#include #define loop(n) for (int ngtkana_is_genius = 0; ngtkana_is_genius < int(n); ngtkana_is_genius++) #define rep(i, begin, end) for(int i = int(begin); i < int(end); i++) #define all(v) v.begin(), v.end() #define rand(l, r) std::uniform_int_distribution<>(l, r)(mt) #define lint long long auto cmn = [](auto& a, auto b){if (a > b) {a = b; return true;} return false;}; auto cmx = [](auto& a, auto b){if (a < b) {a = b; return true;} return false;}; void debug_impl() { std::cerr << std::endl; } template void debug_impl(Head head, Tail... tail){ std::cerr << " " << head; debug_impl(tail...); } #ifndef STOPIT #define debug(...)\ std::cerr << std::boolalpha << "[" << #__VA_ARGS__ << "]:";\ debug_impl(__VA_ARGS__);\ std::cerr << std::noboolalpha; #else #define debug 0; #endif template auto make_vector_impl(size_t sz, T t) {return std::vector(sz, t);} template = nullptr> auto make_vector(size_t sz, U u) {return make_vector_impl(sz, T(u));} template = nullptr> auto make_vector(size_t sz) {return std::vector(sz);} template = nullptr> auto make_vector(size_t a, Args... args) {return make_vector_impl(a, make_vector(args...));} template auto& at(T& t, Size_t i) {return t.at(i);} template auto& at(T& t, Size_t i, Args... args) {return at(t.at(i), args...);} template < typename Container, typename Value = typename Container::value_type, std::enable_if_t::value, std::nullptr_t> = nullptr> std::istream& operator>> (std::istream& is, Container& v) { for (auto & x : v) { is >> x; } return is; } template < typename Container, typename Value = typename Container::value_type, std::enable_if_t::value, std::nullptr_t> = nullptr > std::ostream& operator<< (std::ostream& os, Container const& v) { os << "{"; for (auto it = v.begin(); it != v.end(); it++) {os << (it != v.begin() ? "," : "") << *it;} return os << "}"; } template< typename F > class fixed_point : F { public: explicit constexpr fixed_point (F&& f) noexcept : F(std::forward< F >(f)) {} template< typename ... Args > constexpr decltype(auto) operator()(Args&& ... args) const { return F::operator()(*this, std::forward< Args >(args)...); } }; template< typename F > static inline constexpr decltype(auto) fix (F&& f) noexcept { return fixed_point< F >{std::forward< F >(f)}; } std::chrono::system_clock::time_point chrono_begin; void alice () { std::cout << "Alice" << std::endl; auto chrono_end = std::chrono::system_clock::now(); auto runtime = std::chrono::duration_cast< std::chrono::milliseconds >(chrono_end-chrono_begin).count(); debug(runtime); exit(0); } void bob () { std::cout << "Bob" << std::endl; auto chrono_end = std::chrono::system_clock::now(); auto runtime = std::chrono::duration_cast< std::chrono::milliseconds >(chrono_end-chrono_begin).count(); debug(runtime); exit(0); } auto is_tree(std::vector< std::vector< int > > const &graph) { auto n = (int)graph.size(); auto root = 0; std::vector< int >ckd(n, false); auto cycle = fix([&](auto&& dfs, int x, int p, int d) -> bool { ckd.at(x) = true; bool ret = false; for (auto const& y : graph.at(x)) { if (ckd.at(y)) { if (y != p) { return true; } else { continue; } } ret |= dfs(y, x, d + 1); } return ret; })(root, root, 0); if (cycle) return false; auto k = std::accumulate(all(ckd), 0); return n == k; } int main() { std::cin.tie(0); std::cin.sync_with_stdio(false); chrono_begin = std::chrono::system_clock::now(); int n; std::cin >> n; assert(n <= 100'000); debug(n); auto graph = make_vector< 2, int >(n, 0); auto edges = std::set< std::pair< int, int > >{}; loop(n - 1) { int u, v; std::cin >> u >> v; graph.at(u).emplace_back(v); graph.at(v).emplace_back(u); if (u > v) { std::swap(u, v); } assert(u != v); assert(!edges.count({u, v})); edges.emplace(u, v); } if (is_tree(graph)) { bob(); } for (auto const& v : graph) { if (v.size() != 2 && v.size() != 0) { alice(); } } auto start = -1; rep(i, 0, n) { if (graph.at(i).size() == 2) { start = i; } } std::vector< int >ckd(n, false); fix ([&](auto dfs, int crr) -> void { ckd.at(crr) = true; for (auto const& nxt : graph.at(crr)) { if (ckd.at(nxt)) continue; dfs(nxt); } })(start); auto cnt = std::accumulate(all(ckd), 0); if (cnt != n - 1) alice(); else bob(); return 0; }