老oj3444 && Pku3241 Object Clustering

Description

We have N (N ≤ 10000) objects, and wish to classify them into several groups by judgement of their resemblance. To simply the model, each object has 2 indexes a and b (a, b ≤ 500). The resemblance of object i and object j is defined by d_ij = |a_i - a_j| + |b_i - b_j|, and then we say i is d_ij resemble to j. Now we want to find the minimum value of X, so that we can classify the N objects into K (K < N) groups, and in each group, one object is at most X resemble to another object in the same group, i.e, for every object i, if i is not the only member of the group, then there exists one object j (i ≠ j) in the same group that satisfies d_ij ≤ X

Input

The first line contains two integers N and K. The following N lines each contain two integers a and b, which describe a object.

Output

A single line contains the minimum X.

Sample Input

6 2
1 2
2 3
2 2
3 4
4 3
3 1

Sample Output

2

又是一道曼哈顿距离最小生成树。。。
code：

 #include<cstdio>
 #include<iostream>
 #include<cmath>
 #include<cstring>
 #include<algorithm>
 #define maxn 100005
 #define inf 1061109567
 using namespace std;
 char ch;
 bool ok;
 void read(int &x){
     for (ok=,ch=getchar();!isdigit(ch);ch=getchar()) if (ch=='-') ok=;
     for (x=;isdigit(ch);x=x*+ch-'',ch=getchar());
     if (ok) x=-x;
 }
 struct Point{
     int x,y,d,id;
 }point[maxn],tmp[maxn];
 bool cmp1(Point a,Point b){
     if (a.x!=b.x) return a.x>b.x;
     return a.y>b.y;
 }
 int calc(Point a,Point b){return abs(a.x-b.x)+abs(a.y-b.y);}
 int n,m,k,ans;
 struct DATA{
     int val,pos;
     void init(){val=inf,pos=-;}
     void update(DATA b){if (val>b.val) val=b.val,pos=b.pos;}
 };
 int d[maxn],cntd;
 struct bit{
     #define lowbit(x) ((x)&(-(x)))
     DATA node[maxn];
     void init(){for (int i=;i<=cntd;i++) node[i].init();}
     void insert(int x,DATA p){for (int i=cntd-x+;i<=cntd;i+=lowbit(i)) node[i].update(p);}
     int query(int x){
         DATA ans; ans.init();
         for (int i=cntd-x+;i;i-=lowbit(i)) ans.update(node[i]);
         return ans.pos;
     }
 }T;
 struct Edge{
     int u,v,c;
 }edge[maxn<<];
 bool cmp2(Edge a,Edge b){return a.c<b.c;}
 void prepare(){
     for (int i=;i<=n;i++) d[i]=point[i].d=point[i].y-point[i].x;
     sort(d+,d+n+),cntd=unique(d+,d+n+)-d-;
     for (int i=;i<=n;i++) point[i].d=lower_bound(d+,d+cntd+,point[i].d)-d;
     sort(point+,point+n+,cmp1),T.init();
     for (int i=;i<=n;i++){
         int u=point[i].id,v=T.query(point[i].d);
         if (v!=-) edge[++m]=(Edge){u,v,calc(tmp[u],tmp[v])};
         T.insert(point[i].d,(DATA){point[i].x+point[i].y,u});
     }
 }
 int fa[maxn];
 int find(int x){return x==fa[x]?fa[x]:fa[x]=find(fa[x]);}
 int main(){
     read(n),read(k);
     for (int i=;i<=n;i++) read(point[i].x),read(point[i].y),point[i].id=i;
     for (int i=;i<=n;i++) tmp[i]=point[i]; prepare();
     for (int i=;i<=n;i++) point[i].x=tmp[i].y,point[i].y=tmp[i].x,point[i].id=i; prepare();
     for (int i=;i<=n;i++) point[i].x=-tmp[i].y,point[i].y=tmp[i].x,point[i].id=i; prepare();
     for (int i=;i<=n;i++) point[i].x=tmp[i].x,point[i].y=-tmp[i].y,point[i].id=i; prepare();
     sort(edge+,edge+m+,cmp2);
     for (int i=;i<=n;i++) fa[i]=i;
     for (int i=,cnt=n;i<=m&&cnt>k;i++) if (find(edge[i].u)!=find(edge[i].v))
         cnt--,ans=max(ans,edge[i].c),fa[find(edge[i].u)]=find(edge[i].v);
     printf("%d\n",ans);
     return ;
 }