Vertex Cover

frog has a graph with \(n\) vertices \(v(1), v(2), \dots, v(n)\) and \(m\) edges \((v(a_1), v(b_1)), (v(a_2), v(b_2)), \dots, (v(a_m), v(b_m))\).

She would like to color some vertices so that each edge has at least one colored vertex.

Find the minimum number of colored vertices.

Input

The input consists of multiple tests. For each test:

The first line contains \(2\) integers \(n, m\) (\(2 \leq n \leq 500, 1 \leq m \leq \frac{n(n - 1)}{2}\)). Each of the following \(m\) lines contains \(2\) integers \(a_i, b_i\) (\(1 \leq a_i, b_i \leq n, a_i \neq b_i, \min\{a_i, b_i\} \leq 30\))

Output

For each test, write \(1\) integer which denotes the minimum number of colored vertices.

Sample Input

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

Sample Output

    1
    2

#include <bits/stdc++.h>
#define mp make_pair
#define pb push_back
#define met(a,b) memset(a,b,sizeof a)
using namespace std;
typedef long long ll;
typedef pair<int,int>pii;
const int N = 1e5+5;
const double eps = 1e-8;
int T,n,cnt,m;
bool ok=true;
int k,mi[N];
int a[N],vis[N],match[N];
char str[N],s[N];
vector<int>edg[N];
bool dfs(int now){
    for(int i=0;i<edg[now].size();++i){
        int x=edg[now][i];
        if(!vis[x]){
            vis[x]=1;
            if(!match[x]||dfs(match[x])){
                match[now]=x;
                match[x]=now;
                return true;
            }
        }
    }
    return false;
}
int main()
{
    int u,v;
    while(~scanf("%d%d",&n,&m)){
        for(int i=0;i<N;i++)edg[i].clear(),match[i]=0;
        int ans=0;
        while(m--){
            scanf("%d%d",&u,&v);
            edg[u].pb(v);
            edg[v].pb(u);
        }
        for(int i=1;i<=n;i++){
            if(!match[i]){
                met(vis,0);
                if(dfs(i))ans++;
            }
        }
        printf("%d\n",ans);
    }
    return 0;
}