hdu 4612 Warm up(无向图Tarjan+树的直径)

题意：有N个点，M条边（有重边）的无向图，这样图中会可能有桥，问加一条边后，使桥最少，求该桥树。

思路：这个标准想法很好想到，缩点后，求出图中的桥的个数，然后重建图必为树，求出树的最长直径，在该直径的两端点连一边，则图中的桥会最少。

从这题中学到两点，所以写一下解题报告。

1.官方说judge的栈小，得手动增栈 #pragma comment(linker,"/STACK:102400000,102400000") 以前没见过，算是学习了。

2.对改正了对Tarjan算法的一个错误理解，以前看某人博客说，无向图中，Tarjan后low值相等的点属于同一块，以前这样判断过，也过了挺多题。但跟别人讨论后发现是错的。。。。。

3.以前没用Tarjan写过无向图，不懂正向边访问过，标志反向边，这次学习了。

//937MS    41304K
#pragma comment(linker, "/STACK:102400000,102400000")
#include
#include
const int VM = 200005;
const int EM = 1000005;

struct Edeg
{
    int to,nxt,vis;
}edge[EM<<1],tree[EM<<1];

int head[VM],vis[VM],thead[VM];
int dfn[VM],low[VM],stack[VM],belong[VM];
int ep,bridge,son,maxn,src,n,cnt,scc,top;

int max (int a,int b)
{
    return a > b ? a : b;
}
int min(int a ,int b)
{
    return a > b ? b : a;
}
void addedge (int cu,int cv)
{
    edge[ep].to = cv;
    edge[ep].vis = 0;
    edge[ep].nxt = head[cu];
    head[cu] = ep ++;
    edge[ep].to = cu;
    edge[ep].vis = 0;
    edge[ep].nxt = head[cv];
    head[cv] = ep ++;
}
void Buildtree(int cu,int cv)
{
    tree[son].to = cv;
    tree[son].nxt = thead[cu];
    thead[cu] = son ++;
}
void Tarjan (int u)
{
    int v;
    vis[u] = 1;
    dfn[u] = low[u] = ++cnt;
    stack[top++] = u;
    for (int i = head[u];i != -1;i = edge[i].nxt)
    {
        v = edge[i].to;
        if (edge[i].vis) continue; //
        edge[i].vis = edge[i^1].vis = 1; //正向边访问过了，反向边得标志，否则两点会成一块。
        if (vis[v] == 1)
            low[u] = min(low[u],dfn[v]);
        if (!vis[v])
        {
            Tarjan (v);
            low[u] = min(low[u],low[v]);
            if (low[v] > dfn[u])
                bridge ++;
        }
    }
    if (dfn[u] == low[u])
    {
        ++scc;
        do{
            v = stack[--top];
            vis[v] = 0;
            belong[v] = scc;
        }while (u != v);
    }
}
void BFS(int u)
{
    int que[VM+100];
    int front ,rear,i,v;
    front = rear = 0;
    memset (vis,0,sizeof(vis));
    que[rear++] = u;
    vis[u] = 1;
    while (front != rear)
    {
        u = que[front ++];
        front = front % (n+1);
        for (i = thead[u];i != -1;i = tree[i].nxt)
        {
            v = tree[i].to;
            if (vis[v]) continue;
            vis[v] = 1;
            que[rear++] = v;
            rear = rear%(n+1);
        }
    }
    src = que[--rear];//求出其中一个端点
}
void DFS (int u,int dep)
{
    maxn = max (maxn,dep);
    vis[u] = 1;
    for (int i = thead[u]; i != -1; i = tree[i].nxt)
    {
        int v = tree[i].to;
        if (!vis[v])
            DFS (v,dep+1);
    }
}
void solve()
{
    int u,v;
    memset (vis,0,sizeof(vis));
    cnt = bridge = scc = top = 0;
    Tarjan (1);
    memset (thead,-1,sizeof(thead));
    son = 0;
    for (u = 1;u <= n;u ++)              //重构图
        for (int i = head[u];i != -1;i = edge[i].nxt)
        {
            v = edge[i].to;
            if (belong[u]!=belong[v])
            {
                Buildtree (belong[u],belong[v]);
                Buildtree (belong[v],belong[u]);
            }
        }
    maxn = 0;    //最长直径
    BFS(1);      //求树直径的一个端点
    memset (vis,0,sizeof(vis));
    DFS(src,0); //求树的最长直径
    printf ("%d\n",bridge-maxn);
}

int main ()
{
    #ifdef LOCAL
        freopen ("in.txt","r",stdin);
    #endif
    int m,u,v;
    while (~scanf ("%d%d",&n,&m))
    {
        if (n == 0&&m == 0)
            break;
        memset (head,-1,sizeof(head));
        ep = 0;
        while (m --)
        {
            scanf ("%d%d",&u,&v);
            addedge (u,v);
        }
        solve();
    }
    return 0;
}