杭电oj-1083 C - Courses --mystical_curve

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本文介绍了一种通过二分匹配算法解决课程分配问题的方法。该问题涉及为P门课程分配N名学生，使得每门课程都有唯一的学生代表，并且每位学生只能代表一门课程。文章详细解释了输入文件格式及输出要求，并提供了一个完整的C++实现示例。

C - Courses

Consider a group of N students and P courses. Each student visits zero, one or more than one courses. Your task is to determine whether it is possible to form a committee of exactly P students that satisfies simultaneously the conditions:

. every student in the committee represents a different course (a student can represent a course if he/she visits that course)

. each course has a representative in the committee

Your program should read sets of data from a text file. The first line of the input file contains the number of the data sets. Each data set is presented in the following format:

P N
Count1 Student1 1 Student1 2 … Student1 Count1
Count2 Student2 1 Student2 2 … Student2 Count2
……
CountP StudentP 1 StudentP 2 … StudentP CountP

The first line in each data set contains two positive integers separated by one blank: P (1 <= P <= 100) - the number of courses and N (1 <= N <= 300) - the number of students. The next P lines describe in sequence of the courses . from course 1 to course P, each line describing a course. The description of course i is a line that starts with an integer Count i (0 <= Count i <= N) representing the number of students visiting course i. Next, after a blank, you’ll find the Count i students, visiting the course, each two consecutive separated by one blank. Students are numbered with the positive integers from 1 to N.

There are no blank lines between consecutive sets of data. Input data are correct.

The result of the program is on the standard output. For each input data set the program prints on a single line “YES” if it is possible to form a committee and “NO” otherwise. There should not be any leading blanks at the start of the line.

An example of program input and output:
Input
2
3 3
3 1 2 3
2 1 2
1 1
3 3
2 1 3
2 1 3
1 1
Output
YES
NO
单纯的二分匹配

//单纯的二分匹配
#include <iostream>
#include <cstdio>
#include <cstring>
#include <vector>
using namespace std;
const int N = 420;
int p,n,match[N],used[N];
vector<int> G[N];
void add_edge(int a,int b)
{
    G[a].push_back(b);
    G[b].push_back(a);
}
bool dfs(int a)
{
    used[a]=1;
    for(int i=0;i<G[a].size();i++)
    {
        int &e=G[a][i];int w=match[e];
        if(w<0||!used[w]&&dfs(w))
        {
            match[e]=a;
            match[a]=e;
            return true;
        }
    }
    return false;
}
bool bine()
{
    memset(match,-1,sizeof(match));
    for(int i=1;i<=p;i++)
    {
        if(match[i]<0)
        {
            memset(used,0,sizeof(used));
            if(!dfs(i))
                return false;
        }
    }
    return true;
}
int main()
{
    int t;cin>>t;
    while(t--)
    {
        cin>>p>>n;int c,d;
        for(int i=0;i<=n+p;i++)
        {
            G[i].clear();
        }
        for(int i=1;i<=p;i++)
        {
            cin>>c;
            for(int j=0;j<c;j++)
            {
                cin>>d;
                add_edge(i,p+d);
            }
        }
        if(bine())
            cout<<"YES"<<endl;
        else
            cout<<"NO"<<endl;
    }
    return 0;
}