POJ 3241 Object Clustering 曼哈顿距离最小生成树

标签：mst   poj   曼哈顿距离最小生成树   最小生成树   莫队算法   

题目大意：求出曼哈顿距离最小生成树上的第k大边权。

思路：首先，你要了解：http://blog.csdn.net/acm_cxlove/article/details/8890003

也就是说，我们以每一个点为中心，把平面分成8个部分，每一个部分我们只需要离这个点最近的点。然后加上建一条边连接这个边和最近的点。然后就是MST。

听说这个算法是莫队算法的基础，我现在就去学。

CODE：

#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
#define MAX 10010
#define INF 0x3f3f3f3f
using namespace std;

struct Edge{
	int x,y,length;
	
	bool operator <(const Edge &a)const {
		return length < a.length;
	}
	Edge(int _,int __,int ___):x(_),y(__),length(___) {}
	Edge() {}
}edge[MAX << 3];
struct Point{
	int x,y,_id;
	
	bool operator <(const Point &a)const {
		if(x == a.x)	return y < a.y;
		return x < a.x;
	}
	void Read() {
		scanf("%d%d",&x,&y);
	}
}point[MAX];

int points,k,edges;
int fenwick[MAX];

pair<int,int *> xx[MAX];
int y_x[MAX];

int father[MAX];

inline int CalcM(const Point &a,const Point &b)
{
	return abs(a.x - b.x) + abs(a.y - b.y);
}

inline int GetPos(int x)
{
	int re = 0;
	for(; x <= points; x += x&-x)
		if(point[fenwick[x]].x + point[fenwick[x]].y < point[re].x + point[re].y)
			re = fenwick[x];
	return re;
}

inline void Fix(int x,int pos)
{
	for(; x; x -= x&-x)
		if(point[fenwick[x]].x + point[fenwick[x]].y > point[pos].x + point[pos].y)
			fenwick[x] = pos;
}

void MakeGraph()
{
	for(int dir = 1; dir <= 4; ++dir) {
		if(dir == 2 || dir == 4)
			for(int i = 1; i <= points; ++i)
				swap(point[i].x,point[i].y);
		if(dir == 3)
			for(int i = 1; i <= points; ++i)
				point[i].y *= -1;
				
		sort(point + 1,point + points + 1);
		memset(fenwick,0,sizeof(fenwick));
		for(int i = 1; i <= points; ++i)
			xx[i] = make_pair(point[i].y - point[i].x,&y_x[i]);
		sort(xx + 1,xx + points + 1);
		int t = 0;
		xx[0].first = INF;
		for(int i = 1; i <= points; ++i) {
			t += (xx[i].first != xx[i - 1].first);
			*xx[i].second = t;
		}
		for(int i = points; i; --i) {
			int temp = GetPos(y_x[i]);
			if(temp)
				edge[++edges] = Edge(point[i]._id,point[temp]._id,CalcM(point[i],point[temp]));
			Fix(y_x[i],i);
		}
	}
}

int Find(int x)
{
	if(father[x] == x)	return father[x];
	return father[x] = Find(father[x]);
}

int MST()
{
	sort(edge + 1,edge + edges + 1);
	for(int i = 1; i <= edges; ++i) {
		int fx = Find(edge[i].x);
		int fy = Find(edge[i].y);
		if(fx != fy) {
			father[fx] = fy;
			if(!--k)
				return edge[i].length;
		}
	}
	return 0;
}

int main()
{
	cin >> points >> k;
	k = points - k;
	point[0].x = point[0].y = INF;
	for(int i = 1; i <= points; ++i) {
		point[i].Read();
		point[i]._id = i;
		father[i] = i;
	}
	MakeGraph();
	cout << MST() << endl;
	return 0;
}

POJ 3241 Object Clustering 曼哈顿距离最小生成树

标签：mst   poj   曼哈顿距离最小生成树   最小生成树   莫队算法   

原文地址：http://blog.csdn.net/jiangyuze831/article/details/41045515