【BZOJ】【P1977】【Beijing2010组队】【次小生成树】【题解】

传送门：www.lydsy.com:808/JudgeOnline/problem.php?id=1977

抄gty题解终于A了= =、

Code：

#include<cstdio>
//#include<ctime>
#include<climits>
#include<iostream>
#include<algorithm>
#include<vector>
#include<queue>
using namespace std;
const int maxn=1e5+10;
const int maxm=3e5+10;
struct edge{int u,v,w;edge(int _u=0,int _v=0,int _w=0){u=_u,v=_v,w=_w;} bool operator < (const edge &a)const {return w<a.w;};};
vector<edge>G,Ge[maxn];
int vis[maxm];
int n,m;
int faa[maxn],a[maxn];
int find(int x){    
    if(faa[x]!=x)
        return faa[x]=find(faa[x]);
    return x;
}
long long ans=0;
int p[maxm][18],maxx[maxm][18],maxi[maxm][18],dep[maxn];
void updata(int &a,int &b,int x1,int y1,int x2,int y2){
    if(x1>x2){  
        a=x1;b=max(y1,x2);  
    }else
    if(x1<x2){  
        a=x2;b=max(x1,y2);
    }else{  
        a=x1;b=max(y1,y2);
    }   
}
void initlca(){
    queue<int>q;q.push(1);
    while(!q.empty()){
        int u=q.front();q.pop();
        for(int i=0;i<Ge[u].size();i++){
            int v=Ge[u][i].v,w=Ge[u][i].w;
            if(v!=1&&!dep[v]){
                dep[v]=dep[u]+1;
                p[v][0]=u;
                maxx[v][0]=w;
                maxi[v][0]=0;
                q.push(v);
            }
        }
    }
    for(int k=1;k<18;k++)
    for(int i=1;i<=n;i++){
        p[i][k]=p[p[i][k-1]][k-1];
        updata(maxx[i][k],maxi[i][k],
                maxx[i][k-1],maxi[i][k-1],
                maxx[p[i][k-1]][k-1],maxi[p[i][k-1]][k-1]);
    }
}
 
pair<int,int> Query(int x, int y)  {      
    int Maxx = -1;  
    int Maxi = -1;  
    if (dep[x] < dep[y])  
    swap(x,y);
    for (int i = 17; i >= 0; i--)  
        if (dep[p[x][i]] >= dep[y]){  
            updata(Maxx, Maxi, Maxx, Maxi, maxx[x][i], maxi[x][i]);  
            x = p[x][i];  
        }   
    if (x == y) return pair<int,int>(Maxx,Maxi);  
    for (int i = 17; i >= 0; i--)  
        if (p[x][i] != p[y][i])  
        {  
            updata(Maxx, Maxi, Maxx, Maxi,  
                   maxx[x][i], maxi[x][i]);  
            updata(Maxx, Maxi, Maxx, Maxi,  
                   maxx[y][i], maxi[y][i]);  
            x = p[x][i]; y = p[y][i];  
        }  
    updata(Maxx, Maxi, Maxx, Maxi,  
           maxx[x][0], maxi[x][0]);  
    updata(Maxx, Maxi, Maxx, Maxi,  
           maxx[y][0], maxi[y][0]);  
    return pair<int,int>(Maxx,Maxi);
}  
int main(){
//  double st=clock();
//  freopen("1.txt","r",stdin);
    scanf("%d%d",&n,&m);
    for(int i=1;i<=n;i++)faa[i]=i;
    for(int i=1;i<=m;i++){
        int u,v,w;scanf("%d%d%d",&u,&v,&w);
        G.push_back(edge(u,v,w));
    }sort(G.begin(),G.end());
    for(int i=0;i<m;i++){
        int u=G[i].u,v=G[i].v,w=G[i].w;
        int fau=find(u),fav=find(v);
        if(fau!=fav){
            faa[fau]=fav;
            vis[i]=1;ans+=w;
            Ge[u].push_back(edge(u,v,w));
            Ge[v].push_back(edge(v,u,w));
        }
    }initlca();
    long long res,Ans=1LL<<61;
    for(int i=0;i<m;i++){
        res=ans;
        if(vis[i])continue;
        int u=G[i].u,v=G[i].v,w=G[i].w;
        res+=w;
        pair<int,int> pi=Query(u,v);
        if(pi.first==w)res-=pi.second;else res-=pi.first;
        Ans=min(Ans,res);
    }   
    cout<<Ans<<endl;
//  cerr<<(clock()-st)/CLOCKS_PER_SEC<<endl;
    return 0;
}