[bzoj1941][Sdoi2010]Hide and Seek

平面上n个点，一个点的贡献是离他最远的点的距离减去离他最近的点的距离，求最小的贡献.n<=500000

kdtree模板题，学习一发。

#include<iostream>
#include<cstdio>
#include<algorithm>
#define INF 2000000000
#define MN 500000
using namespace std;
inline int read()
{
    int x = 0 , f = 1; char ch = getchar();
    while(ch < '0' || ch > '9'){ if(ch == '-') f = -1;  ch = getchar();}
    while(ch >= '0' && ch <= '9'){x = x * 10 + ch - '0';ch = getchar();}
    return x * f;
}
int n,now;
inline int abs(int x){return x<0?-x:x;}
struct P{
    int d[2],mx[2],mn[2],l,r;
    int& operator[](int x){return d[x];}
    bool operator<(const P&x)const{return d[now]<x.d[now];}
    friend int dis(P x,P y){return abs(x.d[0]-y.d[0])+abs(x.d[1]-y.d[1]);}
}t[MN+5];

struct KD_TREE{
    P p[MN+5],T;int ans;
    void update(int x)
    {
        int l=p[x].l,r=p[x].r;
        for(int i=0;i<2;i++)
        {
            if(l) p[x].mn[i]=min(p[x].mn[i],p[l].mn[i]),
                  p[x].mx[i]=max(p[x].mx[i],p[l].mx[i]);
            if(r) p[x].mn[i]=min(p[x].mn[i],p[r].mn[i]),
                  p[x].mx[i]=max(p[x].mx[i],p[r].mx[i]);
        }
    }
    int getmn(P x)
    {
        int sum=0;
        for(int i=0;i<2;i++)
        {
            sum+=max(x.mn[i]-T[i],0);
            sum+=max(T[i]-x.mx[i],0); 
        }
        return sum;
    }
    int getmx(P x)
    {
        int sum=0;
        for(int i=0;i<2;i++)
            sum+=max(abs(x.mn[i]-T[i]),abs(x.mx[i]-T[i]));
        return sum;
    }
    int build(int l,int r,int th)
    {
        int mid=l+r>>1;now=th;
        nth_element(t+l,t+mid,t+r+1);
        p[mid]=t[mid];
        for(int i=0;i<2;i++)
            p[mid].mx[i]=p[mid].mn[i]=p[mid][i];
        if(l<mid) p[mid].l=build(l,mid-1,th^1);
        if(mid<r) p[mid].r=build(mid+1,r,th^1);
        update(mid);
        return mid;
    }
    void querymn(int k)
    {
        int t=dis(p[k],T);if(t)ans=min(ans,t);
        int dl=INF,dr=INF;
        if(p[k].l) dl=getmn(p[p[k].l]);
        if(p[k].r) dr=getmn(p[p[k].r]);    
        if(dl>dr)
        {    
            if(dr<ans) querymn(p[k].r);
            if(dl<ans) querymn(p[k].l);
        }
        else 
        {
            if(dl<ans) querymn(p[k].l);
            if(dr<ans) querymn(p[k].r);
        }
    }
    void querymx(int k)
    {
        ans=max(ans,dis(p[k],T));
        int dl=-INF,dr=-INF;
        if(p[k].l) dl=getmx(p[p[k].l]);
        if(p[k].r) dr=getmx(p[p[k].r]);
        if(dl>dr)
        {
            if(dl>ans) querymx(p[k].l);
            if(dr>ans) querymx(p[k].r);
        } 
        else
        {
            if(dr>ans) querymx(p[k].r);
            if(dl>ans) querymx(p[k].l); 
        }
    } 
}kdtree;
int rt,ans=INF;

int main()
{
    n=read();
    for(int i=1;i<=n;i++)
        t[i][0]=read(),t[i][1]=read();
    rt=kdtree.build(1,n,0);
    for(int i=1;i<=n;i++)
    {
        kdtree.T=t[i];
        kdtree.ans=INF; kdtree.querymn(rt);int mn=kdtree.ans;
        kdtree.ans=-INF;kdtree.querymx(rt);int mx=kdtree.ans;
        ans=min(ans,mx-mn);
    }
    cout<<ans;
    return 0;
}