#include using namespace std; using lint = long long; using pint = pair; using plint = pair; struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_; #define ALL(x) (x).begin(), (x).end() #define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i=i##_begin_;i--) #define REP(i, n) FOR(i,0,n) #define IREP(i, n) IFOR(i,0,n) template void ndarray(vector& vec, const V& val, int len) { vec.assign(len, val); } template void ndarray(vector& vec, const V& val, int len, Args... args) { vec.resize(len), for_each(begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); } template bool chmax(T &m, const T q) { if (m < q) {m = q; return true;} else return false; } template bool chmin(T &m, const T q) { if (m > q) {m = q; return true;} else return false; } template pair operator+(const pair &l, const pair &r) { return make_pair(l.first + r.first, l.second + r.second); } template pair operator-(const pair &l, const pair &r) { return make_pair(l.first - r.first, l.second - r.second); } template vector srtunq(vector vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; } template istream &operator>>(istream &is, vector &vec) { for (auto &v : vec) is >> v; return is; } template ostream &operator<<(ostream &os, const vector &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; } #if __cplusplus >= 201703L template istream &operator>>(istream &is, tuple &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; } template ostream &operator<<(ostream &os, const tuple &tpl) { std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os; } #endif template ostream &operator<<(ostream &os, const deque &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; } template ostream &operator<<(ostream &os, const set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const pair &pa) { os << '(' << pa.first << ',' << pa.second << ')'; return os; } template ostream &operator<<(ostream &os, const map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } #ifdef HITONANODE_LOCAL #define dbg(x) cerr << #x << " = " << (x) << " (L" << __LINE__ << ") " << __FILE__ << endl #else #define dbg(x) {} #endif struct UndirectedGraph { int V; // # of vertices int E; // # of edges int k; std::vector>> to; std::vector> edges; std::vector root_ids; // DFS forestの構築で根になった頂点 std::vector is_bridge; // Whether edge i is bridge or not, size = E std::vector is_articulation; // whether vertex i is articulation point or not, size = V // lowlink std::vector order; // visiting order of DFS tree, size = V std::vector lowlink; // size = V std::vector is_dfstree_edge; // size = E int tecc_num; // 二重辺連結成分数 std::vector tecc_id; // 各頂点が何個目の二重辺連結成分か int tvcc_num; // 二重頂点連結成分数 std::vector tvcc_id; // 各辺が何個目の二重頂点連結成分か UndirectedGraph(int V) : V(V), E(0), k(0), to(V), is_articulation(V, 0), order(V, -1), lowlink(V, -1), tecc_num(0), tvcc_num(0) {} void add_edge(int v1, int v2) { assert(v1 >= 0 and v1 < V); assert(v2 >= 0 and v2 < V); to[v1].emplace_back(v2, E); to[v2].emplace_back(v1, E); edges.emplace_back(v1, v2); is_bridge.push_back(0); is_dfstree_edge.push_back(0); tvcc_id.push_back(-1); E++; } std::vector _edge_stack; int _root_now; // Build DFS tree // Complexity: O(V + E) void dfs_lowlink(int now, int prv_eid = -1) { if (prv_eid < 0) _root_now = k; if (prv_eid == -1) root_ids.push_back(now); order[now] = lowlink[now] = k++; for (const auto &nxt : to[now]) if (nxt.second != prv_eid) { if (order[nxt.first] < order[now]) _edge_stack.push_back(nxt.second); if (order[nxt.first] >= 0) { lowlink[now] = std::min(lowlink[now], order[nxt.first]); } else { is_dfstree_edge[nxt.second] = 1; dfs_lowlink(nxt.first, nxt.second); lowlink[now] = std::min(lowlink[now], lowlink[nxt.first]); if ((order[now] == _root_now and order[nxt.first] != _root_now + 1) or (order[now] != _root_now and lowlink[nxt.first] >= order[now])) { is_articulation[now] = 1; } if (lowlink[nxt.first] >= order[now]) { while (true) { int e = _edge_stack.back(); tvcc_id[e] = tvcc_num; _edge_stack.pop_back(); if (std::minmax(edges[e].first, edges[e].second) == std::minmax(now, nxt.first)) { break; } } tvcc_num++; } } } } // Find all bridges // Complexity: O(V + E) void detectBridge() { for (int i = 0; i < E; i++) { int v1 = edges[i].first, v2 = edges[i].second; if (order[v1] < 0) dfs_lowlink(v1); if (order[v1] > order[v2]) std::swap(v1, v2); if (order[v1] < lowlink[v2]) is_bridge[i] = 1; } } // Find two-edge-connected components and classify all vertices // Complexity: O(V + E) void two_edge_connected_components() { tecc_num = 0; tecc_id.assign(V, -1); for (int i = 0; i < V; i++) if (tecc_id[i] == -1) { tecc_id[i] = tecc_num; std::queue que; que.push(i); while (!que.empty()) { int now = que.front(); que.pop(); for (const auto &edge : to[now]) { int nxt = edge.first; if (tecc_id[nxt] >= 0 or is_bridge[edge.second]) continue; tecc_id[nxt] = tecc_num; que.push(nxt); } } tecc_num++; } } }; int main() { int N; cin >> N; UndirectedGraph graph(N); REP(i, N) { int a, b; cin >> a >> b; graph.add_edge(a - 1, b - 1); } graph.detectBridge(); vector ret; REP(i, N) if (!graph.is_bridge[i]) ret.emplace_back(i + 1); cout << ret.size() << '\n'; for (auto x : ret) cout << x << ' '; cout << '\n'; }