BZOJ 3572 世界树(虚树)
http://www.lydsy.com/JudgeOnline/problem.php?id=3572
思路:建立虚树，然后可以发现，每条边不是同归属于一端，那就是切开，一半给上面，一半给下面。
1 #include<algorithm> 2 #include<cstdio> 3 #include<cmath> 4 #include<cstring> 5 #include<iostream> 6 #define N 300005 7 int tot,go[N*2],next[N*2],first[N],sz,deep[N],tmp[N],tree[N]; 8 int son[N],dfn[N],fa[N][20],bin[20],ask[N],In[N],st[N],n,m,ans[N]; 9 int father[N],val[N]; 10 std::pair<int,int>near[N]; 11 int read(){ 12 int t=0,f=1;char ch=getchar(); 13 while (ch<'0'||ch>'9'){if (ch=='-') f=-1;ch=getchar();} 14 while ('0'<=ch&&ch<='9'){t=t*10+ch-'0';ch=getchar();} 15 return t*f; 16 } 17 void insert(int x,int y){ 18 tot++; 19 go[tot]=y; 20 next[tot]=first[x]; 21 first[x]=tot; 22 } 23 void add(int x,int y){ 24 insert(x,y);insert(y,x); 25 } 26 void dfs(int x){ 27 son[x]=1; 28 dfn[x]=++sz; 29 for (int i=1;i<=19;i++) 30 fa[x][i]=fa[fa[x][i-1]][i-1]; 31 for (int i=first[x];i;i=next[i]){ 32 int pur=go[i]; 33 if (pur==fa[x][0]) continue; 34 deep[pur]=deep[x]+1; 35 fa[pur][0]=x; 36 dfs(pur); 37 son[x]+=son[pur]; 38 } 39 } 40 int find(int x,int dep){ 41 for (int i=19;i>=0;i--) 42 if (deep[fa[x][i]]>=dep) x=fa[x][i]; 43 return x; 44 } 45 int lca(int x,int y){ 46 if (deep[x]<deep[y]) std::swap(x,y); 47 int t=deep[x]-deep[y]; 48 for (int i=0;i<=19;i++) 49 if (t&bin[i]) 50 x=fa[x][i]; 51 if (x==y) return x; 52 for (int i=19;i>=0;i--) 53 if (fa[x][i]!=fa[y][i]) 54 x=fa[x][i],y=fa[y][i]; 55 return fa[x][0]; 56 } 57 bool cmp(int a,int b){ 58 return dfn[a]<dfn[b]; 59 } 60 void solve(){ 61 m=read(); 62 for (int i=1;i<=m;i++){ 63 ask[i]=read(),tmp[i]=tree[i]=ask[i]; 64 near[ask[i]]=std::make_pair(0,ask[i]); 65 ans[ask[i]]=0; 66 } 67 std::sort(ask+1,ask+1+m,cmp); 68 int top=0,all=m; 69 for (int i=1;i<=m;i++){ 70 int p=ask[i]; 71 if (!top) father[p]=0,st[++top]=p; 72 else{ 73 int x=lca(st[top],p); 74 father[p]=x; 75 while (top&&deep[st[top]]>deep[x]){ 76 if (deep[st[top-1]]<=deep[x]){ 77 father[st[top]]=x; 78 } 79 top--; 80 } 81 if (st[top]!=x){ 82 father[x]=st[top];tree[++all]=x; 83 st[++top]=x;near[x]=std::make_pair(1<<30,0); 84 } 85 st[++top]=p; 86 } 87 } 88 std::sort(tree+1,tree+1+all,cmp); 89 for (int i=1;i<=all;i++){ 90 int p=tree[i],f=father[p]; 91 val[p]=son[p]; 92 if (i>1) In[p]=deep[p]-deep[f]; 93 } 94 for (int i=all;i>1;i--){ 95 int p=tree[i],f=father[p]; 96 near[f]=std::min(near[f],std::make_pair(near[p].first+In[p],near[p].second)); 97 } 98 for (int i=2;i<=all;i++){ 99 int p=tree[i],f=father[p]; 100 near[p]=std::min(near[p],std::make_pair(near[f].first+In[p],near[f].second)); 101 } 102 for (int i=1;i<=all;i++){ 103 int p=tree[i],f=father[p],sum=son[find(p,deep[f]+1)]-son[p]; 104 if (f==0) ans[near[p].second]+=n-son[p]; 105 else{ 106 val[f]-=sum+son[p]; 107 if (near[p].second==near[f].second) ans[near[p].second]+=sum; 108 else{ 109 int dis=(deep[p]-deep[f]-near[p].first+near[f].first)/2; 110 if (dis+near[p].first==near[f].first+deep[p]-deep[f]-dis&&near[f].second<near[p].second) dis--; 111 int x=find(p,deep[p]-dis); 112 ans[near[p].second]+=son[x]-son[p]; 113 ans[near[f].second]+=sum+son[p]-son[x]; 114 } 115 } 116 } 117 for (int i=1;i<=all;i++){ 118 ans[near[tree[i]].second]+=val[tree[i]]; 119 } 120 for (int i=1;i<=m;i++) 121 printf("%d ",ans[tmp[i]]); 122 puts(""); 123 } 124 int main(){ 125 n=read(); 126 bin[0]=1; 127 for (int i=1;i<=19;i++) bin[i]=bin[i-1]*2; 128 for (int i=1;i<n;i++){ 129 int x=read(),y=read(); 130 add(x,y); 131 } 132 dfs(1); 133 int T=read(); 134 while (T--) solve(); 135 }
