离线求LCA（深搜）

离线求出任意点对u−v的最近公共祖先

不妨令v的深度优先搜索序小于u

深搜到u时，v已经被扫过，答案为v到root路径上没有处理完的第一个灰色点

可用并查集优化，若一个点全部扫完则加入集合中，代表元素为集合最先被搜到的点

也就是答案

交通运输线

#include<iostream>#include<cstdio>using namespace std;int hed[10005],vet[20005],val[20005],Next[20005];int dis[10005];int ull[1000005],vll[1000005];int hedq[10005],vetq[2000005],valq[2000005],Nextq[2000005];int fa[10005],ans[1000005];int tree[10005];int num;int numq;void add(int u,int v,int z){  ++num;  vet[num]=v;  val[num]=z;  Next[num]=hed[u];  hed[u]=num;}void addq(int u,int v,int z){  ++numq;  vetq[numq]=v;  valq[numq]=z;  Nextq[numq]=hedq[u];  hedq[u]=numq;}int find(int x){  if (fa[x]!=x)    fa[x]=find(fa[x]);  return fa[x];}void Union(int u,int v){  int rootu=find(u);  int rootv=find(v);  fa[rootv]=rootu;}void lca(int u,int fath,int hao){  fa[u]=u;  for (int i=hed[u];i!=-1;i=Next[i]){    int v=vet[i];    if (v==fath) continue;    dis[v]=dis[u]+val[i];    lca(v,u,hao);    Union(u,v);  }  tree[u]=hao;  for (int i=hedq[u];i!=-1;i=Nextq[i])  if (ans[valq[i]]==-1)    if (tree[vetq[i]]==hao)      ans[valq[i]]=find(vetq[i]);}int main(){  int t;  scanf("%d",&t);  while (t--){    num=0;    numq=0;    int n,m,c;    scanf("%d%d%d",&n,&m,&c);    for (int i=1;i<=n;++i){      hed[i]=-1;      hedq[i]=-1;      tree[i]=0;      fa[i]=i;      dis[i]=0;    }    for (int i=1;i<=c;++i) ans[i]=-1;    for (int i=1;i<=m;++i){      int u,v,z;      scanf("%d%d%d",&u,&v,&z);      add(u,v,z);      add(v,u,z);    }    for (int i=1;i<=c;++i){      int u,v;      scanf("%d%d",&u,&v);      ull[i]=u;      vll[i]=v;      addq(u,v,i);      addq(v,u,i);    }    for (int i=1;i<=n;++i)      if (tree[i]==0){        dis[i]=0;        lca(i,0,i);      }    for (int i=1;i<=c;++i)    if (ans[i]==-1) printf("Not connected\n");    else printf("%d\n",dis[ull[i]]+dis[vll[i]]-dis[ans[i]]-dis[ans[i]]);  }  return 0;}