题意：在一群男女同学之间存在”浪漫关系”,且该关系只存在于男同学与女同学之间.现在给出你比如2号学生与4号学生有浪漫关系(但是没给出你到底2号是男同学还是4号是男同学).给出所有的关系,要你求出一个由学生构成的集合,该集合中任意两人都不存在”浪漫关系”.
思路：如果把男同学放左边,女同学放右边,如果男i与女j存在关系,那么左i与右j之间就连一条无向边. 其实最终我们要求的就是该二分图的最大独立集.可是现在问题是题目没有给出谁是男，谁是女的，该如何处理呢？其实很简单，不管三七二十一全部按照平常的方法添加进图，那么这个二分图就可以认为左边有一些男，有一些女的，那么匹配完其实就是左边全为男的，和左边全为女的都匹配了一次，显然这两个答案应该相等，所以最后结果除以2就是左边同一性别的答案。最后用总人数减去这个最大匹配即为该最大独立集。
#include<cstdio>
#include<cstring>
#include<vector>
#include<cmath>
using namespace std;
const int maxn=1000;
struct Max_Match
{
int n,m;
vector<int> g[maxn];
bool vis[maxn];
int left[maxn];
void init(int n)
{
this->n=n;
// this->m=m;
for(int i=1;i<=n;i++) g[i].clear();
memset(left,-1,sizeof(left));
}
bool match(int u)
{
for(int i=0;i<g[u].size();i++)
{
int v=g[u][i];
if(!vis[v])
{
vis[v]=true;
if(left[v]==-1 || match(left[v]))
{
left[v]=u;
return true;
}
}
}
return false;
}
int solve()
{
int ans=0;
for(int i=0;i<n;i++)
{
memset(vis,0,sizeof(vis));
if(match(i)) ans++;
}
return ans;
}
}MM;
int T;
int main()
{
int n,k;
while (scanf("%d",&n)!=EOF)
{
MM.init(n);
for (int i = 1;i<=n;i++)
{
int u,num;
scanf("%d: (%d)",&u,&num);
while (num--)
{
int v;
scanf("%d",&v);
MM.g[u].push_back(v);
// MM.g[v].push_back(u);
}
}
printf("%d\n",n-MM.solve()/2);
}
}
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
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
Sample Output
5 2
