[SDOI2010]捉迷藏 K-Dtree

Posted 2022-04-22 dsrdsr

[SDOI2010]捉迷藏

链接

luogu

思路

k-dtree模板题

代码

#include <bits/stdc++.h>
#define ls (t[u].ch[0])
#define rs (t[u].ch[1])
#define cmin(a,b) (a>b?a=b:a)
#define cmax(a,b) (a>b?a:a=b)
using namespace std;
const int N=5e5+7;
const int INF=0x3f3f3f3f;
int read() 
    int x=0,f=1;char s=getchar();
    for(;s>'9'||s<'0';s=getchar()) if(s=='-') f=-1;
    for(;s>='0'&&s<='9';s=getchar()) x=x*10+s-'0';
    return x*f;

int n,rt,WD;
struct point 
    int x[2];
    bool operator < (const point &b) const 
        return x[WD]<b.x[WD];
    
p[N];
struct node
    int mi[2],ma[2],ch[2];
    point a;
t[N];
void update(int x,int y) 
    cmin(t[x].mi[0],t[y].mi[0]);
    cmin(t[x].mi[1],t[y].mi[1]);
    cmax(t[x].ma[0],t[y].ma[0]);
    cmax(t[x].ma[1],t[y].ma[1]);

void up(int u) 
    t[u].mi[0]=t[u].ma[0]=t[u].a.x[0];
    t[u].mi[1]=t[u].ma[1]=t[u].a.x[1];
    if(ls) update(u,ls);
    if(rs) update(u,rs);

int build(int l,int r,int wd) 
    if(l>r) return 0;
    int mid=(l+r)>>1;
    WD=wd;
    nth_element(p+l,p+mid,p+r+1);
    int u=mid;
    t[u].a=p[mid];
    ls=build(l,mid-1,wd^1);
    rs=build(mid+1,r,wd^1);
    up(u);
    return u;

int dis(point a,point b) 
    return abs(a.x[0]-b.x[0])+abs(a.x[1]-b.x[1]);

int get_min(int u,point a) 
    int rec=0;
    for(int i=0;i<2;++i)
        rec+=max(t[u].mi[i]-a.x[i],0)+max(a.x[i]-t[u].ma[i],0);
    return rec;

int get_max(int u,point a) 
    int rec=0;
    for(int i=0;i<2;++i)
        rec+=max(abs(a.x[i]-t[u].ma[i]),abs(a.x[i]-t[u].mi[i]));
    return rec;

int ans1,ans2;
void query_min(point a,int u) 
    if(dis(a,t[u].a)) ans1=min(ans1,dis(a,t[u].a));
    int dl=INF,dr=INF;
    if(ls) dl=get_min(ls,a);
    if(rs) dr=get_min(rs,a);
    if(dl<dr) 
        if(ans1>dl) query_min(a,ls);
        if(ans1>dr) query_min(a,rs);
     else 
        if(ans1>dr) query_min(a,rs);
        if(ans1>dl) query_min(a,ls);
    

void query_max(point a,int u) 
    ans2=max(ans2,dis(a,t[u].a));
    int dl=-INF,dr=-INF;
    if(ls) dl=get_max(ls,a);
    if(rs) dr=get_max(rs,a);
    if(dl<dr) 
        if(ans2<dr) query_max(a,rs);
        if(ans2<dl) query_max(a,ls);
     else 
        if(ans2<dl) query_max(a,ls);
        if(ans2<dr) query_max(a,rs);
    

int main() 
    n=read();
    for(int i=1;i<=n;++i) p[i].x[0]=read(),p[i].x[1]=read();
    rt=build(1,n,0);
    int ans=INF;
    for(int i=1;i<=n;++i) 
        ans1=INF,ans2=0;
        query_min(p[i],rt);
        query_max(p[i],rt);
//      printf("(%d,%d) min=%d max=%d\n",p[i].x[0],p[i].x[1],ans1,ans2);
        ans=min(ans,ans2-ans1);
    
    printf("%d",ans);
    return 0;