【最大匹配】COURSES POJ1469

COURSES

Time Limit: 1000MS Memory Limit: 10000K

Description

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 
  

Input

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

P N 
Count1 Student_{1 1} Student_{1 2} ... Student_{1 Count1} 
Count2 Student_{2 1} Student_{2 2} ... Student_{2 Count2} 
... 
CountP Student_{P 1} Student_{P 2} ... Student_{P 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抣l 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. 

Output

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.

Sample Input

23 33 1 2 32 1 21 13 32 1 32 1 31 1

Sample Output

YESNO

题意：给出P个课程和N个人，每个人只能选一个课程，问这P个课程能不能被这N个人选完

题意清楚了，很容易想到就是二分图最大匹配，最后判断最大匹配是否等于P即可

这是第一道二分图匹配的练习题，一次AC

测评情况（POJ）

/*http://blog.csdn.net/jiangzh7By Jiangzh*/#include<cstdio>#include<cstring>const int N=300+10;int n,m;bool map[N][N];bool h[N];int pre[N];bool search(int x){for(int i=1;i<=m;i++)if(map[x][i]&&!h[i]){h[i]=true;if(pre[i]==-1||search(pre[i])){pre[i]=x;return true;}}return false;}void work(){scanf("%d%d",&n,&m);for(int i=1;i<=n;i++){int cnt;scanf("%d",&cnt);while(cnt--){int x;scanf("%d",&x);map[i][x]=true;}}int res=0;for(int i=1;i<=n;i++){memset(h,0,sizeof(h));if(search(i)) res++;}if(res==n) puts("YES");else puts("NO");}int main(){freopen("poj1469.in","r",stdin);freopen("poj1469.out","w",stdout);int g;scanf("%d",&g);while(g--){memset(map,0,sizeof(map));memset(pre,-1,sizeof(pre));work();}return 0;}