[BZOJ 2735]世博会 主席树 切比雪夫距离转曼哈顿距离

#include<iostream>
#include<cstdio>
#include<cstring>
#include<cstdlib>
#include<vector>
#include<algorithm>
#define N 101000
#define pos(i,a,b) for(int i=(a);i<=(b);i++)
using namespace std;
#define LL long long
int n,q;
LL a[N],b[N];
vector<LL> v;
int findx(int x){
	return lower_bound(v.begin(),v.end(),x)-v.begin()+1;
}
struct haha{
	int lc,rc,num;LL sum;
}tree1[N*25],tree2[N*25];
int root1[N],root2[N];
int size1,size2,len;
void update1(int &rt,int l,int r,int pos,LL num){
	tree1[++size1]=tree1[rt];
	int t=size1;tree1[t].num++;tree1[t].sum+=num;
	rt=t;
	if(l==r) return;
	int mid=(l+r)>>1;
	if(pos<=mid) update1(tree1[rt].lc,l,mid,pos,num);
	else update1(tree1[rt].rc,mid+1,r,pos,num);
}
void update2(int &rt,int l,int r,int pos,LL num){
	tree2[++size2]=tree2[rt];
	int t=size2;tree2[t].num++;tree2[t].sum+=num;
	rt=t;
	if(l==r) return;
	int mid=(l+r)>>1;
	if(pos<=mid) update2(tree2[rt].lc,l,mid,pos,num);
	else update2(tree2[rt].rc,mid+1,r,pos,num);
}
LL tot1_l;
int query1(int rtl,int rtr,int l,int r,int k){
	if(l==r){
		tot1_l+=v[l-1];
		return l;
	} 
	int num=tree1[tree1[rtr].lc].num-tree1[tree1[rtl].lc].num;
	LL sum=tree1[tree1[rtr].lc].sum-tree1[tree1[rtl].lc].sum;
	int mid=(l+r)>>1;
	if(num>=k){
		return query1(tree1[rtl].lc,tree1[rtr].lc,l,mid,k);
	}
	else{
		tot1_l+=sum;
		return query1(tree1[rtl].rc,tree1[rtr].rc,mid+1,r,k-num);
	}
}
LL tot2_l;
int query2(int rtl,int rtr,int l,int r,int k){
	if(l==r){
		tot2_l+=v[l-1];
		return l;
	} 
	int num=tree2[tree2[rtr].lc].num-tree2[tree2[rtl].lc].num;
	LL sum=tree2[tree2[rtr].lc].sum-tree2[tree2[rtl].lc].sum;
	int mid=(l+r)>>1;
	if(num>=k){
		return query2(tree2[rtl].lc,tree2[rtr].lc,l,mid,k);
	}
	else{
		tot2_l+=sum;
		return query2(tree2[rtl].rc,tree2[rtr].rc,mid+1,r,k-num);
	}
}
int main(){
	scanf("%d%d",&n,&q);len=n*2;
	pos(i,1,n) scanf("%lld",&a[i]);
	pos(i,1,n) scanf("%lld",&b[i]);
	pos(i,1,n){
		LL x=a[i],y=b[i];
		a[i]=(x+y);b[i]=(x-y);
		v.push_back(a[i]);
		v.push_back(b[i]);
	}
	sort(v.begin(),v.end());
	v.erase(unique(v.begin(),v.end()),v.end());
	pos(i,1,n){
		root1[i]=root1[i-1];
		update1(root1[i],1,len,findx(a[i]),a[i]);
		root2[i]=root2[i-1];
		update2(root2[i],1,len,findx(b[i]),b[i]);
	}
	pos(i,1,q){
		int x,y;double ans=0.0;scanf("%d%d",&x,&y);
		LL cnt1(0),tot1(0),cnt1_l(0),mid1(0);
		cnt1=tree1[root1[y]].num-tree1[root1[x-1]].num;
		tot1=tree1[root1[y]].sum-tree1[root1[x-1]].sum;
		tot1_l=0;cnt1_l=(cnt1>>1)+1;
		mid1=v[query1(root1[x-1],root1[y],1,len,cnt1_l)-1];
		ans+=cnt1_l*mid1-tot1_l+(tot1-tot1_l)-mid1*(cnt1-cnt1_l);
		LL cnt2(0),tot2(0),cnt2_l(0),mid2(0);
		cnt2=tree2[root2[y]].num-tree2[root2[x-1]].num;
		tot2=tree2[root2[y]].sum-tree2[root2[x-1]].sum;
		tot2_l=0;cnt2_l=(cnt2>>1)+1;
		mid2=v[query2(root2[x-1],root2[y],1,len,cnt2_l)-1];
		ans+=cnt2_l*mid2-tot2_l+(tot2-tot2_l)-mid2*(cnt2-cnt2_l);
		printf("%.2f\n",ans/2);
	}
	return 0;
}