hdu 2444 二分图判定+求二分图最大匹配

分手后的思念是犯贱 2022-08-02 13:36 259阅读 0赞

# The Accomodation of Students #

**Time Limit: 5000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)  
Total Submission(s): 3259    Accepted Submission(s): 1524**

Problem Description

There are a group of students. Some of them may know each other, while others don't. For example, A and B know each other, B and C know each other. But this may not imply that A and C know each other.  
  
Now you are given all pairs of students who know each other. Your task is to divide the students into two groups so that any two students in the same group don't know each other.If this goal can be achieved, then arrange them into double rooms. Remember, only paris appearing in the previous given set can live in the same room, which means only known students can live in the same room.  
  
Calculate the maximum number of pairs that can be arranged into these double rooms.

Input

For each data set:  
The first line gives two integers, n and m(1<n<=200), indicating there are n students and m pairs of students who know each other. The next m lines give such pairs.  
  
Proceed to the end of file.

Output

If these students cannot be divided into two groups, print "No". Otherwise, print the maximum number of pairs that can be arranged in those rooms.

Sample Input

4 4
    1 2
    1 3
    1 4
    2 3
    6 5
    1 2
    1 3
    1 4
    2 5
    3 6

Sample Output

No
    3

Source

[2008 Asia Harbin Regional Contest Online ][2008 Asia Harbin Regional Contest Online]

#include<map>
    #include<vector>
    #include<cstdio>
    #include<iostream>
    #include<cstring>
    #include<string>
    #include<algorithm>
    #include<cmath>
    #include<stack>
    #include<queue>
    #include<set>
    #define inf 0x3f3f3f3f
    #define mem(a,x) memset(a,x,sizeof(a))
    
    using namespace std;
    
    typedef long long ll;
    typedef pair<int,int> pii;
    
    inline int in()
    {
        int res=0;char c;
        while((c=getchar())<'0' || c>'9');
        while(c>='0' && c<='9')res=res*10+c-'0',c=getchar();
        return res;
    }
    
    
    int n,m;
    vector<int> v[222];
    int vis[222];
    int color[222];
    int a[222];
    int flag;
    
    void init()
    {
        for(int i=0;i<=n;i++)v[i].clear();
        mem(color,0);
        mem(vis,0);
        flag=1;
        mem(a,0);
    }
    void dfs(int x)//dfs染色法判断是不是二分图
    {
        for(int i=0;i<(int)v[x].size();i++)
        {
            int t = v[x][i];
            if(!color[t])
            {
                color[t]=3-color[x];
                dfs(t);
            }
            else if(color[t]==color[x])
            {
                flag=0;
            }
        }
    
    }
    bool DFS(int x)//DFS求二分图最大匹配
    {
        for(int i=0;i<(int)v[x].size();i++)
        {
            int t=v[x][i];
            if(vis[t]!=flag)
            {
                vis[t]=flag;
                if(a[t]==0 || DFS(a[t]))
                {
                    a[t]=x;
                    a[x]=t;
                    return 1;
                }
            }
        }
        return 0;
    }
    int main()
    {
        while(scanf("%d%d",&n,&m)!=EOF)
        {
            init();
            for(int i=1;i<=m;i++)
            {
                int t1=in(),t2=in();
                v[t1].push_back(t2);
                v[t2].push_back(t1);
    
            }
            int ans=0;
            for(int i=1;i<=n;i++)
            {
                if(!color[i])
                {
                    color[i]=1;
                    dfs(i);
    
                }
            }
            if(!flag)
            {
                puts("No");
                continue;
            }
            for(int i=1;i<=n;i++)
            {
                if(!a[i])
                {
                    flag=i;
                    if(DFS(i))
                    ans++;
                }
            }
            printf("%d\n",ans);
        }
        return 0;
    }

[2008 Asia Harbin Regional Contest Online]: http://acm.hdu.edu.cn/search.php?field=problem&key=2008+Asia+Harbin+Regional+Contest+Online&source=1&searchmode=source