Poj (1466), maximum independent set, Hungarian algorithm

Title Link: http://poj.org/problem?id=1466

Girls and Boys

Time Limit: 5000MS		Memory Limit: 10000K
Total Submissions: 12026		Accepted: 5355

Description

In the second, 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 was necessary to find out the the maximum set satisfying the condition:there was no and the students in T He set who has been "romantically involved". The result of the program was the number of students in such a set.

Input

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 a integer number between 0 and n-1 (n <=500), for n subjects.

Output

For each given data set, the program should write to standard output a line containing the result.

Sample Input

70: (3) 4 5 61: (2) 4 62: (0) 3: (0) 4: (2) 0 15: (1) 06: (2) 0 130: (2) 1 21: (1) 02: (1) 0

Sample Output

52

Source

Southeastern Europe 2000 Test instructions: There are n individuals, each with a certain number of other people, the relationship is called the romantic relationship, and then finally the largest collection, so that there is no romantic relationship between all the people in the collection 22. Analysis: 1, maximum independent set = number of vertices-maximum number of matches 2, Hungarian algorithm 3, where the male and female sex is not given, the matching relationship magnified one times, then the actual number of matches is/2.

#include <stdio.h>#include<string.h>#defineMAX 505intN;BOOLMaps[max][max];BOOLUse[max];intMatch[max];BOOLDFS (intStu) {    intnum =0;  for(intI=0; i<n; i++)    {        if(!use[i]&&Maps[stu][i]) {Use[i]=true; if(match[i]==-1||DFS (Match[i])) {Match[i]=Stu; return true; }        }    }    return false;}intMain () { while(SCANF ("%d", &n)! =EOF) {memset (match,-1,sizeof(match)); memset (Maps,false,sizeof(maps));  for(intI=0; i<n; i++)        {            intU,num; scanf ("%d: (%d)",&u,&num);  for(intI=0; i<num; i++)            {                intv; scanf ("%d",&4); MAPS[U][V]=true; }        }        intnum =0;  for(intI=0; i<n; i++) {memset (use,false,sizeof(use)); if(DFS (i)) num++; } printf ("%d\n", n-num/2); }    return 0;}

Poj (1466), maximum independent set, Hungarian algorithm