/* preprocessor start */ #ifdef LOCAL //* #define _GLIBCXX_DEBUG // gcc /*/ #define _LIBCPP_DEBUG 0 // clang //*/ #define __clock__ // #define __buffer_check__ #else #pragma GCC optimize("Ofast") /* #define _GLIBCXX_DEBUG // gcc /*/ // #define _LIBCPP_DEBUG 0 // clang //*/ // #define __buffer_check__ // #define NDEBUG #endif #define __precision__ 10 #define iostream_untie true #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #define __all(v) std::begin(v), std::end(v) #define __rall(v) std::rbegin(v), std::rend(v) #define __popcount(n) __builtin_popcountll(n) #define __clz32(n) __builtin_clz(n) #define __clz64(n) __builtin_clzll(n) #define __ctz32(n) __builtin_ctz(n) #define __ctz64(n) __builtin_ctzll(n) /* preprocessor end */ namespace std { // hash template size_t hash_combine(size_t seed, T const &key) { return seed ^ (hash()(key) + 0x9e3779b9 + (seed << 6) + (seed >> 2)); } template struct hash> { size_t operator()(pair const &pr) const { return hash_combine(hash_combine(0, pr.first), pr.second); } }; template ::value - 1> struct tuple_hash_calc { static size_t apply(size_t seed, tuple_t const &t) { return hash_combine(tuple_hash_calc::apply(seed, t), get(t)); } }; template struct tuple_hash_calc { static size_t apply(size_t seed, tuple_t const &t) { return hash_combine(seed, get<0>(t)); } }; template struct hash> { size_t operator()(tuple const &t) const { return tuple_hash_calc>::apply(0, t); } }; // iostream template istream &operator>>(istream &is, pair &p) { return is >> p.first >> p.second; } template ostream &operator<<(ostream &os, const pair &p) { return os << p.first << ' ' << p.second; } template struct tupleis { static istream &apply(istream &is, tuple_t &t) { tupleis::apply(is, t); return is >> get(t); } }; template struct tupleis { static istream &apply(istream &is, tuple_t &t) { return is; } }; template istream &operator>>(istream &is, tuple &t) { return tupleis, tuple_size>::value - 1>::apply(is, t); } template <> istream &operator>>(istream &is, tuple<> &t) { return is; } template struct tupleos { static ostream &apply(ostream &os, const tuple_t &t) { tupleos::apply(os, t); return os << ' ' << get(t); } }; template struct tupleos { static ostream &apply(ostream &os, const tuple_t &t) { return os << get<0>(t); } }; template ostream &operator<<(ostream &os, const tuple &t) { return tupleos, tuple_size>::value - 1>::apply(os, t); } template <> ostream &operator<<(ostream &os, const tuple<> &t) { return os; } template , string>::value, nullptr_t> = nullptr> istream& operator>>(istream& is, Container &cont) { for(auto&& e : cont) is >> e; return is; } template , string>::value, nullptr_t> = nullptr> ostream& operator<<(ostream& os, const Container &cont) { bool flag = 1; for(auto&& e : cont) flag ? flag = 0 : (os << ' ', 0), os << e; return os; } } // namespace std namespace setting { using namespace std; using namespace chrono; system_clock::time_point start_time, end_time; long long get_elapsed_time() { end_time = system_clock::now(); return duration_cast(end_time - start_time).count(); } void print_elapsed_time() { cerr << "\n----- Exec time : " << get_elapsed_time() << " ms -----\n\n"; } void buffer_check() { char bufc; if(cin >> bufc) cerr << "\n\033[1;35mwarning\033[0m: buffer not empty.\n"; } struct setupper { setupper() { if(iostream_untie) ios::sync_with_stdio(false), cin.tie(nullptr); cout << fixed << setprecision(__precision__); #ifdef stderr_path if(freopen(stderr_path, "a", stderr)) cerr << fixed << setprecision(__precision__); #endif #ifdef LOCAL cerr << "\n----- stderr at LOCAL -----\n\n"; #endif #ifdef __buffer_check__ atexit(buffer_check); #endif #ifdef __clock__ start_time = system_clock::now(); atexit(print_elapsed_time); #endif } } __setupper; // struct setupper } // namespace setting #ifdef __clock__ #include "C:\Users\euler\OneDrive\Documents\Competitive_Programming\Library\local\Clock.hpp" #else #define build_clock() ((void)0) #define set_clock() ((void)0) #define get_clock() ((void)0) #endif #ifdef LOCAL #include "C:\Users\euler\OneDrive\Documents\Competitive_Programming\Library\local\Dump.hpp" #else #define dump(...) ((void)0) #endif /* function utility start */ template T read(types... args) noexcept { typename std::remove_const::type obj(args...); std::cin >> obj; return obj; } #define input(type, var, ...) type var{read(__VA_ARGS__)} // substitute y for x if x > y. template inline bool sbmin(T &x, const T &y) { return x > y ? x = y, true : false; } // substitute y for x if x < y. template inline bool sbmax(T &x, const T &y) { return x < y ? x = y, true : false; } // binary search on discrete range. template iter_type binary(iter_type __ok, iter_type __ng, pred_type pred) { std::ptrdiff_t dist(__ng - __ok); while(std::abs(dist) > 1) { iter_type mid(__ok + dist / 2); if(pred(mid)) __ok = mid, dist -= dist / 2; else __ng = mid, dist /= 2; } return __ok; } // binary search on real numbers. template long double binary(long double __ok, long double __ng, const long double eps, pred_type pred) { while(std::abs(__ok - __ng) > eps) { long double mid{(__ok + __ng) / 2}; (pred(mid) ? __ok : __ng) = mid; } return __ok; } // reset all bits. template void reset(A &array) { memset(array, 0, sizeof(array)); } // be careful that val is type-sensitive. template void init(A (&array)[N], const T &val) { std::fill((T*)array, (T*)(array + N), val); } /* functon utility end */ /* using alias start */ using namespace std; using i32 = int_least32_t; using i64 = int_least64_t; using u32 = uint_least32_t; using u64 = uint_least64_t; using p32 = pair; using p64 = pair; template > using heap = priority_queue, Comp>; template using hashset = unordered_set; template using hashmap = unordered_map; /* using alias end */ /* library start */ // #line 2 "Union_find.hpp" #ifndef Union_find_hpp #define Union_find_hpp #include #include #include #include class union_find { const size_t n; std::vector link; bool *const cyc, *const clr, *const flip; size_t comp, isol; bool bipart; public: explicit union_find(const size_t _n) : n(_n), link(n, -1), cyc(new bool[n]{}), clr(new bool[n]{}), flip(new bool[n]{}), comp(n), isol(n), bipart(true) {} ~union_find() { delete[] cyc; delete[] clr; delete[] flip; } size_t find(const size_t x) { assert(x < n); if(link[x] < 0) return x; const size_t r = find(link[x]); if(flip[link[x]]) clr[x] = !clr[x], flip[x] = !flip[x]; return link[x] = r; } size_t size() const { return n; } size_t size(const size_t x) { return -link[find(x)]; } size_t count() const { return comp; } size_t isolated() const { return isol; } bool color(const size_t x) { return find(x), clr[x]; } bool cyclic(const size_t x) { return cyc[find(x)]; } bool same(const size_t x, const size_t y) { return find(x) == find(y); } bool bipartite() const { return bipart; } bool unite(size_t x, size_t y) { const size_t _x = find(x), _y = find(y); const bool f = clr[x] == clr[y]; x = _x, y = _y; if(x == y) { bipart &= !f; cyc[x] = true; return false; } if(link[x] > link[y]) std::swap(x, y); if(link[x] == -1) --isol; if(link[y] == -1) --isol; link[x] += link[y], link[y] = x; cyc[x] = cyc[x] || cyc[y]; if(f) clr[y] = !clr[y], flip[y] = !flip[y]; --comp; return true; } }; // class union_find #endif /* library end */ /* The main code follows. */ struct solver { solver() { input(int,n); union_find uf(n); vector deg(n,0); for(int i=1; i>a>>b; uf.unite(a,b); deg[a]++,deg[b]++; } if(uf.count()!=1 && (uf.count()>2 || *min_element(__all(deg))!=0 || *max_element(__all(deg))!=2)) { cout << "Alice" << "\n"; return; } cout << "Bob" << "\n"; } }; // struct solver int main(int argc, char *argv[]) { u32 t; // loop count #ifdef LOCAL t = 1; #else t = 1; // single test case #endif // t = -1; // infinite loop // cin >> t; // case number given while(t--) { solver(); } }