# Codeforces 1198C Matching vs Independent Set

Portal

Idea: The way to find a matching set is greed. For edges (u,v), if u and V are not covered by other edges already in the set, then add edges (u,v) to the set, and finally determine whether the number of edges in the set is greater than or equal to n. If it is greater than or equal to n, it can output n edges directly. If it is less than n, there must be an independent edge. Except for the points covered by edges in the matching set, there must be other edges. Because the number of edges in the matching set is less than n, then the number of points covered by edges in the matching set is less than 2*n, then there must be more than n points outside the matching set, and these points are independent of each other, that is, there is no edge connection.

```#include <algorithm>
#include <iostream>
#include <cstdlib>
#include <cstring>
#include <cstdio>
#include <string>
#include <queue>
#include <cmath>
#include <stack>
#include <time.h>
#include <map>
#include <set>
#define mem(a,x) memset(a,x,sizeof(a))
#define gi(x) scanf("%d",&x)
#define gi2(x,y) scanf("%d%d",&x,&y)
#define gi3(x,y,z) scanf("%d%d%d",&x,&y,&z)
#define gll(x) scanf("%lld",&x)
#define gll2(x,y) scanf("%lld%lld",&x,&y)
#define random(x) (rand()%x)
using namespace std;
const double eps=1e-8;
typedef long long ll;
const int MAXN=300005;
const ll mod=1e9+7;
const int inf=0x3f3f3f3f;
int book[MAXN];
vector<int>ans;
int main(){
int T;gi(T);
while(T--){
int n,m;
gi2(n,m);
for(int i=1;i<=3*n;i++)book[i]=0;
ans.clear();
for(int i=1;i<=m;i++){
int u,v;gi2(u,v);
if(!book[u]&&!book[v]){
book[u]=book[v]=1;
ans.push_back(i);
}
}
if(ans.size()>=n){
puts("Matching");
for(int i=0;i<n;i++){
printf("%d%c",ans[i],i==n-1?'\n':' ');
}
}
else{
puts("IndSet");
int cnt=0;
for(int i=1;i<=3*n;i++){
if(book[i]==0){
cnt++;
printf("%d",i);
printf("%c",cnt==n?'\n':' ');
}
if(cnt==n)break;
}
}
}
return 0;
}```

Keywords: less

Added by lances on Thu, 10 Oct 2019 19:06:11 +0300