poj-1469-COURSES

poj-1469-COURSES

COURSES

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 24542		Accepted: 9557

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

2
3 3
3 1 2 3
2 1 2
1 1
3 3
2 1 3
2 1 3
1 1

Sample Output

YES
NO

Source

Southeastern Europe 2000

17919736

1469

Accepted

512K

407MS

G++

906B

2017-12-04 22:09:08

经典的匈牙利算法解决方法。

利用二分图，找到每一个学生和course之间的match，使用匈牙利算法。

// poj-1469 

#include <cstdio> 
#include <cstring> 
const int MAXN = 300 + 10; 

int P, N, num[MAXN], course[MAXN][MAXN]; 

int match[MAXN], vis[MAXN]; 

bool dfs(int x){
	for(int i=1; i<=num[x]; ++i){
		int y = course[x][i]; 
		if( vis[y] == 0 ){
			vis[y] = 1;
			if(match[y] < 0 || dfs(match[y])){
				match[y] = x; 
				return true; 
			}
		}
	}
	return false; 
}

int main(){
	freopen("in.txt", "r", stdin); 

	int test_num; 
	scanf("%d", &test_num); 

	int ans; 
	while(test_num--){
		scanf("%d %d", &P, &N); 
		for(int i=1; i<=P; ++i){
			scanf("%d", &num[i]); 
			for(int j=1; j<=num[i]; ++j){
				scanf("%d", &course[i][j]); 
			} 
		}

		if(P > N){
			printf("NO
");
			continue; 
		}

		ans = 0; 
		memset(match, -1, sizeof(match));  

		for(int i=1; i<=P; ++i){
			memset(vis, 0, sizeof(vis));  
			if( dfs(i) ){
				++ans; 
			}
		} 

		if(ans >= P){ 
			printf("YES
");
		}else{
			printf("NO
");
		} 
	}
	return 0; 
}