https://codeforces.com/contest/1133/problem/F2

题解：先把与1无关的点合并，然后找与一相关必须连接的边，对于答案树想连必须的边，再连其他一相关边，最后连其他边

C++版本一

/*
*@Author:   STZG
*@Language: C++
*/
#include <bits/stdc++.h>
#include<iostream>
#include<algorithm>
#include<cstdlib>
#include<cstring>
#include<cstdio>
#include<string>
#include<vector>
#include<bitset>
#include<queue>
#include<deque>
#include<stack>
#include<cmath>
#include<list>
#include<map>
#include<set>
//#define DEBUG
#define RI register int
using namespace std;
typedef long long ll;
//typedef __int128 lll;
const int N=200000+10;
const int M=100000+10;
const int MOD=1e9+7;
const double PI = acos(-1.0);
const double EXP = 1E-8;
const int INF = 0x3f3f3f3f;
int t,n,m,k,q;
int ans,cnt,flag,temp,sum,u,v,d;
int a[N];
int pre[N];
int preans[N];
int vis[N];
bool broken[N];
char str;
vector<int>G[N];
struct Node{
    int u,v;
    bool operator <(const Node&S)const{
        if(u==S.u)
            return v<S.v;
        return u<S.u;
    }
}x;
vector <Node>ANS;
int find(int x){return (pre[x]==x)?x:pre[x]=find(pre[x]);}
int findans(int x){return (preans[x]==x)?x:preans[x]=findans(preans[x]);}
int main()
{
#ifdef DEBUG
	freopen("input.in", "r", stdin);
	//freopen("output.out", "w", stdout);
#endif
    //ios::sync_with_stdio(false);
    //cin.tie(0);
    //cout.tie(0);
    //scanf("%d",&t);
    //while(t--){
    scanf("%d%d%d",&n,&m,&d);
    for(int i=1;i<=m;i++){
        scanf("%d%d",&u,&v);
        G[u].push_back(v);
        G[v].push_back(u);
    }
    if((int)G[1].size()<d){
        cout<<"NO"<<endl;
        return 0;
    }
    for(int i=1;i<=n;i++){
        pre[i]=i;
        preans[i]=i;
    }
    for(int i=2;i<=n;i++){
        for(int j=0,k=G[i].size();j<k;j++){
            u=i;
            v=G[i][j];
            if(v==1)
                continue;
            int tx=find(u);
            int ty=find(v);
            if(tx!=ty){
                pre[tx]=ty;
            }
        }
    }
    for(int i=0,j=G[1].size();i<j;i++){
            u=1;
            v=G[1][i];
            int tx=find(u);
            int ty=find(v);
            if(tx!=ty){
                pre[tx]=ty;
                //cout<<u<<" "<<v<<endl;
                x.u=u;
                x.v=v;
                int ta=findans(u);
                int tb=findans(v);
                preans[ta]=tb;
                ANS.push_back(x);
                if(++cnt>=d)
                    break;
            }
    }
    for(int i=0,j=G[1].size();i<j;i++){
            u=1;
            v=G[1][i];
            int ta=findans(u);
            int tb=findans(v);
            if(cnt>=d)
                    break;
            if(ta!=tb){
                //cout<<u<<" "<<v<<endl;
                cnt++;
                x.u=u;
                x.v=v;
                preans[ta]=tb;
                ANS.push_back(x);
            }
    }
    for(int i=2;i<=n;i++){
        for(int j=0,k=G[i].size();j<k;j++){
            u=i;
            v=G[i][j];
            if(v==1)
                continue;
            int ta=findans(u);
            int tb=findans(v);
            if(ta!=tb){
                //cout<<u<<" "<<v<<endl;
                x.u=u;
                x.v=v;
                preans[ta]=tb;
                ANS.push_back(x);
            }
        }
    }
    flag=0;
    for(int i=1;i<=n;i++){
        if(pre[i]==i){
            flag++;
        }
    }
    if(flag>1){
        cout<<"NO"<<endl;
    }else{
        cout<<"YES"<<endl;
        sort(ANS.begin(),ANS.end());
        for(int i=0,j=ANS.size();i<j;i++){
            x=ANS[i];
            cout<<x.u<<" "<<x.v<<endl;
        }
    }

    //}

#ifdef DEBUG
	printf("Time cost : %lf s\n",(double)clock()/CLOCKS_PER_SEC);
#endif
    //cout << "Hello world!" << endl;
    return 0;
}

C++版本二

#include <cstdio>
#include <algorithm>
#include <cstring>
using namespace std;
const int MAX_N=2e5+10;
int par[MAX_N];     //父亲
int ranks[MAX_N];    //树的高度
struct Edge{int u,v;};
Edge edges[MAX_N];
int cnt[MAX_N]={0,};
int n,m,k;
int ans[MAX_N],q=0;
void init(){
    for(int i=1;i<=n;i++){
        par[i]=i;
        ranks[i]=0;
    }
}

int findit(int x){
    if(par[x]==x)
        return x;
    else
        return par[x]=findit(par[x]);
}

void unite(int x, int y){
    x=findit(x);
    y=findit(y);
    if(x==y) return;
    if(ranks[x]<ranks[y])
        par[x]=y;
    else par[y]=x;
    if(ranks[x]==ranks[y])
        ranks[x]++;
}

bool same(int x, int y){
    return findit(x)==findit(y);
}


int main(void){
    scanf("%d %d %d",&n,&m,&k);
    init();
    for(int i=0;i<m;++i)
    {
        scanf("%d %d",&edges[i].u,&edges[i].v);
        cnt[edges[i].u]++;
        cnt[edges[i].v]++;
    }
    if(cnt[1]<k){
        printf("NO\n");
        return 0;
    }
    //先把剩下的点连起来
    for(int i=0;i<m;++i)
        if(edges[i].u!=1&&edges[i].v!=1)
            if(!same(edges[i].u,edges[i].v))
                unite(edges[i].u,edges[i].v);
    //得到顶点1必须选用的边
    for(int i=0;i<m;++i){
        if(edges[i].u==1||edges[i].v==1){
            if(!same(edges[i].u,edges[i].v)){
                unite(edges[i].u,edges[i].v);
                ans[q++]=i;
            }
        }
    }
    if(q>k){
        printf("NO\n");
        return 0;
    }
    //重新初始化
    init();
    printf("YES\n");
    for(int i=0;i<q;++i){
        unite(edges[ans[i]].u,edges[ans[i]].v);
        printf("%d %d\n",edges[ans[i]].u,edges[ans[i]].v);
    }
    for(int i=0;i<m&&q<k;++i){
        if(edges[i].u==1||edges[i].v==1){
            if(!same(edges[i].u,edges[i].v)){
                unite(edges[i].u,edges[i].v);
                printf("%d %d\n",edges[i].u,edges[i].v);
                q++;
            }
        }
    }
    //再连其他点
    for(int i=0;i<m;++i){
        if(edges[i].u!=1&&edges[i].v!=1){
            if(!same(edges[i].u,edges[i].v)){
                unite(edges[i].u,edges[i].v);
                printf("%d %d\n",edges[i].u,edges[i].v);
            }
        }
    }
}