P3707 [SDOI2017]相关分析

线段树裸题？但是真的很麻烦QAQ

题目给的式子是什么不用管，大力拆开，就是\(\frac{\sum x_iy_i-\overline xy_i-\overline yx_i+\overline x\overline y}{\sum x_i^2-2x_i\overline x+\overline x^2}\)

然后发现需要维护\(\sum x,\sum y,\sum xy,\sum x^2\)

剩下的就是维护两个标记，具体自己推吧，懒得写了，看代码，咕咕咕咕

#include<bits/stdc++.h>
#define il inline
#define vd void
#define rg register
typedef long long ll;
il int gi(){int x=0,f=1;char ch=getchar();while(!isdigit(ch)){if(ch=='-')f=-1;ch=getchar();}while(isdigit(ch))x=x*10+ch-'0',ch=getchar();return x*f;
}
struct data{double xy,x,y,x2;}s[400010];
il data operator +(const data&a,const data&b){return(data){a.xy+b.xy,a.x+b.x,a.y+b.y,a.x2+b.x2};}
bool lz0[400010],lz1[400010];
double lz0x[400010],lz0y[400010];
double lz1x[400010],lz1y[400010];
#define mid ((l+r)>>1)
il double ssum(int x){return 0.50*x*(x+1);}
il double ssqr(int x){return 1.00/6*x*(x+1)*(x*2+1);}
il vd Overwrite(int x,int l,int r,double x0,double y0){lz1[x]=1,lz0[x]=0;lz1x[x]=x0,lz1y[x]=y0;s[x]=(data){x0*y0*(r-l+1)+(x0+y0)*ssum(r-l+1)+ssqr(r-l+1),x0*(r-l+1)+ssum(r-l+1),y0*(r-l+1)+ssum(r-l+1),x0*x0*(r-l+1)+ssqr(r-l+1)+ssum(r-l+1)*x0*2};
}
il vd Modify(int x,int l,int r,double x1,double y1){if(!lz0[x])lz0[x]=1,lz0x[x]=lz0y[x]=0;lz0x[x]+=x1,lz0y[x]+=y1;s[x]=s[x]+(data){s[x].x*y1+s[x].y*x1+x1*y1*(r-l+1),(r-l+1)*x1,(r-l+1)*y1,s[x].x*x1*2+x1*x1*(r-l+1)};
}
il vd down(int x,int l,int r){if(lz1[x])Overwrite(x<<1,l,mid,lz1x[x],lz1y[x]),Overwrite(x<<1|1,mid+1,r,lz1x[x]+(mid-l+1),lz1y[x]+(mid-l+1)),lz1[x]=0;if(lz0[x])Modify(x<<1,l,mid,lz0x[x],lz0y[x]),Modify(x<<1|1,mid+1,r,lz0x[x],lz0y[x]),lz0[x]=0;
}
double X[100010],Y[100010];
il vd build(int x,int l,int r){if(l==r){s[x]=(data){X[l]*Y[l],X[l],Y[l],X[l]*X[l]};return;}build(x<<1,l,mid),build(x<<1|1,mid+1,r);s[x]=s[x<<1]+s[x<<1|1];
}
il vd update_M(int x,int l,int r,const int&L,const int&R,const double&x0,const double&y0){if(L<=l&&r<=R)return Modify(x,l,r,x0,y0);down(x,l,r);if(L<=mid)update_M(x<<1,l,mid,L,R,x0,y0);if(mid<R)update_M(x<<1|1,mid+1,r,L,R,x0,y0);s[x]=s[x<<1]+s[x<<1|1];
}
il vd update_O(int x,int l,int r,const int&L,const int&R,const double&x0,const double&y0){if(L<=l&&r<=R)return Overwrite(x,l,r,x0,y0);down(x,l,r);if(L<=mid){update_O(x<<1,l,mid,L,R,x0,y0);if(mid<R)update_O(x<<1|1,mid+1,r,L,R,x0+(mid-std::max(l,L)+1),y0+(mid-std::max(l,L)+1));}else update_O(x<<1|1,mid+1,r,L,R,x0,y0);s[x]=s[x<<1]+s[x<<1|1];
}
il data query(int x,int l,int r,const int&L,const int&R){if(L<=l&&r<=R)return s[x];down(x,l,r);if(L<=mid)if(mid<R)return query(x<<1,l,mid,L,R)+query(x<<1|1,mid+1,r,L,R);else return query(x<<1,l,mid,L,R);else return query(x<<1|1,mid+1,r,L,R);
}
int main(){
#ifndef ONLINE_JUDGEfreopen("3707.in","r",stdin);freopen("3707.out","w",stdout);
#endifint n=gi(),m=gi();for(rg int i=1;i<=n;++i)X[i]=gi();for(rg int i=1;i<=n;++i)Y[i]=gi();build(1,1,n);int o,l,r;double S,T;while(m--){o=gi();l=gi(),r=gi();if(o==1){data D=query(1,1,n,l,r);rg double px=D.x/(r-l+1),py=D.y/(r-l+1);printf("%.10lf\n",(D.xy-px*D.y-py*D.x+px*py*(r-l+1))/(D.x2-2*px*D.x+px*px*(r-l+1)));}else{S=gi(),T=gi();if(o==2)update_M(1,1,n,l,r,S,T);else update_O(1,1,n,l,r,S+l-1,T+l-1);}}return 0;
}