POJ 1466 Girls and Boys（最大独立集）

题目地址：点击打开链接

题意：

有n个学生，一些学生之间存在关系，现在要把学生弄到一个集合，这个集合中的学生两两不能有关系，求这个集合的

最大学生数是多少。

思路：

将每个点拆成两个点，一个当作是男的点，一个当作是女的点了，然后连边。由于关系是相互的，这样就造成了边的重

复。也就是边集是刚才的二倍，从而导致了最大匹配变成了

二倍。那么答案就是最大独立集=顶点数-最大匹配/2

代码：

#include<iostream>#include<cstdio>#include<cstring>#include<vector>using namespace std;const int maxn = 505;vector<int> g[maxn];int n, m, match[maxn];bool vis[maxn];bool dfs(int x){    for(int i = 0; i < g[x].size(); i++)    {        int v = g[x][i];        if(!vis[v])        {            vis[v] = 1;            if(match[v] == -1 || dfs(match[v]))            {                match[v] = x;                return 1;            }        }    }    return 0;}int Hungary(){    int res = 0;    for(int i = 1; i <= n; i++)    {        memset(vis, 0, sizeof(vis));        res += dfs(i);    }    return res;}int main(void){    while(cin >> n)    {        memset(match, -1, sizeof(match));        for(int i = 0; i < maxn; i++)            g[i].clear();        for(int i = 1; i <= n; i++)        {            int t = 0;            scanf("%d: (%d)", &t, &m);            while(m--)            {                scanf("%d", &t);                t++;                g[i].push_back(t);                g[t].push_back(i);            }        }        printf("%d\n", n-Hungary()/2);    }    return 0;}

Girls and Boys

Time Limit: 5000MS Memory Limit: 10000KTotal Submissions: 12485 Accepted: 5578

Description

In 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.

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 an 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