POJ 3694 Network

大意略。

思路：开始的每加一次边就用Tarjan求一次桥边，这样肯定超时了。后来发现，只要在x->y之间连一条边的话，那么在x->y以及到它们的LCA之间形成了一个环，那么之间割边都不存在了。

求LCA的做法：把它们上升到同一个层次，然后一起往父亲节点走即可。

#include <iostream>
#include <cstdlib>
#include <cstdio>
#include <string>
#include <cstring>
#include <cmath>
#include <vector>
#include <queue>
#include <algorithm>
#include <map>
using namespace std;

const int maxn = 100010;
const int maxm = 200010*2;

struct Edge
{
    int u, v;
    int next;
}edge[maxm];

int n, m;
int cnt;

int first[maxn];
int dfn[maxn], low[maxn], ins[maxn];

int top, scnt, tot;

int bridge[maxn];

int p[maxn];
int num;

void init()
{
    cnt = 0;
    top = scnt = tot = 0;
    memset(first, -1, sizeof(first));
    memset(ins, 0, sizeof(ins));
    memset(dfn, 0, sizeof(dfn));
    memset(low, 0, sizeof(low));
    memset(bridge, 0, sizeof(bridge));
    for(int i = 0; i <= n; i++) p[i] = i;
}

void read_graph(int u, int v)
{
    edge[cnt].v = v;
    edge[cnt].next = first[u], first[u] = cnt++;
}

void Tarjan(int u, int fa)
{
    low[u] = dfn[u] = ++tot;
    bool repeat = 0;
    for(int e = first[u]; e != -1; e = edge[e].next)
    {
        int v = edge[e].v;
        if(v == fa && !repeat) { repeat = 1; continue; }
        if(!dfn[v])
        {
            p[v] = u;
            Tarjan(v, u);
            low[u] = min(low[u], low[v]);
            if(dfn[u] < low[v]) { bridge[v] = 1; num++; }
        }
        else low[u] = min(low[u], dfn[v]);
    }
}

void LCA(int x, int y)
{
    if(dfn[x] < dfn[y]) swap(x, y);
    
    /*while(dfn[x] > dfn[y])
    {
        if(bridge[x]) { num--; bridge[x] = 0; }
        x = p[x];
    }*/
    
    while(x != y)
    {
        if(bridge[x]) { num--; bridge[x] = 0;}
        if(bridge[y]) { num--; bridge[y] = 0; }
        x = p[x];
        y = p[y];
    }
}

int main()
{
    int times = 0;
    while(~scanf("%d%d", &n, &m) && (n || m))
    {
        init();
        while(m--)
        {
            int u, v;
            scanf("%d%d", &u, &v);
            read_graph(u, v), read_graph(v, u);
        }
        
        num = 0;
        
        Tarjan(1, -1);
        printf("Case %d:\n", ++times);
        int Q;
        scanf("%d", &Q);
        while(Q--)
        {
            int x, y;
            scanf("%d%d", &x, &y);
            LCA(x, y);
            printf("%d\n", num);
        }
        printf("\n");
    }
    return 0;
}