#include #include using namespace std; using namespace atcoder; using ll=long long; using ld=long double; ld pie=3.14159265359; ll inf=10010010010010010; ll mod=998244353; template< typename G > struct LowLink { const G &g; vector< int > used, ord, low; vector< int > articulation; vector< pair< int, int > > bridge; LowLink(const G &g) : g(g) {} int dfs(int idx, int k, int par) { used[idx] = true; ord[idx] = k++; low[idx] = ord[idx]; bool is_articulation = false; int cnt = 0; for(auto &to : g[idx]) { if(!used[to]) { ++cnt; k = dfs(to, k, idx); low[idx] = min(low[idx], low[to]); is_articulation |= ~par && low[to] >= ord[idx]; if(ord[idx] < low[to]) bridge.emplace_back(minmax(idx, (int) to)); } else if(to != par) { low[idx] = min(low[idx], ord[to]); } } is_articulation |= par == -1 && cnt > 1; if(is_articulation) articulation.push_back(idx); return k; } virtual void build() { used.assign(g.size(), 0); ord.assign(g.size(), 0); low.assign(g.size(), 0); int k = 0; for(int i = 0; i < g.size(); i++) { if(!used[i]) k = dfs(i, k, -1); } } }; struct unionfind { vectorpar,siz; unionfind(ll n): par(n,-1),siz(n,1){} ll root(ll x){ if (par[x]==-1) { return x; }else{ return par[x]=root(par[x]); } } bool issame(ll x,ll y){ return root(x)==root(y); } bool unite(ll x,ll y){ x=root(x); y=root(y); if (x==y) { return false; } if (siz[x]> n; unionfind uf(n); vectoru(n-1),v(n-1); vector>g(n); for (ll i = 0; i < n-1; i++) { cin >> u[i] >> v[i]; g[u[i]].push_back(v[i]); g[v[i]].push_back(u[i]); uf.unite(u[i],v[i]); } ll ans=0; vectormemo(n,0); for (ll i = 0; i < n; i++) { if (memo[uf.root(i)]==0) { ans+=1; } memo[uf.root(i)]+=1; } if (ans==1) { cout << "Bob" << endl; return 0; }else if (ans!=2) { cout << "Alice" << endl; return 0; } LowLink>>lowlink(g); lowlink.build(); if (lowlink.bridge.empty()) { cout << "Bob" <