=a[i];
        if(i+lowbit(i)<=n)
            c[i+lowbit(i)]+=c[i];   //!!c[i] or while
    }
}

//interval-interval
void initB(ll *b,ll *a){
    b[1]=a[1];
    for(int i=2;i<=n;i++) b[i]=a[i]-a[i-1];
}
void addRange(int l,int r,ll v){
    addPoint(c1,l,v);        addPoint(c2,l,v*l);
    addPoint(c1,r+1,-v);    addPoint(c2,r+1,-v*(r+1));
}
ll sumRange(int l,int r){
    return query(c1,1,l)*(r-l+1)+ query(c1,l+1,r)*(r+1) -query(c2,l+1,r);
}

int t,l,r;
ll v;
int main(){
    
    //freopen("in.txt","r",stdin);
    //freopen("1.txt","w",stdout);
    
    cin>>n>>t;
    for(int i=1;i<=n;i++) cin>>a[i];
//    for(int i=1;i<=n;i++){
//        addRange(i,i,a[i]);
//    }

    initB(b,a);
    build(c1,b,n);
    for(int i=1;i<=n;i++) b[i]*=i;
    build(c2,b,n);
    
    while(t--){
        int flag;
        cin>>flag;
        if(flag==1){
            cin>>l>>r;
            cout<<sumRange(l,r)<<"
";
        }else{
            cin>>l>>r>>v;
            addRange(l,r,v);
            cout<<sumRange(l,r)<<"
";
        }
    }
}