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POJ 3241 Object Clustering 莫队算法

2024-08-09 00:17:51   218人阅读


第n-k大曼哈顿距离,莫队算法裸题


Object Clustering
Time Limit: 2000MS Memory Limit: 131072K
Total Submissions: 1584 Accepted: 366

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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