Girls and Boys（二分匹配）

Girls and Boys

Time Limit : 20000/10000ms (Java/Other) Memory Limit : 65536/32768K (Java/Other)
Total Submission(s) : 9 Accepted Submission(s) : 7
[align=left]Problem Description[/align]
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.

[align=left]Sample Input[/align]

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

[align=left]Sample Output[/align]

5
2

[align=left]Source[/align]
Southeastern Europe 2000

题意：有男孩和女孩一共n个，给你一些关系对，表示他们会谈恋爱，求一个最大的子集，令其中的男孩女孩不会谈恋爱。

输入：

3 ----男孩和女孩一共3个

0: (2)
1 2 ---- 0号与两个人会恋爱：1，2号

1: (1) 0 ---同上解释

2: (1) 0

分析：题目是明显的二分图模型，但是输入没有指明那些是男孩/女孩。所以要拆点，把
i 拆成 i 跟 i' 分别放入X、Y，构造二分图。原先U = V - M，所以 2U = 2V - 2M。 分析：

故U = n - M'/2。