POJ3164 Command Network(最小树形图)

图论填个小坑。以前就一直在想，无向图有最小生成树，那么有向图是不是也有最小生成树呢，想不到还真的有，叫做最小树形图，网上的介绍有很多，感觉下面这个博客介绍的靠谱点：

http://www.cnblogs.com/vongang/archive/2012/07/18/2596851.html

所以下面的代码也是抄上面的模板的。里面还给出了不定根情况下的最小树形图的做法，新增一个虚拟根，连向其它所有点的费用是总费用＋1，然后跑一次算法就可以了，这样可以保证虚拟根一定连出去某个顶点，而且不可能连两个，最后跑出来把多的费用减掉就可以了。感觉想法挺神奇的。

#pragma warning(disable:4996)

#include <iostream>

#include <cstring>

#include <string>

#include <vector>

#include <cstdio>

#include <algorithm>

#include <cmath>

using namespace std;



#define maxn 120

#define maxm 12000



int n, m;



struct Edge{

	int u, v;

	double w;

	Edge(int ui, int vi, double wi) :u(ui), v(vi), w(wi){}

	Edge(){}

};



vector<Edge> E;



double x[maxn], y[maxn];



double dist(int i, int j){

	return sqrt((x[i] - x[j])*(x[i] - x[j]) + (y[i] - y[j])*(y[i] - y[j]));

}



double in[maxn]; // minimum pre edge weight

int pre[maxn]; // pre vertex

int vis[maxn]; // vis array

int id[maxn]; // mark down the id

int nv; // nv is the number of vertex after shrinking



double directed_mst(int root)

{

	double ret = 0; int nv = n;

	while (1){

		for (int i = 0; i < nv; ++i) in[i] = 1e10;

		for (int i = 0; i < m; ++i){

			int u = E[i].u, v = E[i].v;

			if (E[i].w < in[v] && u != v){

				in[v] = E[i].w;

				pre[v] = u;

			}

		}

		// found not connected means impossible

		for (int i = 0; i < nv; ++i){

			if (i == root) continue;

			if (in[i]>1e9) return -1;

		}

		int cnt = 0;

		memset(id, -1, sizeof(id));

		memset(vis, -1, sizeof(vis));

		in[root] = 0;



		for (int i = 0; i < nv; ++i){

			ret += in[i];

			int v = i;



			while (vis[v] != i&&id[v] == -1 && v != root){

				vis[v] = i;

				v = pre[v];

			}

			// v!=root means we find a circle,id[v]==-1 guarantee that it's not shrinked.

			if (v != root&&id[v] == -1){

				for (int u = pre[v]; u != v; u = pre[u]){

					id[u] = cnt;

				}

				id[v] = cnt++;

			}

		}

		if (cnt == 0) break;

		for (int i = 0; i < nv; ++i){

			if (id[i] == -1) id[i] = cnt++;

		}

		// change the cost of edge for each (u,v,w)->(u,v,w-in[v])

		for (int i = 0; i < m; ++i){

			int v = E[i].v;

			E[i].u = id[E[i].u];

			E[i].v = id[E[i].v];

			if (E[i].u != E[i].v) E[i].w -= in[v];

		}

		// mark down the new root

		root = id[root];

		// mark down the new vertex number

		nv = cnt;

	}

	return ret;

}



int main()

{

	while (cin >> n >> m){

		E.clear();

		for (int i = 0; i < n; ++i){

			scanf("%lf%lf", x + i, y + i);

		}

		int ui, vi;

		for (int i = 0; i < m; ++i){

			scanf("%d%d", &ui, &vi);

			--ui; --vi;

			if (ui != vi) E.push_back(Edge(ui, vi, dist(ui,vi)));

		}

		m = E.size();

		double ans = directed_mst(0);

		if (ans < 0) puts("poor snoopy");

		else printf("%.2f\n", ans);

	}

	return 0;

}