HDU3367-Pseudoforest-优快云博客

本文链接：https://blog.youkuaiyun.com/a664607530/article/details/52503701

本文介绍了一种求解最大伪森林问题的算法实现，通过输入顶点和边的数据，利用并查集和贪心策略找到图中每个连通分量最多只包含一个环的最大权重子图。

摘要生成于 C知道，由 DeepSeek-R1 满血版支持，前往体验 >

Pseudoforest

Time Limit: 10000/5000 MS (Java/Others) Memory Limit: 65536/65536 K (Java/Others)
Total Submission(s): 2701 Accepted Submission(s): 1068

Problem Description

In graph theory, a pseudoforest is an undirected graph in which every connected component has at most one cycle. The maximal pseudoforests of G are the pseudoforest subgraphs of G that are not contained within any larger pseudoforest of G. A pesudoforest is larger than another if and only if the total value of the edges is greater than another one’s.

Input

The input consists of multiple test cases. The first line of each test case contains two integers, n(0 < n <= 10000), m(0 <= m <= 100000), which are the number of the vertexes and the number of the edges. The next m lines, each line consists of three integers, u, v, c, which means there is an edge with value c (0 < c <= 10000) between u and v. You can assume that there are no loop and no multiple edges.
The last test case is followed by a line containing two zeros, which means the end of the input.

Output

Output the sum of the value of the edges of the maximum pesudoforest.

Sample Input

Sample Output

3
5

Source

“光庭杯”第五届华中北区程序设计邀请赛暨 WHU第八届程序设计竞赛

题目意思就是给出一个图，要求出最大的pseudoforest，所谓pseudoforest就是指这个图的一个子图，这个子图的每个连通分量中最多只能有一个环，而且这个子图的所有权值之和最大。这个就是所谓的伪森林。

#include <iostream>
#include <string.h>
#include <stdio.h>
#include <algorithm>

using namespace std;

int n,m,k;
int parent[10009];
int visit[10009];
int sum,ans;

struct node
{
    int a,b,w;
}edge[100009];

int Find(int x)
{
    int s=x;
    while(parent[s]>=0) s=parent[s];
    while(s!=x)
    {
        int tmp=parent[x];
        parent[x]=s;
        x=tmp;
    }
    return s;
}

int cmp(node a,node b)
{
    return a.w>b.w;
}

int main()
{
    while(~scanf("%d %d",&n,&m))
    {
        if(n==0&&m==0) break;
        sum=0;
        memset(visit,0,sizeof visit);
        memset(parent,-1,sizeof parent);
        for(int i=0; i<m; i++)
            scanf("%d %d %d",&edge[i].a,&edge[i].b,&edge[i].w);
        sort(edge,edge+m,cmp);
        for(int i=0; i<m; i++)
        {
            int a1=Find(edge[i].a),b1=Find(edge[i].b);
            if(a1==b1&&!visit[a1])
            {
                sum+=edge[i].w;visit[a1]=1;
            }
            else
            {
                if(visit[a1]&&visit[b1]) continue;
                if((!visit[a1]&&visit[b1])||(!visit[b1]&&visit[a1]))
                {
                    int a1=Find(edge[i].a),b1=Find(edge[i].b);
                    parent[a1]=b1;
                    sum+=edge[i].w;
                    visit[a1]=1;visit[b1]=1;
                }
                else if(!visit[a1]&&!visit[b1])
                {
                    int a1=Find(edge[i].a),b1=Find(edge[i].b);
                    parent[a1]=b1;
                    sum+=edge[i].w;
                }
            }
        }
        printf("%d\n",sum);
    }
    return 0;
}