【BZOJ1941】Hide and Seek（KD-Tree）
题面
题解
\(KD-Tree\)对于每个点搜一下最近点和最远点就好了
#include<iostream>
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<cmath>
#include<algorithm>
#include<set>
#include<map>
#include<vector>
#include<queue>
using namespace std;
#define ll long long
#define RG register
#define MAX 555555
#define cmin(a,b) (a=(a>b?b:a));
#define cmax(a,b) (a=(a<b?b:a));
#define ls (t[o].ch[0])
#define rs (t[o].ch[1])
inline int read()
{
RG int x=0,t=1;RG char ch=getchar();
while((ch<'0'||ch>'9')&&ch!='-')ch=getchar();
if(ch=='-')t=-1,ch=getchar();
while(ch<='9'&&ch>='0')x=x*10+ch-48,ch=getchar();
return x*t;
}
struct Node{int d[2];}a[MAX];
int D;
bool operator<(Node a,Node b){return a.d[D]<b.d[D];}
struct KD_Node
{
int mn[2],mx[2],ch[2];
Node a;
}t[MAX];
int n,rt;
int mxd[MAX],mnd[MAX];
void pushup(int x,int y)
{
cmin(t[x].mn[0],t[y].mn[0]);cmin(t[x].mn[1],t[y].mn[1]);
cmax(t[x].mx[0],t[y].mx[0]);cmax(t[x].mx[1],t[y].mx[1]);
}
int Build(int l,int r,int nd)
{
D=nd;int o=(l+r)>>1;
nth_element(&a[l],&a[o],&a[r+1]);
t[o].mn[0]=t[o].mx[0]=t[o].a.d[0]=a[o].d[0];
t[o].mn[1]=t[o].mx[1]=t[o].a.d[1]=a[o].d[1];
if(l<o)ls=Build(l,o-1,nd^1),pushup(o,ls);
if(r>o)rs=Build(o+1,r,nd^1),pushup(o,rs);
return o;
}
int Dis(Node a,Node b){return abs(a.d[0]-b.d[0])+abs(a.d[1]-b.d[1]);}
int min_Dis(Node a,KD_Node t)
{
return max(t.mn[0]-a.d[0],0)+max(a.d[0]-t.mx[0],0)+max(t.mn[1]-a.d[1],0)+max(a.d[1]-t.mx[1],0);
}
int max_Dis(Node a,KD_Node t)
{
return max(abs(a.d[0]-t.mn[0]),abs(a.d[0]-t.mx[0]))+max(abs(a.d[1]-t.mn[1]),abs(a.d[1]-t.mx[1]));
}
int Ans,Min,Max;
void Query_mn(int o,Node a)
{
int tmp=Dis(a,t[o].a),d[2];
if(tmp)cmin(Min,tmp);
if(ls)d[0]=min_Dis(a,t[ls]);else d[0]=1e9;
if(rs)d[1]=min_Dis(a,t[rs]);else d[1]=1e9;
tmp=d[0]>=d[1];
if(d[tmp]<Min)Query_mn(t[o].ch[tmp],a);tmp^=1;
if(d[tmp]<Min)Query_mn(t[o].ch[tmp],a);tmp^=1;
}
void Query_mx(int o,Node a)
{
if(Max-Min>=Ans)return;
int tmp=Dis(a,t[o].a),d[2];
if(tmp)cmax(Max,tmp);
if(ls)d[0]=max_Dis(a,t[ls]);else d[0]=0;
if(rs)d[1]=max_Dis(a,t[rs]);else d[1]=0;
tmp=d[0]<=d[1];
if(d[tmp]>Max)Query_mx(t[o].ch[tmp],a);tmp^=1;
if(d[tmp]>Max)Query_mx(t[o].ch[tmp],a);tmp^=1;
}
int main()
{
n=read();
for(int i=1;i<=n;++i)a[i].d[0]=read(),a[i].d[1]=read();
rt=Build(1,n,0);Ans=1e9;
for(int i=1;i<=n;++i)
{
Min=1e9;Query_mn(rt,a[i]);
Max=000;Query_mx(rt,a[i]);
Ans=min(Ans,Max-Min);
}
printf("%d\n",Ans);
return 0;
}