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 = 100005;
const int MAXM = 555555;

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 = -1){
        point[u].low = dfnNum;
        point[u].dfn = dfnNum ++;
        vis[u] = true;
        stk.push(u);
        for(int i = first[u]; i != -1; i = edge[i].next){
            int to = edge[i].to;
            if((i^1) == 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^1].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 = 1; i <= n; i ++){
            first[i] = -1;
            pre[i] = -1;
            vis[i] = 0;
            point[i].dfn = 0;
        }
        sign = colorNum = bridge = 0;
        dfnNum = 1;
        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 = 1; i <= sumOfPoint; i ++){
            if(!point[i].dfn)
                tarjan(i);
        }
    }
    int getAns(int a, int b){
        for(int i = 1; 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 != -1) ta = pre[ta];
            if(tb != -1) 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 != -1; i = edge[i].next){
                int to = edge[i].to;
                if(to == pre[a] && edge[i].bridge){
                    bridge --;
                    edge[i].bridge = false;
                    edge[i^1].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 != -1; i = edge[i].next){
                int to = edge[i].to;
                if(to == pre[b] && edge[i].bridge){
                    bridge --;
                    edge[i].bridge = false;
                    edge[i^1].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 = 1;
    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:
", cas ++);
        while(q --){
            int a, b;
            scanf("%d%d", &a, &b);
            printf("%d
", graph.getAns(a, b));
        }
        putchar('
');
    }
    return 0;
}