次小生成树

Posted 2020-10-29 hyf

#include<iostream>
#include<cstdio>
#include<algorithm>
#include<cmath>
#include<cstring>
#include<complex>
#define N 400010
#define M 900010
#define INF 2147483647000000
#define ll long long
using namespace std;
ll read()
{
    int x=0,f=1;char s=getchar();
    while(s>‘9‘ || s<‘0‘){if(s==‘-‘)f=-1;s=getchar();}
    while(s<=‘9‘ && s>=‘0‘){x=x*10+s-‘0‘;s=getchar();}
    return x*f;
}
struct edge{ll to,next,v;}a[N<<1];
struct node{ll x,y,v;}e[M];
bool operator < (node a,node b){return a.v<b.v;}
ll cnt,head[N],t=0;
void add(ll x,ll y,ll v){a[++cnt].to=y;a[cnt].v=v;a[cnt].next=head[x];head[x]=cnt;}
ll bz[N][21],deep[N],m1[N][21],m2[N][21],f[N],V[N];
ll find(ll x){if(x==f[x])return x;f[x]=find(f[x]);return f[x];}
int n,m;
void dfs(ll x,ll fa)
{
    bz[x][0]=fa;
    for(int i=head[x];i;i=e[i].next)
    {
        ll v=a[i].to;
        if(v==fa)continue;
        deep[v]=deep[x]+1;
        m1[v][0]=a[i].d;
        m2[v][0]=-INF;
        dfs(v,x);
    }
}
void twofold()
{
    for(int i=1;i<=20;i++)
        for(int j=1;j<=n;j++)
        {
            bz[j][i]=bz[bz[j][i-1]][i-1];
            m1[j][i]=max(m1[j][i-1],m1[bz[j][i-1]][i-1]);
            m2[j][i]=max(m2[j][i-1],m2[bz[j][i-1]][i-1]);
            if(m1[j][i-1]>m1[bz[j][i-1]][i-1])m2[j][i]=max(m2[j][i],m1[bz[j][i-1]][i-1]);
            else if(m1)
        }
}
int main()
{
    n=read();m=read();
    for(int i=1;i<=m;i++)e[i].x=read(),e[i].y=read(),e[i].v=read();    sort(e+1,e+m+1);
    for(int i=1;i<=n;i++)f[i]=i;
    for(int i=1;i<=m;i++)
    {
        ll p=find(e[i].x),q=find(e[i].y);
        if(p!=q)
        {
            t+=e[i].v;f[p]=q;V[i]=1;
            add(e[i].x,e[i].y,e[i].v);add(e[i].y,e[i].x,e[i].v);
        }
    }
    deep[1]=1;m2[1][0]=-INF;
    dfs(1,-1);twofold();
    ll ans=INF;
    for(int i=1;i<=m;i++)
        if(!V[i])
        {
            ll x=a[i].x,y=a[i].y,d=a[i].d,l=lca(x,y);
            ans=min(ans,t-max(qmax(x,lca,d),qmax(lca,y,d))+d);
        }
    printf("%d\n",ans);
    return 0;
}