K-D树：bzoj 1941: [Sdoi2010]Hide and Seek (板子)

  1 #include<cstdio>
  2 #include<cstring>
  3 #include<iostream>
  4 #include<algorithm>
  5 #define ls(x) a[x].l
  6 #define rs(x) a[x].r
  7 using namespace std;
  8 const int N=500066;
  9 int abss(int x){return x<0?-x:x;}
 10 int maxn(int a,int b){return a>b?a:b;}
 11 int minn(int a,int b){return a<b?a:b;}
 12 void swap(int &x,int &y){x^=y;y^=x;x^=y;}
 13
 14 int cmpid,n,ans;
 15 struct son
 16 {
 17     int x[2];
 18     friend bool operator < (son a,son b)
 19     {
 20         return a.x[cmpid]>b.x[cmpid];
 21     }
 22 }p[N];
 23
 24 struct tree
 25 {
 26     son p;
 27     int mx[2],mn[2],l,r;
 28 }a[N];
 29 int dis(son a,son b){return abss(a.x[0]-b.x[0])+abss(a.x[1]-b.x[1]);}
 30 int maxdis(tree t,son c)
 31 {
 32     int temp1=maxn( abss(c.x[0]-t.mn[0]),abss(c.x[0]-t.mx[0]) );
 33     int temp2=maxn( abss(c.x[1]-t.mn[1]),abss(c.x[1]-t.mx[1]) );
 34     return temp1+temp2;
 35 }
 36 int mindis(tree t,son c)
 37 {
 38     int temp1=maxn(t.mn[0]-c.x[0],0)+maxn(c.x[0]-t.mx[0],0);
 39     int temp2=maxn(t.mn[1]-c.x[1],0)+maxn(c.x[1]-t.mx[1],0);
 40     return temp1+temp2;
 41 }
 42
 43 struct KDtree
 44 {
 45     int ans,root,tot,temp;
 46     void qqmax(son q,int x,int k)
 47     {
 48         if(!x)return ;
 49         temp=dis(a[x].p,q);
 50         if(temp>ans)ans=temp;
 51         int l=ls(x),r=rs(x);
 52         if(q.x[k]<a[x].p.x[k])swap(l,r);//右边更有可能
 53         if(ans<maxdis(a[l],q))qqmax(q,l,k^1);
 54         if(ans<maxdis(a[r],q))qqmax(q,r,k^1);
 55     }
 56     int qqmax(son q)
 57     {
 58         ans=-0x7fffffff;
 59         qqmax(q,root,0);
 60         return ans;
 61     }
 62     void qqmin(son q,int x,int k)
 63     {
 64         if(!x)return ;
 65         temp=dis(a[x].p,q);
 66         if(temp<ans&&temp)ans=temp;
 67         int l=ls(x),r=rs(x);
 68         if(q.x[k]>a[x].p.x[k])swap(l,r);//也是右边更有可能
 69         if(mindis(a[l],q)<ans)qqmin(q,l,k^1);
 70         if(mindis(a[r],q)<ans)qqmin(q,r,k^1);
 71     }
 72     int qqmin(son q)
 73     {
 74         ans=0x7fffffff;
 75         qqmin(q,root,0);
 76         return ans;
 77     }
 78     void pushup(int x)
 79     {
 80         if(!x)return ;
 81         if(ls(x))
 82           for(int i=0;i<2;++i)
 83             {
 84                 a[x].mn[i]=minn(a[x].mn[i],a[ls(x)].mn[i]);
 85                 a[x].mx[i]=maxn(a[x].mx[i],a[ls(x)].mx[i]);
 86             }
 87         if(rs(x))
 88           for(int i=0;i<2;++i)
 89           {
 90                 a[x].mn[i]=minn(a[x].mn[i],a[rs(x)].mn[i]);
 91                 a[x].mx[i]=maxn(a[x].mx[i],a[rs(x)].mx[i]);
 92             }
 93     }
 94     void build(int l,int r,int &x,int k)
 95     {
 96         if(l>r)return ;
 97         x=++tot;
 98         int mid=(l+r)>>1;
 99         cmpid=k;
100         nth_element(p+l,p+mid,p+r+1);
101         a[x].p=p[mid];
102         for(int i=0;i<2;++i)
103           a[x].mn[i]=a[x].mx[i]=a[x].p.x[i];
104         build(l,mid-1,ls(x),k^1);
105         build(mid+1,r,rs(x),k^1);
106         pushup(x);
107     }
108     void build()
109     {
110         tot=0;
111         build(1,n,root,0);
112     }
113 }T;
114 int main(){
115
116     scanf("%d",&n);
117     for(int i=1;i<=n;++i)
118       scanf("%d%d",&p[i].x[0],&p[i].x[1]);
119
120     T.build();
121
122     ans=0x7fffffff;
123
124     for(int i=1;i<=n;++i)
125       ans=minn(ans,T.qqmax(p[i])-T.qqmin(p[i]));
126
127     cout<<ans;
128     //while(1);
129     return 0;
130 }

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