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第n-k大曼哈顿距离,莫队算法裸题
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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 dij = |ai - aj| + |bi - bj|, and then we say i is dij 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 dij ≤ 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 Source
POJ Monthly--2007.08.05, Li, Haoyuan
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/* ***********************************************
Author :CKboss
Created Time :2014年12月20日 星期六 00时27分00秒
File Name :POJ3241.cpp
************************************************ */
#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <string>
#include <cmath>
#include <cstdlib>
#include <vector>
#include <queue>
#include <set>
#include <map>
using namespace std;
const int maxn=22000;
const int INF=0x3f3f3f3f;
int n,k;
struct Edge
{
int u,v,w;
}edge[maxn<<2];
int tot;
bool cmp_E(Edge a,Edge b)
{
return a.w<b.w;
}
struct Point
{
int x,y,id;
}pt[maxn];
bool cmp_P(Point a,Point b)
{
if(a.x!=b.x) return a.x<b.x;
return a.y<b.y;
}
int lowbit(int x) { return x&(-x); }
int C[4000],D[4000];
void update(int id,int pos,int val)
{
pos+=1000;
for(int i=pos;i;i-=lowbit(i))
{
if(C[i]>val)
{
C[i]=val; D[i]=id;
}
}
}
void query(int id,int pos,int val)
{
pos+=1000;
int Fr=-1,ret=INF;
for(int i=pos;i<4000;i+=lowbit(i))
{
if(ret>C[i])
{
ret=C[i]; Fr=D[i];
}
}
if(Fr!=-1) edge[tot++]=(Edge){id,Fr,ret-val};
}
void gao()
{
memset(C,63,sizeof(C));
sort(pt,pt+n,cmp_P);
for(int i=n-1;i>=0;i--)
{
int pos=pt[i].y-pt[i].x;
int sum=pt[i].y+pt[i].x;
int id=pt[i].id;
query(id,pos,sum);
update(id,pos,sum);
}
}
int fa[maxn];
int find(int x)
{
if(x==fa[x]) return x;
return fa[x]=find(fa[x]);
}
bool merge(int a,int b)
{
a=find(a); b=find(b);
if(a==b) return false;
fa[a]=b;
return true;
}
int solve()
{
if(n==k) return 0;
tot=0;
gao();
for(int i=0;i<n;i++)
swap(pt[i].x,pt[i].y);
gao();
for(int i=0;i<n;i++)
pt[i].y=-pt[i].y;
gao();
for(int i=0;i<n;i++)
swap(pt[i].x,pt[i].y);
gao();
for(int i=0;i<n;i++) fa[i]=i;
sort(edge,edge+tot,cmp_E);
for(int i=0;i<tot;i++)
{
if(merge(edge[i].u,edge[i].v)==true)
{
n--; if(n==k) return edge[i].w;
}
}
return -1;
}
int main()
{
//freopen("in.txt","r",stdin);
//freopen("out.txt","w",stdout);
while(scanf("%d%d",&n,&k)!=EOF)
{
for(int i=0;i<n;i++)
{
int x,y;
scanf("%d%d",&x,&y);
pt[i].x=x; pt[i].y=y; pt[i].id=i;
}
printf("%d\n",solve());
}
return 0;
}
POJ 3241 Object Clustering 莫队算法
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原文地址：http://blog.csdn.net/ck_boss/article/details/42037223
