poj 3694 Network ： o(n) tarjan + O(n) lca + O(m) 维护 总复杂度 O(m*q)

 /**
 problem: http://poj.org/problem?id=3694

 问每加一条边后剩下多少桥
 因为是无向图，所以使用tarjan缩点后会成一棵树并维护pre数组
 在树上连一条边(a,b)减少的桥数就是
 a点到a点和b点的最近公共祖先（lca）的所有边+b点到a点和b点的最近公共祖先的所有边
 在算桥的同时将这些点缩成一个点
 即每个点color = 最近公共祖先color
 同时维护pre数组 每个点的pre = 最近公共祖先的pre 即可
 **/
 #include<stdio.h>
 #include<stack>
 #include<queue>
 #include<algorithm>
 using namespace std;

 const int MAXN = ;
 const int MAXM = ;

 class Graphics{
 private:
     struct Edge{
         int to, next;
         bool bridge;
     }edge[MAXM];
     struct Point{
         int dfn, low, color;
     }point[MAXN];
     int first[MAXN], pre[MAXN], sign, sumOfPoint, dfnNum, colorNum, bridge;
     bool vis[MAXN];
     stack<int> stk;
     queue<int> bfs;
     void tarjan(int u, int preEdge = -){
         point[u].low = dfnNum;
         point[u].dfn = dfnNum ++;
         vis[u] = true;
         stk.push(u);
         for(int i = first[u]; i != -; i = edge[i].next){
             int to = edge[i].to;
             if((i^) == preEdge) continue;
             if(!point[to].dfn){
                 pre[to] = u; ///如果下一个点没被访问过则更新一下下个点的pre
                 tarjan(to, i);
                 point[u].low = min(point[u].low, point[to].low);
                 if(point[to].low > point[u].dfn){
                     edge[i].bridge = true;
                     edge[i^].bridge = true;
                     bridge ++;
                 }
             }else if(vis[to]){
                 point[u].low = min(point[to].dfn, point[u].low);
             }
         }
         if(point[u].dfn == point[u].low){
             vis[u] = false;
             point[u].color = ++ colorNum;
             while(stk.top() != u){
                 pre[stk.top()] = pre[u]; ///缩点时，该环中的所有点pre等于时间戳最小点的pre
                 point[stk.top()].color = colorNum;
                 vis[stk.top()] = false;
                 stk.pop();
             }
             stk.pop();
         }
     }
 public:
     void clear(int n){
         sumOfPoint = n;
         for(int i = ; i <= n; i ++){
             first[i] = -;
             pre[i] = -;
             vis[i] = ;
             point[i].dfn = ;
         }
         sign = colorNum = bridge = ;
         dfnNum = ;
         while(!stk.empty()) stk.pop();
     }
     void addEdgeOneWay(int u, int v){
         edge[sign].to = v;
         edge[sign].next = first[u];
         edge[sign].bridge = false;
         first[u] = sign ++;
     }
     void addEdgeTwoWay(int u, int v){
         addEdgeOneWay(u, v);
         addEdgeOneWay(v, u);
     }
     void tarjanAllPoint(){
         for(int i = ; i <= sumOfPoint; i ++){
             if(!point[i].dfn)
                 tarjan(i);
         }
     }
     int getAns(int a, int b){
         for(int i = ; i <= colorNum; i ++){
             vis[i] = false;
         }
         vis[point[a].color] = true;
         vis[point[b].color] = true;
         int lca, lcacolor, ta = a, tb = b;
         while(true){
             if(ta != -) ta = pre[ta];
             if(tb != -) tb = pre[tb];
             if(vis[point[ta].color]){
                 lcacolor = point[ta].color;
                 lca = ta;
                 break;
             }
             if(vis[point[tb].color]){
                 lcacolor = point[tb].color;
                 lca = tb;
                 break;

             }
             vis[point[ta].color] = true;
             vis[point[tb].color] = true;
         }
         while(point[a].color != lcacolor){
             for(int i = first[a]; i != -; i = edge[i].next){
                 int to = edge[i].to;
                 if(to == pre[a] && edge[i].bridge){
                     bridge --;
                     edge[i].bridge = false;
                     edge[i^].bridge = false;
                     break;
                 }
             }
             point[a].color = lcacolor;
             int tmp = pre[a];
             pre[a] = pre[lca];
             a = tmp;
         }
         while(point[b].color != lcacolor){
             for(int i = first[b]; i != -; i = edge[i].next){
                 int to = edge[i].to;
                 if(to == pre[b] && edge[i].bridge){
                     bridge --;
                     edge[i].bridge = false;
                     edge[i^].bridge = false;
                     break;
                 }
             }
             point[b].color = lcacolor;
             int tmp = pre[b];
             pre[b] = pre[lca];
             b = tmp;
         }
         addEdgeTwoWay(a, b);
         return bridge;
     }
 }graph;

 int main(){
     int n, m, cas = ;
     while(scanf("%d%d", &n, &m) != EOF && m + n){
         graph.clear(n);
         while(m --){
             int a, b;
             scanf("%d%d", &a, &b);
             graph.addEdgeTwoWay(a, b);
         }
         graph.tarjanAllPoint();
         int q;
         scanf("%d", &q);
         printf("Case %d:\n", cas ++);
         while(q --){
             int a, b;
             scanf("%d%d", &a, &b);
             printf("%d\n", graph.getAns(a, b));
         }
         putchar('\n');
     }
     return ;
 }