BZOJ 1977 次小生成树（最近公共祖先）

  1 #include<algorithm>
  2 #include<cstdio>
  3 #include<cmath>
  4 #include<cstring>
  5 #include<iostream>
  6 #define ll long long
  7 struct edge{
  8     int u,v,id;
  9     ll w;
 10 }e[300005];
 11 int tot,go[600005],first[300005],next[600005];
 12 ll val[600005];
 13 int fa[100005][18],deep[100005],F[100005],bin[105],n,m;
 14 ll mx1[100005][18],mx2[100005][18],ans1,ans2;
 15 int read(){
 16     char ch=getchar();int t=0,f=1;
 17     while (ch<‘0‘||ch>‘9‘){if (ch==‘-‘) f=-1;ch=getchar();}
 18     while (‘0‘<=ch&&ch<=‘9‘){t=t*10+ch-‘0‘;ch=getchar();}
 19     return t*f;
 20 }
 21 ll Read(){
 22     char ch=getchar();ll t=0,f=1;
 23     while (ch<‘0‘||ch>‘9‘){if (ch==‘-‘) f=-1;ch=getchar();}
 24     while (‘0‘<=ch&&ch<=‘9‘){t=t*10+ch-‘0‘;ch=getchar();}
 25     return t*f;
 26 }
 27 bool cmp(edge a,edge b){
 28     return a.w<b.w;
 29 }
 30 void insert(int x,int y,ll z){
 31     tot++;
 32     go[tot]=y;
 33     next[tot]=first[x];
 34     first[x]=tot;
 35     val[tot]=z;
 36 }
 37 void add(int x,int y,int z){
 38     insert(x,y,z);insert(y,x,z);
 39 }
 40 int find(int x){
 41     if (F[x]==x) return x;
 42     else return (find(F[x]));
 43 }
 44 void up(ll x,ll &y){
 45     if (x>y) y=x;
 46 }
 47 void work(int x,int i){
 48      mx1[x][i]=std::max(mx1[fa[x][i-1]][i-1],mx1[x][i-1]);
 49      if (mx1[fa[x][i-1]][i-1]<mx1[x][i]) up(mx1[fa[x][i-1]][i-1],mx2[x][i]);
 50      if (mx1[x][i-1]<mx1[x][i]) up(mx1[x][i-1],mx2[x][i]);
 51      up(mx2[x][i-1],mx2[x][i]);
 52      up(mx2[fa[x][i-1]][i-1],mx2[x][i]);
 53 }
 54 void dfs(int x,int f){
 55     for (int i=1;i<=17;i++)
 56      fa[x][i]=fa[fa[x][i-1]][i-1],work(x,i);
 57     for (int i=first[x];i;i=next[i]){
 58         int pur=go[i];
 59         if (pur==f) continue;
 60         deep[pur]=deep[x]+1;
 61         fa[pur][0]=x;
 62         mx1[pur][0]=val[i];
 63         mx2[pur][0]=0;
 64         dfs(pur,x);
 65     } 
 66 }
 67 void up(ll x,ll &a,ll &b){
 68     if (x>a) b=a,a=x;
 69     else
 70     if (x>b&&x<a) b=x;
 71 }
 72 void lca(int x,int y){
 73     ans1=0,ans2=0;
 74     if (deep[x]<deep[y]) std::swap(x,y);
 75     int t=deep[x]-deep[y];
 76     for (int i=0;i<=17;i++)
 77      if (t&bin[i]) {
 78      up(mx1[x][i],ans1,ans2);
 79      up(mx2[x][i],ans1,ans2);
 80      x=fa[x][i];
 81      }
 82     for (int i=17;i>=0;i--)
 83      if (fa[x][i]!=fa[y][i]) {
 84             up(mx1[x][i],ans1,ans2);
 85             up(mx2[x][i],ans1,ans2);
 86             up(mx1[y][i],ans1,ans2);
 87             up(mx2[y][i],ans1,ans2);   
 88             x=fa[x][i];
 89             y=fa[y][i];
 90      }
 91     if (x!=y){
 92         up(mx1[x][0],ans1,ans2);
 93         up(mx2[x][0],ans1,ans2);
 94         up(mx1[y][0],ans1,ans2);
 95         up(mx2[y][0],ans1,ans2);  
 96     }
 97 }
 98 int main(){
 99     bin[0]=1;
100     for (int i=1;i<=17;i++) bin[i]=bin[i-1]*2;
101     n=read();m=read();
102     for (int i=1;i<=m;i++){
103         e[i].u=read();
104         e[i].v=read();
105         e[i].w=Read();
106         e[i].id=0;
107     }
108     for (int i=1;i<=n;i++)
109      for (int j=0;j<=17;j++)
110       mx1[i][j]=mx2[i][j]=0;
111     std::sort(e+1,e+1+m,cmp);
112     ll sum=0;
113     for (int i=1;i<=n;i++) F[i]=i;
114     for (int i=1;i<=m;i++)
115      if (find(e[i].u)!=find(e[i].v)){
116         F[find(e[i].u)]=find(e[i].v);    
117         e[i].id=1;
118         add(e[i].u,e[i].v,e[i].w);
119         sum+=e[i].w;
120      }
121     dfs(1,0);
122     ll Ans=10000000000000000LL;
123     for (int i=1;i<=m;i++)
124      if (!e[i].id){
125             lca(e[i].u,e[i].v);
126             if (e[i].w==ans1) Ans=std::min(Ans,sum-ans2+e[i].w);
127             else Ans=std::min(Ans,sum-ans1+e[i].w);
128      }
129     printf("%lld\n",Ans);
130 }