【HDU1068】Girls and Boys（最大独立集数，匈牙利算法）

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本文介绍了一种用于找出学生间浪漫关系中最大不冲突匹配集合的算法。通过具体实例展示了如何利用图论中的匹配理论来解决实际问题，并提供了一段C++代码实现，帮助读者理解算法的具体操作流程。

http://acm.hdu.edu.cn/showproblem.php?pid=1068

Girls and Boys

Time Limit: 20000/10000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 12150 Accepted Submission(s): 5725

Problem Description
the second year of the university somebody started a study on the romantic relations between the students. The relation “romantically involved” is defined between one girl and one boy. For the study reasons it is necessary to find out the maximum set satisfying the condition: there are no two students in the set who have been “romantically involved”. The result of the program is the number of students in such a set.

The input contains several data sets in text format. Each data set represents one set of subjects of the study, with the following description:

the number of students
the description of each student, in the following format
student_identifier:(number_of_romantic_relations) student_identifier1 student_identifier2 student_identifier3 …
or
student_identifier:(0)

The student_identifier is an integer number between 0 and n-1, for n subjects.
For each given data set, the program should write to standard output a line containing the result.

Sample Input
7
0: (3) 4 5 6
1: (2) 4 6
2: (0)
3: (0)
4: (2) 0 1
5: (1) 0
6: (2) 0 1
3
0: (2) 1 2
1: (1) 0
2: (1) 0

Sample Output
5
2

#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
int k;
int vis[515];
int fr[515][515];
int f[515];

bool find(int x)
{
    for(int i=0;i< k;i++)
    {
        if(!vis[i] && fr[x][i])
        {
            vis[i]=true;
            if(f[i]==-1||find(f[i]))
            {
                f[i]=x;
                return true;
            }
        }
    }
    return false;
}

int main()
{
    int a,b;
    int ans;
    while(~scanf("%d",&k))
    {
        memset(f,-1,sizeof(f));
        memset(fr,false,sizeof(fr));
        for(int i=0;i< k;i++)
        {
            scanf("%d: (%d)",&a,&b);
            while(b--)
            {
                int t;
                scanf("%d",&t);
                fr[a][t]=true;
                fr[t][a]=true;
            }
        }
        ans=0;
        for(int i=0;i< k;i++)
        {
            memset(vis,false,sizeof(vis));
            if(find(i))  
            ans++;
        }
        ans=k-(ans/2);
        printf("%d\n",ans);
    }
return 0;
}