ZOJ1137 二分图的最大独立点集 匈牙利算法

本文介绍了一种求解二分图中最大独立点集的方法,通过使用匈牙利算法找到最大匹配数,并据此推算出最大独立集的大小。文章提供了一个具体的实现案例,对比了邻接矩阵和邻接表两种数据结构的效率。

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Girls and Boys


Time Limit: 10 Seconds      Memory Limit: 32768 KB


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.

An example is given in Figure 1.


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


Output

5
2

 

求二分图的最大独立点集 , 用匈牙利算法先求出最大匹配数 , 然后用总数减去最大匹配数就是题目要求的答案 . 刚开始用了邻接矩阵 , 严重超时 , 改成邻接表就过了 .

 

代码如下 :

 


 

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