codefoeces-1000E We Need More Bosses(tarjan+最长链)

E. We Need More Bosses

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

Your friend is developing a computer game. He has already decided how the game world should look like — it should consist of $\mathrm{n locations\; connected\; by m two-way passages.\; The\; passages\; are\; designed\; in\; such\; a\; way\; that\; it\; should\; be\; possible\; to\; get\; from\; any\; location\; to\; any\; other\; location.}$

Of course, some passages should be guarded by the monsters (if you just can go everywhere without any difficulties, then it's not fun, right?). Some crucial passages will be guarded by really fearsome monsters, requiring the hero to prepare for battle and designing his own tactics of defeating them (commonly these kinds of monsters are called bosses). And your friend wants you to help him place these bosses.

The game will start in location $\mathrm{s and\; end\; in\; location t,\; but\; these\; locations\; are\; not\; chosen\; yet.\; After\; choosing\; these\; locations,\; your\; friend\; will\; place\; a\; boss\; in\; each\; passage\; such\; that\; it\; is\; impossible\; to\; get\; from s to t without\; using\; this\; passage.\; Your\; friend\; wants\; to\; place\; as\; much\; bosses\; as\; possible\; (because\; more\; challenges\; means\; more\; fun,\; right?),\; so\; he\; asks\; you\; to\; help\; him\; determine\; the\; maximum\; possible\; number\; of\; bosses,\; considering\; that\; any\; location\; can\; be\; chosen\; as s or\; as t.}$

Input

The first line contains two integers $\mathrm{n and m (2\le n\le 3\cdot 105, n-1\le m\le 3\cdot 105)\; —\; the\; number\; of\; locations\; and\; passages,\; respectively.}$

Then $\mathrm{m lines\; follow,\; each\; containing\; two\; integers x and y (1\le x,y\le n, x\ne y)\; describing\; the\; endpoints\; of\; one\; of\; the\; passages.}$

It is guaranteed that there is no pair of locations directly connected by two or more passages, and that any location is reachable from any other location.

Output

Print one integer — the maximum number of bosses your friend can place, considering all possible choices for $\mathrm{s and t.}$

Examples

input

Copy

5 5
1 2
2 3
3 1
4 1
5 2

output

Copy

2

input

Copy

4 3
1 2
4 3
3 2

output

Copy

3

题意：n个点m条边的无向图, 对于任意的两个点, 最多有多少条特殊边, 特殊边就是去掉这条边这两个点就无法互达(割边）

思路：tarjan缩点完，建图跑最长链(双dfs

#include<bits/stdc++.h>
#define ll long long
#define pb push_back
using namespace std;
const int maxn=300010;
vector<int> mp[maxn];
vector<int> G[maxn];
int stc[maxn],scc[maxn],dfn[maxn],low[maxn],dis[maxn];
int top,times,scc_cnt;
void tarjan(int u,int fa)
{
    stc[++top]=u;
    dfn[u]=low[u]=++times;
    for(auto x:mp[u])
    {
        if(x==fa) continue;
        if(!dfn[x])
        {
            tarjan(x,u);
            low[u]=min(low[u],low[x]);
        }
        else low[u]=min(low[u],dfn[x]);
    }
    if(dfn[u]==low[u])
    {
        scc_cnt++;
        while(true)
        {
            int x=stc[top--];
            scc[x]=scc_cnt;
            if(x==u) break;
        }
    }

}
void dfs(int u,int fa)
{
    dis[u]=dis[fa]+1;
    for(auto x:G[u])
    {
        if(x==fa) continue;
        dfs(x,u);
    }
}
int main()
{
    int n,m,u,v;
    scanf("%d %d",&n,&m);
    for(int i=1;i<=m;i++)
    {
        scanf("%d %d",&u,&v);
        mp[u].pb(v);
        mp[v].pb(u);
    }
    tarjan(1,0);
    for(int i=1;i<=n;i++)
        for(auto x:mp[i])
        if(scc[x]!=scc[i])
            G[scc[i]].pb(scc[x]);
    int s=0;
    dfs(1,0);
    for(int i=1;i<=scc_cnt;i++) if(dis[i]>dis[s]) s=i;
    dfs(s,0);
    int ans=0;
    for(int i=1;i<=scc_cnt;i++) ans=max(ans,dis[i]);
    cout<<ans-1<<"\n";
    return 0;
}

View Code

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