题目大意:
有一张无向连通图,问从一条边走到另一条边必定要经过的点有几个。
思路:
先用tarjan将双连通分量都并起来,剩下的再将割点独立出来,建成一棵树,之后记录每个点到根有几个割点,再用RMQ求LCA计算。
注意:数组范围。
代码:
#include<cstdio>
#include<vector>
#include<iostream>
#include<algorithm>
using namespace std;
const int N=,M=;
int u[M<<],v[M<<],nex[M<<],id[M<<],hea[N<<],dfn[N<<],low[N],st[M],sub[N],edge[M],
fa[N<<][],f[N<<],pos[N<<],dep[N<<];
bool vis[M<<],iscut[N],treecut[N<<];
int tim,top,tot,cnt,num;
vector <int> belo[N]; int read()
{
int x=; char ch=getchar();
while (ch<'' || ch>'') ch=getchar();
while (ch>='' && ch<='') x=(x<<)+(x<<)+ch-,ch=getchar();
return x;
} void add(int x,int y) { v[cnt]=y,u[cnt]=x,nex[cnt]=hea[x],vis[cnt]=,hea[x]=cnt++; } void tarjan(int x)
{
dfn[x]=low[x]=++tim;
for (int i=hea[x];~i;i=nex[i])
if (!vis[i])
{
int y=v[i]; st[++top]=i;
vis[i]=vis[i^]=;
if (!dfn[y])
{
tarjan(y);
low[x]=min(low[x],low[y]);
if (low[y]>=dfn[x])
{
++sub[x],++num;
iscut[x]=;
do
{
int now=st[top--];
belo[u[now]].push_back(num);
belo[v[now]].push_back(num);
edge[id[now]]=num;
y=u[now];
}while (y^x);
}
}
else low[x]=min(low[x],dfn[y]);
}
} void dfs(int x)
{
dfn[x]=++tim; fa[++tot][]=dfn[x];
f[tim]=x; pos[x]=tot;
for (int i=hea[x];~i;i=nex[i])
{
int y=v[i];
if (!dfn[y])
{
dep[y]=dep[x]+treecut[x];
dfs(y); fa[++tot][]=dfn[x];
}
}
} void RMQ(int n)
{
for (int j=;(<<j)<=n;++j)
for (int i=;i+j-<=n;++i)
fa[i][j]=min(fa[i][j-],fa[i+(<<j-)][j-]);
} int lca(int x,int y)
{
if (pos[x]<pos[y]) swap(x,y);
int k=;
while (<<(k+)<=pos[x]-pos[y]+) ++k;
return f[min(fa[pos[y]][k],fa[pos[x]-(<<k)+][k])];
} void wk(int n)
{
int i,m,x,y;
for (tim=tot=i=;i<=n;++i) dfn[i]=;
for (i=;i<=n;++i)
if (!dfn[i]) dep[i]=,dfs(i);
RMQ(tot);
for (m=read();m--;)
{
x=edge[read()],y=edge[read()];
if (x< || y<) { puts(""); continue; }
int z=lca(x,y);
if (x==z) printf("%d\n",dep[y]-dep[x]-treecut[x]);
else if (y==z) printf("%d\n",dep[x]-dep[y]-treecut[y]);
else printf("%d\n",dep[x]+dep[y]-(dep[z]<<)-treecut[z]);
}
} int main()
{
int n,m;
while (~scanf("%d%d",&n,&m))
{
int i; cnt=top=num=tim=;
if (!(n+m)) break;
for (i=;i<=n;++i) hea[i]=-,dfn[i]=sub[i]=iscut[i]=,belo[i].clear();
for (i=;i<=m;++i)
{
int x=read(),y=read();
id[cnt]=i,add(x,y),id[cnt]=i,add(y,x);
}
for (i=;i<=n;++i)
if (!dfn[i])
{
tarjan(i);
if (--sub[i]<=) iscut[i]=;
}
for (i=;i<=num;++i) treecut[i]=;
for (i=;i<=num+n;++i) hea[i]=-;
cnt=;
for (i=;i<=n;++i)
if (iscut[i])
{
sort(belo[i].begin(),belo[i].end());
treecut[++num]=;
add(belo[i][],num),add(num,belo[i][]);
for (int j=;j<belo[i].size();++j)
if (belo[i][j]^belo[i][j-]) add(belo[i][j],num),add(num,belo[i][j]);
}
wk(num);
}
return ;
}