Boruvka

时间复杂度： $O(m \log n)$

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<ll,ll> PLL;
#define x first
#define y second
const ll N=1e5+1e3,M=1e1+1e2;
ll n,m;
ll x,y,z;
ll t[2*N],weigh[2*N],nex[2*N],h[5*M],cnt;
PLL minm[5*M];
ll fa[5*M];
ll ans;
ll find(ll x)
{
    if(x!=fa[x])fa[x]=find(fa[x]);
    return fa[x];
}
void add(ll u,ll v,ll w)
{
    ++cnt;
    t[cnt]=v;
    weigh[cnt]=w;
    nex[cnt]=h[u];
    h[u]=cnt;
}
void boruvka()
{
    for(ll i=1;i<=n;i++)fa[i]=i;
    ll res=n,last=n;
    while(true)
    {
        memset(minm,127,sizeof minm);
        for(ll i=1;i<=n;i++)
        {
            for(ll j=h[i];j;j=nex[j])
            {
                ll a=find(i),b=find(t[j]);
                if(a==b)continue;
                if(minm[a].x>weigh[j])
                {
                    minm[a].x=weigh[j];
                    minm[a].y=t[j];
                }
            }
        }
        for(ll i=1;i<=n;i++)
        {
            if(i!=find(i)||minm[i].x==minm[0].x)continue;
            res--;
            fa[find(minm[i].y)]=i;
            ans+=minm[i].x;
        }
        if(res==last)
        {
            puts("impossible");
            exit(0);
        }
        if(res==1)break;
        last=res;
    }
    cout<<ans;
}
signed main()
{
    ios::sync_with_stdio(false);
    cin>>n>>m;
    for(ll i=1;i<=m;i++)
    {
        cin>>x>>y>>z;
        add(x,y,z);
        add(y,x,z);
    }
    boruvka();
}