(beginer) 最小生成树 UVA 11747 Heavy Cycle Edges

Problem F: Heavy Cycle Edges

Given an undirected graph with edge weights, a minimum spanning tree is a subset of edges of minimum total weight such that any two nodes are connected by some path containing only these edges. A popular algorithm for finding the minimum spanning tree T in a graph proceeds as follows:

• let T be initially empty
• consider the edges e₁, ..., e_m in increasing order of weight
  • add e_i to T if the endpoints of e_i are not connected by a path in T

An alternative algorithm is the following:

• let T be initially the set of all edges
• while there is some cycle C in T
  • remove edge e from T where e has the heaviest weight in C

Your task is to implement a function related to this algorithm. Given an undirected graph G with edge weights, your task is to output all edges that are the heaviest edge in some cycle of G.

Input Format

The first input of each case begins with integers n and m with 1 ≤ n ≤ 1,000 and 0 ≤ m ≤ 25,000 where n is the number of nodes and m is the number of edges in the graph. Following this are m lines containing three integers u, v, and w describing a weight w edge connecting nodes u and v where 0 ≤ u, v < n and 0 ≤ w < 2³¹. Input is terminated with a line containing n = m = 0; this case should not be processed. You may assume no two edges have the same weight and no two nodes are directly connected by more than one edge.

Output Format

Output for an input case consists of a single line containing the weights of all edges that are the heaviest edge in some cycle of the input graph. These weights should appear in increasing order and consecutive weights should be separated by a space. If there are no cycles in the graph then output the text forest instead of numbers.

Sample Input

3 3
0 1 1
1 2 2
2 0 3
4 5
0 1 1
1 2 2
2 3 3
3 1 4
0 2 0
3 1
0 1 1
0 0

Sample Output

3
2 4
forest

题意：把找最小生成树的步骤改成是删除环中最大的边。输出边的长度。

思路：其实和一开始是空的然后加边是一样的，因为我们在加边的时候就要判断会不会形成环，那么我们照样用kruskal算法，然后如果加边会形成环就把他输出就行了。

代码：

#include<iostream>
#include<stdio.h>
#include<string.h>
#include<cstring>
#include<algorithm>
using namespace std;
const int maxn = 1010;
const int maxm = 25010;
int n , m;
int p[maxn];

int find(int x)
{
	if (x==p[x]) return x;
	return p[x] = find(p[x]);
}

struct Edge
{
	Edge() { }
	Edge(int uu,int vv,int ww)
		:u(uu) , v(vv) , w(ww) { }
	int u , v , w;
}edge[maxm];

inline bool operator<(const Edge&e1,const Edge&e2)
{
	return e1.w < e2.w;
}

void input()
{
	for (int i = 0 ; i < m ; ++i)
	{
		int u , v , w;
		scanf("%d%d%d",&u,&v,&w);
		edge[i] = Edge(u,v,w);
	}
	sort(edge,edge+m);
}

void solve()
{
	bool flag = true;
	for (int i = 0 ; i < n ; ++i) p[i] = i;
	for (int i = 0 ; i < m ;  ++i)
	{
		int u = find(edge[i].u);
		int v = find(edge[i].v);
		if (u==v) {
			if (flag) printf("%d",edge[i].w);
			else printf(" %d",edge[i].w);
			flag = false;
			continue;
		}
		p[u] = v;
	}
	if (flag) printf("forest");
	cout << endl;
}

int main()
{
	while (scanf("%d%d",&n,&m)==2,n+m)
	{
		input();
		solve();
	}
}