POJ-3694-Network（Tarjan+LCA+并查集）_加边动态tarjan-优快云博客

本文链接：https://blog.youkuaiyun.com/qq978874169/article/details/70432150

本文介绍了一种算法，该算法能够处理无向图中动态添加边的情况，并实时更新图中桥的数量。通过使用并查集和DFS序来查找最近公共祖先(LCA)，实现了高效的桥数量更新。

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给出无向图，动态加边，求每次加边后图中桥的个数。

缩点求并查集，然后按照DFS序找LCA维护桥的个数。

//#pragma comment(linker, "/STACK:1024000000,1024000000")
#include <cstring>
#include <cstdio>
#include <algorithm>
#include <iostream>
#include <queue>
#include <cmath>
#include <string>
#include <map>
#include <stack>
using namespace std;
#define INF 0x3f3f3f3f
#define MAXN 100007
#define MAXM 200007
const int mod=499999;
#define eps 1e-8
int ind,head[MAXN];
struct node
{
    int u,v,next,vis;
}edge[MAXM<<1];
void add_(int u, int v)
{
    edge[ind].u=u;
    edge[ind].v=v;
    edge[ind].vis=0;
    edge[ind].next=head[u];
    head[u]=ind++;
    edge[ind].u=v;
    edge[ind].v=u;
    edge[ind].vis=0;
    edge[ind].next=head[v];
    head[v]=ind++;
}
int low[MAXN],DFN[MAXN],stack_[MAXN],in_stack[MAXN],top,dps,cir;
int set_[MAXN],cnt,pre[MAXN],bri[MAXN];
int find_set(int x)
{
    if(set_[x]==-1)return x;
    return set_[x]=find_set(set_[x]);
}
bool link_set(int x, int y)
{
    x=find_set(x);
    y=find_set(y);
    if(x==y)return 0;
    set_[y]=x;
    return 1;
}
void Tarjan(int u)
{
    in_stack[u]=1;
    low[u]=DFN[u]=++dps;
    stack_[top++]=u;
    for(int i=head[u]; i+1; i=edge[i].next)
    {
        int v=edge[i].v;
        if(edge[i].vis)continue;
        edge[i].vis=edge[i^1].vis=1;
        if(!DFN[v])
        {
            pre[v]=u;
            Tarjan(v);
            low[u]=min(low[u],low[v]);
            if(low[v]>DFN[u])
                cnt++;
            else link_set(u,v);
        }
        else if(in_stack[v])
            low[u]=min(low[u],DFN[v]);
    }
}
void LCA(int x, int y)
{
    if(DFN[x]>DFN[y])
        swap(x,y);
    if(find_set(x)==find_set(y))return ;
    int bb=y,aa=x;
    while(DFN[y]>DFN[x])
    {
        y=pre[y];
        if(link_set(bb,y))
            cnt--;
    }
    while(x!=y)
    {
        x=pre[x];
        if(link_set(aa,x))
            cnt--;
    }
}
int main()
{
    int n,m,cas=0;
    while(scanf("%d%d",&n,&m)!=EOF)
    {
        if(n==m&&m==0)break;
        int a, b;
        cnt=dps=cir=ind=0;
        memset(head,-1,sizeof(head));
        memset(DFN,0,sizeof(DFN));
        memset(low,0,sizeof(low));
        memset(set_,-1,sizeof(set_));
        for(int i=0; i<m; ++i)
        {
            scanf("%d%d",&a,&b);
            add_(a,b);
        }
        Tarjan(1);
        int qu;
        scanf("%d",&qu);
        printf("Case %d:\n",++cas);
        for(int i=0; i<qu; ++i)
        {
            scanf("%d%d",&a,&b);
            LCA(a,b);
            printf("%d\n",cnt);
        }
    }
    return 0;
}
/*
3 2
1 2
2 3
2
1 2
1 3


4 4
1 2
2 1
2 3
1 4
2
1 2
3 4
0 0
*/