1977: [BeiJing2010组队]次小生成树 Tree

#include <bits/stdc++.h>
#define ll long long
const int MAXN=1e5+10;
const int maxn=3e5+10;
const int inf=1e9+20;
using namespace std;
ll read(){
    ll x=0,f=1;char ch=getchar();
    while(!isdigit(ch)){if(ch==‘-‘)f=-1;ch=getchar();}
    while(isdigit(ch))x=x*10+ch-‘0‘,ch=getchar();
    return f*x;
}
vector<pair<int,int> >vec[MAXN];
typedef struct Edge{
    int u,v,vul;bool flag;
    friend bool operator<(Edge aa,Edge bb){return aa.vul<bb.vul;}
}Edge;
Edge edge[maxn];
int n,m,f[MAXN];
int find1(int x){
    if(f[x]==x)return x;
    else return f[x]=find1(f[x]);
}
int key[MAXN],fa[MAXN],dep[MAXN],num[MAXN],son[MAXN];
void dfs(int v,int pre,int deep){
    dep[v]=deep+1;num[v]=1;fa[v]=pre;
    for(int i=0;i<vec[v].size();i++){
	int u=vec[v][i].first;
	if(u!=pre){
	    key[u]=vec[v][i].second;
	    dfs(u,v,deep+1);
	    num[v]+=num[u];
	    if(son[v]==-1||num[son[v]]<num[u])son[v]=u;
	}
    }
}
int tp[MAXN],cnt,p[MAXN],fp[MAXN];
void dfs1(int v,int td){
    p[v]=++cnt;fp[p[v]]=v;tp[v]=td;
    if(son[v]!=-1)dfs1(son[v],td);
    for(int i=0;i<vec[v].size();i++){
	if(vec[v][i].first!=fa[v]&&vec[v][i].first!=son[v])dfs1(vec[v][i].first,vec[v][i].first);
    }
}
int maxx[MAXN<<2],maxx1[MAXN<<2];
void up(int x){
    maxx[x]=max(maxx[x<<1],maxx[x<<1|1]);
    maxx1[x]=maxx1[x<<1];
    if(maxx[x<<1]!=maxx[x])maxx1[x]=max(maxx1[x],maxx[x<<1]);
    if(maxx[x<<1|1]!=maxx[x])maxx1[x]=max(maxx1[x],maxx[x<<1|1]);
    if(maxx1[x<<1|1]!=maxx[x])maxx1[x]=max(maxx1[x],maxx1[x<<1|1]);
}
void built(int rt,int l,int r){
    if(l==r){maxx[rt]=key[fp[l]];maxx1[rt]=-1;return ;}
    int mid=(l+r)>>1;
    built(rt<<1,l,mid);
    built(rt<<1|1,mid+1,r);
    up(rt);
}
int ans1;
void querty(int rt,int l,int r,int ql,int qr,int vul){
    if(ql<=l&&r<=qr){
	if(maxx[rt]==vul)ans1=max(ans1,maxx1[rt]);
	else ans1=max(ans1,maxx[rt]);
	return ;
    }
    int mid=(l+r)>>1;
    if(ql<=mid)querty(rt<<1,l,mid,ql,qr,vul);
    if(qr>mid)querty(rt<<1|1,mid+1,r,ql,qr,vul);
}
int slove(int u,int v,int t){
    int uu=tp[u];int vv=tp[v];
    ans1=-1*inf;
    while(uu!=vv){
	if(dep[uu]<dep[vv])swap(uu,vv),swap(u,v);
	querty(1,1,n,p[uu],p[u],t);
	u=fa[uu];uu=tp[u];
    }
    if(dep[u]>dep[v])swap(u,v);
    if(u!=v)querty(1,1,n,p[son[u]],p[v],t);
    return ans1;
}
int main(){
    n=read();m=read();int u,v,vul;
    for(int i=1;i<=m;i++)edge[i].u=read(),edge[i].v=read(),edge[i].vul=read();
    for(int i=1;i<=n;i++)f[i]=i,son[i]=-1;
    sort(edge+1,edge+m+1);ll ans=0;
    for(int i=1;i<=m;i++){
	int t1=find1(edge[i].u);
	int t2=find1(edge[i].v);
	if(t1==t2)continue;
	ans+=edge[i].vul;
	f[t1]=t2;vec[edge[i].u].push_back(make_pair(edge[i].v,edge[i].vul));
	vec[edge[i].v].push_back(make_pair(edge[i].u,edge[i].vul));edge[i].flag=1;
    }
    //cout<<ans<<endl;
    dfs(1,0,0);dfs1(1,1);built(1,1,n);
   // cout<<"sb"<<endl;
    ll ans2=1e18;
    for(int i=1;i<=m;i++){
	if(edge[i].flag)continue;
	vul=slove(edge[i].u,edge[i].v,edge[i].vul);
	if(vul<0)continue;
	ans2=min(ans2,ans-vul+1ll*edge[i].vul);
    }
    printf("%lld\n",ans2);
    return 0;
}