bzoj1977次小生成树（重要）

#include<cstdio>
#include<iostream>
#include<cstring>
#include<queue>
#include<algorithm>
#define Maxn 300010
#define maxn 300005
using namespace std;
#define ll long long
struct edge{
    int to,w,nxt;
}edge[Maxn];
int head[Maxn/],tot;
void addedge(int a,int b,int c){
    edge[tot].to=b;
    edge[tot].w=c;
    edge[tot].nxt=head[a];
    head[a]=tot++;
}
struct line{
    int u,v,w;
    bool operator<(const line &a)const{
        return w<a.w;
    }
}q[Maxn];

int vis[Maxn];
int fa[Maxn/];
int findset(int x){
    return fa[x]==x?x:(fa[x]=findset(fa[x]));
}
int unionset(int a,int b){
    return fa[findset(a)]=findset(b);
}
ll d[maxn],f[maxn][],dp[maxn][][];//dp[i][j][0|1]用来表示向上倍增的最大边，严格次大边
void bfs(){
    queue<int>q;
    q.push();
    d[]=;
    while(!q.empty()){
        int x=q.front();q.pop();
        for(int i=head[x];i!=-;i=edge[i].nxt){
            int y=edge[i].to;
            if(d[y])continue;
            d[y]=d[x]+;
            f[y][]=x;
            dp[y][][]=edge[i].w;
            dp[y][][]=-0x3f3f3f3f;
            for(int k=;k<=;k++){
                f[y][k]=f[f[y][k-]][k-];
                int a=dp[y][k-][];//y向上下一半的最大值
                int b=dp[y][k-][];//y向上下一半的严格次大值
                int c=dp[f[y][k-]][k-][];//y向上上一半的最大值
                int d=dp[f[y][k-]][k-][];//y向上上一半的严格次大值
                dp[y][k][]=max(a,c);
                if(a==c)dp[x][k][]=max(b,d);
                else if(a>c)dp[x][k][]=max(c,b);
                else if(a<c)dp[x][k][]=max(a,d);
            }
            q.push(y);
        }
    }
}
inline void calc(ll &val1,ll &val2,ll a,ll b){//更新最大和次大
    if(a<=val1)val2=max(a,val2);
    else val2=val1,val1=a;
}
int lca(int x,int y,int z){//处理加入(x,y,z)后的次小生成树
    ll val1=-,val2=-;
    if(d[x]<d[y])swap(x,y);
    for(int i=;i>=;i--)
        if(d[f[x][i]]>=d[y]){
            calc(val1,val2,dp[x][i][],dp[x][i][]);
            x=f[x][i];
        }
    if(x==y){
        if(val1!=z)return val1;
        return val2;
    }

    for(int i=;i>=;i--)
        if(f[x][i]!=f[y][i]){
            calc(val1,val2,dp[x][i][],dp[x][i][]);
            calc(val1,val2,dp[y][i][],dp[y][i][]);
            x=f[x][i],y=f[y][i];
        }
    calc(val1,val2,dp[x][][],dp[x][][]);
    calc(val1,val2,dp[y][][],dp[y][][]);
    x=f[x][];
    if(val1!=z)return val1;
    else return val2;
}

int main(){
    int n,m;
    scanf("%d%d",&n,&m);
    for(int i=;i<m;i++)
        scanf("%d%d%d",&q[i].u,&q[i].v,&q[i].w);
    sort(q,q+m);
    for(int i=;i<=n;i++) fa[i]=i;
    memset(head,-,sizeof head);
    memset(vis,,sizeof vis);
    tot=;
    int cnt=;
    long long ans=;
    for(int i=;i<m;i++){
        int u=q[i].u,v=q[i].v;
        if(findset(u)==findset(v)) continue;
        unionset(u,v);
        vis[i]=;
        addedge(u,v,q[i].w);
        addedge(v,u,q[i].w);
        ans+=q[i].w;
        if(++cnt==n-) break;
    }
    bfs();
    int z=0x3f3f3f3f;
    for(int i=;i<m;i++)
        if(!vis[i]) {
            int t=lca(q[i].u,q[i].v,q[i].w);
            if(t>)z=min(z,-t+q[i].w);
        }
    printf("%lld\n",ans+z);
    return ;
}