洛谷3707 [SDOI2017] 相关分析 【线段树】

分析：

化简一下就行了，注意一下平方和公式的运用以及精度的误差。

代码：

 #include<bits/stdc++.h>
 using namespace std;

 const int maxn = ;

 int n,m;

 int x[maxn],y[maxn];

 struct node{
     int lazx1,lazx2,lazy1,lazy2;
     double multi,sumx,sumy,sqr;
 }T[maxn<<];

 long long ump(int l,int r){
     return (1ll*r*(r+)*(*r+)-1ll*(l-)*l*(*l-))/;
 }

 void fugai(int now,int tl,int tr,int s,int t){
     T[now].lazx2 = T[now].lazy2 = ;
     T[now].lazx1 = s; T[now].lazy1 = t;
     T[now].sumx = 1ll*((s+tl)+(s+tr))*(tr-tl+)/;
     T[now].sumy = 1ll*((t+tl)+(t+tr))*(tr-tl+)/;
     T[now].sqr = 1ll*(tr-tl+)*s*s+1ll*s*(tl+tr)*(tr-tl+)+ump(tl,tr);
     T[now].multi=1ll*(tr-tl+)*s*t+1ll*(s+t)*(tl+tr)*(tr-tl+)/+ump(tl,tr);
 }

 void add(int now,int tl,int tr,int s,int t){
     T[now].lazx2+=s;T[now].lazy2 += t;
     T[now].multi+=1ll*s*T[now].sumy+1ll*t*T[now].sumx+1ll*s*t*(tr-tl+);
     T[now].sqr +=1ll*s*s*(tr-tl+)+2ll*s*T[now].sumx;
     T[now].sumx += 1ll*s*(tr-tl+); T[now].sumy += 1ll*t*(tr-tl+);
 }

 void push_up(int now){
     T[now].multi = T[now<<].multi+T[now<<|].multi;
     T[now].sumx = T[now<<].sumx+T[now<<|].sumx;
     T[now].sumy = T[now<<].sumy+T[now<<|].sumy;
     T[now].sqr = T[now<<].sqr+T[now<<|].sqr;
 }

 void push_down1(int now,int tl,int tr){
     int mid = (tl+tr)/;
     fugai(now<<,tl,mid,T[now].lazx1,T[now].lazy1);
     fugai(now<<|,mid+,tr,T[now].lazx1,T[now].lazy1);
     T[now].lazx1 = T[now].lazy1 = ;
 }

 void push_down2(int now,int tl,int tr){
     int mid = (tl+tr)/;
     add(now<<,tl,mid,T[now].lazx2,T[now].lazy2);
     add(now<<|,mid+,tr,T[now].lazx2,T[now].lazy2);
     T[now].lazx2 = T[now].lazy2 = ;
 }

 void read(){
     scanf("%d%d",&n,&m);
     for(int i=;i<=n;i++)scanf("%d",&x[i]);
     for(int i=;i<=n;i++) scanf("%d",&y[i]);
 }

 node merge(node ai,node bi){
     return (node){,,,,ai.multi+bi.multi,ai.sumx+bi.sumx,ai.sumy+bi.sumy,ai.sqr+bi.sqr};
 }

 void build_tree(int now,int l,int r){
     if(l == r){
     T[now].lazx1 = T[now].lazy1 = ;
     T[now].multi = 1ll*x[l]*y[l];
     T[now].sumx = x[l];T[now].sumy = y[l];
     T[now].sqr = 1ll*x[l]*x[l];
     }else{
     int mid = (l+r)/;
     build_tree(now<<,l,mid);
     build_tree(now<<|,mid+,r);
     T[now].lazx1 = T[now].lazy1 = ;
     push_up(now);
     }
 }

 node Query(int now,int tl,int tr,int l,int r){
     if(tl >= l && tr <= r){return T[now];}
     if(tl > r || tr < l){return (node){,,,,,,,};}
     if(T[now].lazx1<=maxn||T[now].lazy1<=maxn) push_down1(now,tl,tr);
     if(T[now].lazx2||T[now].lazy2) push_down2(now,tl,tr);
     int mid = (tl+tr)/;
     node ans = merge(Query(now<<,tl,mid,l,r),Query(now<<|,mid+,tr,l,r));
     push_up(now);
     return ans;
 }

 void Modify1(int now,int tl,int tr,int l,int r,int s,int t){
     if(tl >= l && tr <= r){
     add(now,tl,tr,s,t);
     return;
     }
     if(tl > r || tr < l){return;}
     if(T[now].lazx1<=maxn||T[now].lazy1<=maxn) push_down1(now,tl,tr);
     if(T[now].lazx2||T[now].lazy2) push_down2(now,tl,tr);
     int mid = (tl+tr)/;
     Modify1(now<<,tl,mid,l,r,s,t);
     Modify1(now<<|,mid+,tr,l,r,s,t);
     push_up(now);
 }

 void Modify2(int now,int tl,int tr,int l,int r,int s,int t){
     if(tl >= l && tr <= r){
     fugai(now,tl,tr,s,t);
     return;
     }
     if(tl > r || tr < l){return;}
     if(T[now].lazx1<=maxn||T[now].lazy1<=maxn) push_down1(now,tl,tr);
     if(T[now].lazx2||T[now].lazy2) push_down2(now,tl,tr);
     int mid = (tl+tr)/;
     Modify2(now<<,tl,mid,l,r,s,t);
     Modify2(now<<|,mid+,tr,l,r,s,t);
     push_up(now);
 }

 void work(){
     build_tree(,,n);
     for(int i=;i<=m;i++){
     int cas; scanf("%d",&cas);
     if(cas == ){
         int l,r; scanf("%d%d",&l,&r);
         node forw = Query(,,n,l,r);
         double pjx = 1.0*forw.sumx/(r-l+),pjy = 1.0*forw.sumy/(r-l+);
         double res=forw.multi+pjx*pjy*(r-l+)-pjx*forw.sumy-pjy*forw.sumx;
         res /= 1.0*(forw.sqr+pjx*pjx*(r-l+)-2.0*pjx*forw.sumx);
         printf("%.10lf\n",res);
     }else{
         if(cas == ){
         int l,r,s,t; scanf("%d%d%d%d",&l,&r,&s,&t);
         Modify1(,,n,l,r,s,t);
         }else{
         int l,r,s,t; scanf("%d%d%d%d",&l,&r,&s,&t);
         Modify2(,,n,l,r,s,t);
         }
     }
     }
 }

 int main(){
     read();
     work();
     return ;
 }