我们把方差公式展开

所以只需要维护一个区间平方和和区间和

当我们更新一个区间加时

#include <cstdio>
#include <iostream>
#define lson rt<<1,l,mid
#define rson rt<<1|1,mid+1,r
#define Maxn 300010
using namespace std;
double tree1[Maxn],tree2[Maxn],a[Maxn],lazy[Maxn];
void pushup(int x)
{
    tree1[x]=tree1[x<<1]+tree1[x<<1|1];
    tree2[x]=tree2[x<<1]+tree2[x<<1|1];
}
void pushdown(int rt,int x)
{
    if (lazy[rt])
    {
        tree2[rt<<1]+=2*lazy[rt]*tree1[rt<<1]+(x-x>>1)*lazy[rt]*lazy[rt];
        tree2[rt<<1|1]+=2*lazy[rt]*tree1[rt<<1|1]+(x>>1)*lazy[rt]*lazy[rt];
        tree1[rt<<1]+=(x-x>>1)*lazy[rt];
        tree1[rt<<1|1]+=(x>>1)*lazy[rt];
        lazy[rt<<1]+=lazy[rt];
        lazy[rt<<1|1]+=lazy[rt];
        lazy[rt]=0;
    }
}
void build(int rt,int l,int r)
{
    if (l==r)
        tree1[rt]=a[l],tree2[rt]=tree1[rt]*tree1[rt];
    else
    {
        int mid=(l+r)>>1;
        build(lson);
        build(rson);
        pushup(rt);
    }
}
double query_a(int rt,int l,int r,int L,int R)
{
    if (l>=L && r<=R)
        return tree1[rt];
    else
    {
        pushdown(rt,r-l+1);
        int mid=(r+l)>>1;
        double ret=0;
        if (mid>=L)
            ret+=query_a(lson,L,R);
        if (mid<R)
            ret+=query_a(rson,L,R);
        return ret;
    }
}
double query_b(int rt,int l,int r,int L,int R)
{
    if (l>=L && r<=R)
        return tree2[rt];
    else
    {
        pushdown(rt,r-l+1);
        int mid=(r+l)>>1;
        double ret=0;
        if (mid>=L)
            ret+=query_b(lson,L,R);
        if (mid<R)
            ret+=query_b(rson,L,R);
        return ret;
    }
}
void update(int rt,int l,int r,int L,int R,double x)
{
    if (l>=L && r<=R)
        lazy[rt]+=x,tree2[rt]+=2*x*tree1[rt]+x*x*(r-l+1),tree1[rt]+=(r-l+1)*x;
    else
    {
        pushdown(rt,r-l+1);
        int mid=(r+l)>>1;
        if (mid>=L)
            update(lson,L,R,x);
        if (mid<R)
            update(rson,L,R,x);
        pushup(rt);
    }
}

main()
{
    int n,m,x,y,c;
    double z;
    scanf("%d %d",&n,&m);
    for(int i=1;i<=n;i++)
        scanf("%lf",&a[i]);
    build(1,1,n);
    for (int i=1;i<=m;i++)
    {
        scanf("%d",&c);
        if (c==2)
            scanf("%d%d",&x,&y),printf("%.4lf\n",query_a(1,1,n,x,y)/(y-x+1));
        if (c==1)
            scanf("%d%d",&x,&y),cin>>z,update(1,1,n,x,y,z);
        if (c==3)
        {
            scanf("%d%d",&x,&y);
            double sum1=query_b(1,1,n,x,y)/(y-x+1),sum2=query_a(1,1,n,x,y)/(y-x+1);
            double ans=sum1-sum2*sum2;
            printf("%.4lf\n",ans);
        }
    }
}