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=0,ch=getchar();!isdigit(ch);ch=getchar()) if (ch=='-') ok=1;
    for (x=0;isdigit(ch);x=x*10+ch-'0',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=-1;}
    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=1;i<=cntd;i++) node[i].init();}
    void insert(int x,DATA p){for (int i=cntd-x+1;i<=cntd;i+=lowbit(i)) node[i].update(p);}
    int query(int x){
        DATA ans; ans.init();
        for (int i=cntd-x+1;i;i-=lowbit(i)) ans.update(node[i]);
        return ans.pos;
    }
}T;
struct Edge{
    int u,v,c;
}edge[maxn<<2];
bool cmp2(Edge a,Edge b){return a.c<b.c;}
void prepare(){
    for (int i=1;i<=n;i++) d[i]=point[i].d=point[i].y-point[i].x;
    sort(d+1,d+n+1),cntd=unique(d+1,d+n+1)-d-1;
    for (int i=1;i<=n;i++) point[i].d=lower_bound(d+1,d+cntd+1,point[i].d)-d;
    sort(point+1,point+n+1,cmp1),T.init();
    for (int i=1;i<=n;i++){
        int u=point[i].id,v=T.query(point[i].d);
        if (v!=-1) 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=1;i<=n;i++) read(point[i].x),read(point[i].y),point[i].id=i;
    for (int i=1;i<=n;i++) tmp[i]=point[i]; prepare();
    for (int i=1;i<=n;i++) point[i].x=tmp[i].y,point[i].y=tmp[i].x,point[i].id=i; prepare();
    for (int i=1;i<=n;i++) point[i].x=-tmp[i].y,point[i].y=tmp[i].x,point[i].id=i; prepare();
    for (int i=1;i<=n;i++) point[i].x=tmp[i].x,point[i].y=-tmp[i].y,point[i].id=i; prepare();
    sort(edge+1,edge+m+1,cmp2);
    for (int i=1;i<=n;i++) fa[i]=i;
    for (int i=1,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
",ans);
    return 0;
}