HDU - 2121 Ice_cream’s world II （不定根树形图）

Ice_cream’s world II Time Limit: 3000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others) Total Submission(s): 6367    Accepted Submission(s): 1658   Problem Description After awarded lands to ACMers, the queen want to choose a city be her capital. This is an important event in ice_cream world, and it also a very difficult problem, because the world have N cities and M roads, every road was directed. Wiskey is a chief engineer in ice_cream world. The queen asked Wiskey must find a suitable location to establish the capital, beautify the roads which let capital can visit each city and the project’s cost as less as better. If Wiskey can’t fulfill the queen’s require, he will be punishing.   Input Every case have two integers N and M (N<=1000, M<=10000), the cities numbered 0…N-1, following M lines, each line contain three integers S, T and C, meaning from S to T have a road will cost C.   Output If no location satisfy the queen’s require, you must be output “impossible”, otherwise, print the minimum cost in this project and suitable city’s number. May be exist many suitable cities, choose the minimum number city. After every case print one blank.   Sample Input 3 1 0 1 1 4 4 0 1 10 0 2 10 1 3 20 2 3 30   Sample Output impossible 40 0   Author Wiskey   Source HDU 2007-10 Programming Contest_WarmUp   Recommend 威士忌

       大体题意就是让你看能否找到一个不定根的最小树形图。这样的话和多起点的最短路一样，虚拟一个超级源点，建一条比所有边总和sum多1的边，看最后的结果是否大于2*（sum+1），不是的话就是原图有最小树形图，是的话就代表没有。

#include<iostream>
#include<cstdio>
#include<string>
#include<algorithm>
using namespace std;
#define inf 0x3f3f3f3f
struct fuck
{
	int from, to, len;
}ed[1000005];
int id[1005];
int pre[1005];
int vis[1005];
int in[1005];
int n, m, pos;
int zhuliu(int root)
{
	int res = 0;
	while (1)
	{
		for (int s = 0; s < n; s++)
			in[s] = inf;
		for (int s = 0; s < m; s++)
		{
			if (ed[s].from != ed[s].to&&in[ed[s].to] > ed[s].len)
			{
				in[ed[s].to] = ed[s].len;
				pre[ed[s].to] = ed[s].from;
				if (ed[s].from == root)
				{
					//	cout << s << " " << ed[s].from << " " << ed[s].to << endl;
					pos = s;
				}
			}
		}
		for (int s = 0; s < n; s++)
			if (in[s] == inf && s != root)
				return -1;
		int sum_huan = 0;
		in[root] = 0;
		memset(id, -1, sizeof(id));
		memset(vis, -1, sizeof(vis));
		for (int s = 0; s < n; s++)
		{
			res += in[s];
			int v = s;
			while (vis[v] != s&&id[v] == -1 && v != root)
			{
				vis[v] = s;
				v = pre[v];
			}
			if (v != root&&id[v] == -1)
			{
				for (int w = pre[v]; w != v; w = pre[w])
					id[w] = sum_huan;
				id[v] = sum_huan++;
			}
		}
		if (sum_huan == 0)
			break;
		for (int s = 0; s < n; s++)
		{
			if (id[s] == -1)
				id[s] = sum_huan++;
		}
		for (int s = 0; s < m; s++)
		{
			int v = ed[s].to;
			ed[s].from = id[ed[s].from];
			ed[s].to = id[ed[s].to];
			if (ed[s].from != ed[s].to)
			{
				ed[s].len -= in[v];
			}
		}
		n = sum_huan;
		root = id[root];
	}
	return res;
}
int main()
{
	while (~scanf("%d%d", &n, &m))
	{
		int k = m;
		int sum = 0;
		for (int s = 0; s < m; s++)
		{
			int a, b, c;
			scanf("%d%d%d", &a, &b, &c);
			ed[s].from = a, ed[s].to = b, ed[s].len = c;
			sum += c;
		}
		sum++;
		for (int s = 0; s < n; s++)
		{
			ed[m + s].from = n;
			ed[m + s].to = s;
			ed[m + s].len = sum;
		}
		m = m + n;
		n = n + 1;
		int ans = zhuliu(n-1);
		if (ans ==-1|| ans - sum >= sum)
		{
			printf("impossible\n\n");
		}
		else
		{
			printf("%d %d\n\n", ans - sum, pos - k);
		}
	}
}