HDU4966 GGS-DDU(最小树形图)

之前几天想着补些算法的知识，学了一下最小树形图的朱刘算法，不是特别理解，备了份模板以备不时之需，想不到多校冷不丁的出了个最小树形图，没看出来只能表示对算法不太理解吧,用模板写了一下，然后就过了。－ －0

之前听到是最小树形图的时候觉得恍然大悟，非常裸，但是后来想想也不是特别裸，其实关键就是要想清楚要加回流的边，贴一份代码吧－ －0

#pragma warning(disable:4996)

#include<cstdio>

#include<set>

#include<cstring>

#include<iostream>

#include<stdlib.h>

#include<vector>

#include<map>

#include<algorithm>

#include<queue>

#include<cmath>

#include<functional>

#include<string>

using namespace std;



#define maxn 550



int n, m;

int a[55];



struct Edge{

	int u, v, w;

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

	Edge(){}

};



vector<Edge> E;

vector<int> vid[55];



int 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



int directed_mst(int root,int vertex_num)

{

	int ret = 0; int nv = vertex_num;

	while (1){

		for (int i = 0; i < nv; ++i) in[i] = 1e9;

		for (int i = 0; i < E.size(); ++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;

			}

		}

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

			if (i == root) continue;

			if (in[i]>1e8) 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 < E.size(); ++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){

		if (n == 0 && m == 0) break;

		int tot = 0;

		for (int i = 1; i <= n; ++i) {

			vid[i].clear();

			scanf("%d", a + i);

			for (int j = 0; j <= a[i]; ++j){

				vid[i].push_back(++tot);

			}

		}

		++tot;

		E.clear();

		for (int i = 1; i <= n; ++i){

			for (int j = 0; j < vid[i].size(); ++j){

				for (int k = j + 1; k < vid[i].size(); ++k){

					E.push_back(Edge(vid[i][k], vid[i][j], 0));

				}

			}

		}

		int ci, l1, di, l2, wi;

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

			scanf("%d%d%d%d%d", &ci, &l1, &di, &l2, &wi);

			E.push_back(Edge(vid[ci][l1], vid[di][l2], wi));

		}

		for (int i = 1; i <= n; ++i){

			E.push_back(Edge(0, vid[i][0], 0));

		}

		int ans = directed_mst(0,tot);

		printf("%d\n", ans);

	}

	return 0;

}