P1471 方差

Lisa

运用一点初中知识可以知道

维护一下区间平方和和区间和就可以处理了

#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>

using namespace std;
int n,m;
int f;
int x,y;
double k;
struct p{
	double sum;
	double sqr;
}po[400005];
double lazy[400005];
void pushdown(int ro,int l,int r){
	if(lazy[ro]){
		int mid=(l+r)>>1;
		double k=lazy[ro];lazy[ro]=0;
		lazy[ro<<1]+=k;lazy[ro<<1|1]+=k;
		po[ro<<1].sqr=po[ro<<1].sqr+2*k*po[ro<<1].sum+k*k*(mid-l+1);
		po[ro<<1].sum+=k*(mid-l+1);
		po[ro<<1|1].sqr=po[ro<<1|1].sqr+2*k*po[ro<<1|1].sum+k*k*(r-mid);
		po[ro<<1|1].sum+=k*(r-mid);
	}
}
void pushup(int r){
	po[r].sqr=po[r<<1].sqr+po[r<<1|1].sqr;
	po[r].sum=po[r<<1].sum+po[r<<1|1].sum;
}
void add(int ro,int l,int r,int L,int R,double k){
	if(L<=l&&r<=R){
		po[ro].sqr=po[ro].sqr+2*k*po[ro].sum+k*k*(r-l+1);
		po[ro].sum+=k*(r-l+1);
		lazy[ro]+=k;
		return ;
	}
	pushdown(ro,l,r);
	int mid=(r+l)>>1;
	if(L<=mid) add(ro<<1,l,mid,L,R,k);
	if(R>mid) add(ro<<1|1,mid+1,r,L,R,k);
	pushup(ro);
}
double qsum(int ro,int l,int r,int L,int R){
	if(L<=l&&r<=R){
		return po[ro].sum;
	}
	pushdown(ro,l,r);
	int mid=(l+r)>>1;
	double ans=0;
	if(L<=mid) ans+=qsum(ro<<1,l,mid,L,R);
	if(R>mid) ans+=qsum(ro<<1|1,mid+1,r,L,R); 
	return ans;
}
double qsqr(int ro,int l,int r,int L,int R){
	if(L<=l&&r<=R){
		return po[ro].sqr;
	}
	pushdown(ro,l,r);
	int mid=(l+r)>>1;
	double ans=0;
	if(L<=mid) ans+=qsqr(ro<<1,l,mid,L,R);
	if(R>mid) ans+=qsqr(ro<<1|1,mid+1,r,L,R); 
	return ans;
}
int main(){
	scanf("%d%d",&n,&m);
	for(int i=1;i<=n;++i){
		scanf("%lf",&k);
		add(1,1,n,i,i,k);
	}
	for(int i=1;i<=m;++i){
		scanf("%d",&f);
		if(f==1){
			scanf("%d%d%lf",&x,&y,&k);
			add(1,1,n,x,y,k);
		}
		if(f==2){
			scanf("%d%d",&x,&y);
			double su=qsum(1,1,n,x,y);
			//cout<<qsum(1,1,n,x,y)<<endl;
			//cout<<su<<endl;
			printf("%.4lf
",(double)su/(y-x+1));
		}
		if(f==3){
			scanf("%d%d",&x,&y);
			double su=qsum(1,1,n,x,y);
			double sq=qsqr(1,1,n,x,y);
			printf("%.4lf
",(double)sq/(y-x+1)-su*su/(double)(y-x+1)/(double)(y-x+1));
		}
	}
	return 0;
}