严格次小生成树[BJWC2010]

Posted 2022-09-01 lsyyy

题目

维护环内最大值与严格次大值

与未放入最小生成树的边枚举加入

#include<bits/stdc++.h>
#define re return
#define dec(i,l,r) for(ll i=l;i>=r;--i)
#define inc(i,l,r) for(ll i=l;i<=r;++i)

typedef long long ll;

using namespace std;
template<typename T>inline void rd(T&x)

    char c;bool f=0;
    while((c=getchar())<‘0‘||c>‘9‘)if(c==‘-‘)f=1;
    x=c^48;
    while((c=getchar())>=‘0‘&&c<=‘9‘)x=x*10+(c^48);
    if(f)x=-x;


const int maxn=100005,maxm=300005;
ll n,m,k=1,hd[maxn],deep[maxn];
ll max1[maxn][21],max2[maxn][21],fa[maxn][21];
ll vis[maxm],f[maxn];
ll sum,ans=999999999999999999;

struct node

    ll fr,to,nt,val;
    bool operator<(node p)const 
    
        re val<p.val;
    
e[maxm],e1[maxn<<1];

inline void add1(int x,int y,int z)

    e1[++k].to=y;e1[k].nt=hd[x];hd[x]=k;e1[k].val=z;
    e1[++k].to=x;e1[k].nt=hd[y];hd[y]=k;e1[k].val=z;
    


inline void dfs(int x)

    deep[x]=deep[fa[x][0]]+1;
    for(int i=0;fa[fa[x][i]][i];++i)
    
        fa[x][i+1]=fa[fa[x][i]][i];
        if(max1[x][i]==max1[fa[x][i]][i])
        
            max1[x][i+1]=max1[x][i];
            max2[x][i+1]=max(max2[x][i],max2[fa[x][i]][i]);
        
        else if(max1[x][i]>max1[fa[x][i]][i])
        
            max1[x][i+1]=max1[x][i];
            max2[x][i+1]=max(max1[fa[x][i]][i],max2[x][i]);
        
        else 
        
            max1[x][i+1]=max1[fa[x][i]][i];
            max2[x][i+1]=max(max1[x][i],max2[fa[x][i]][i]);
            
     
    
    for(ll i=hd[x];i;i=e1[i].nt)
    
        ll v=e1[i].to;
        if(v==fa[x][0])continue;
        fa[v][0]=x;
        max1[v][0]=e1[i].val;
        max2[v][0]=-2147483647;
        dfs(v);
    



inline ll find(ll x)

    re x==f[x]?x:f[x]=find(f[x]);

int main()

    
//    freopen("in.txt","r",stdin);
freopen("tree8.in","r",stdin);
    
    ll x,y,z; 
    
    rd(n),rd(m);
    inc(i,1,n)f[i]=i;
    
    inc(i,1,m)
    
        rd(x),rd(y),rd(z);
        e[i]=(node)x,y,0,z;
    
    
    sort(e+1,e+m+1);
    
    k=0;
    ll cnt=0;
    inc(i,1,m)
    
        x=find(e[i].to),y=find(e[i].fr);
        if(x!=y)
        
            add1(e[i].to,e[i].fr,e[i].val);
            sum+=e[i].val; 
            vis[i]=1;
            f[x]=y;
            ++cnt;
            if(cnt==n-1)break;
        
    
    
    dfs(1);
    
    inc(j,1,m)
    if(!vis[j])
    
        x=e[j].to;y=e[j].fr;
//--------------------------------------------------------------------------------        
        ll d1=0,d2=0;
        if(deep[x]<deep[y])swap(x,y);
        
        dec(i,20,0)
        if(deep[fa[x][i]]>=deep[y])
        
            if(max1[x][i]>d1)
            
                d2=max(d1,max2[x][i]);
                d1=max1[x][i];
            
            else if(max1[x][i]!=d1)
                 d2=max(d2,max1[x][i]);
            
            x=fa[x][i];
        
        if(x!=y)
        
            dec(i,20,0)
            if(fa[x][i]!=fa[y][i])
            
                if(max1[x][i]>d1)
                
                    d2=max(d1,max2[x][i]);
                    d1=max1[x][i];
                
                else if(max1[x][i]!=d1)
                     d2=max(d2,max1[x][i]);
                     
                if(max1[y][i]>d1)
                
                    d2=max(d1,max2[y][i]);
                    d1=max1[y][i];
                
                else if(max1[y][i]!=d1)
                     d2=max(d2,max1[y][i]);
                x=fa[x][i];y=fa[y][i];
            
            if(max1[x][0]>d1)
            
                d2=d1;
                d1=max1[x][0]; 
             
            else if(max1[x][0]!=d1)
                d2=max(d2,max1[x][0]);
            if(max1[y][0]>d1)
            
                d2=d1;
                d1=max1[y][0]; 
             
            else if(max1[y][0]!=d1)
                d2=max(d2,max1[y][0]);
            
         
//-----------------------------------------------------------------------------------------------------        
        if(d1==e[j].val)ans=min(ans,sum+e[j].val-d2);
        else ans=min(ans,sum+e[j].val-d1);
    
    
    printf("%lld",ans); 
    re 0;