#include #include #include #include #include #include #include #include #define rep(i,n) for(int i=0; i=0; i--) const char* yn(bool x){ return x ? "Yes" : "No"; } #include namespace nachia{ template class CsrArray{ public: struct ListRange{ using iterator = typename std::vector::iterator; iterator begi, endi; iterator begin() const { return begi; } iterator end() const { return endi; } int size() const { return (int)std::distance(begi, endi); } Elem& operator[](int i) const { return begi[i]; } }; struct ConstListRange{ using iterator = typename std::vector::const_iterator; iterator begi, endi; iterator begin() const { return begi; } iterator end() const { return endi; } int size() const { return (int)std::distance(begi, endi); } const Elem& operator[](int i) const { return begi[i]; } }; private: int m_n; std::vector m_list; std::vector m_pos; public: CsrArray() : m_n(0), m_list(), m_pos() {} static CsrArray Construct(int n, std::vector> items){ CsrArray res; res.m_n = n; std::vector buf(n+1, 0); for(auto& [u,v] : items){ ++buf[u]; } for(int i=1; i<=n; i++) buf[i] += buf[i-1]; res.m_list.resize(buf[n]); for(int i=(int)items.size()-1; i>=0; i--){ res.m_list[--buf[items[i].first]] = std::move(items[i].second); } res.m_pos = std::move(buf); return res; } static CsrArray FromRaw(std::vector list, std::vector pos){ CsrArray res; res.m_n = pos.size() - 1; res.m_list = std::move(list); res.m_pos = std::move(pos); return res; } ListRange operator[](int u) { return ListRange{ m_list.begin() + m_pos[u], m_list.begin() + m_pos[u+1] }; } ConstListRange operator[](int u) const { return ConstListRange{ m_list.begin() + m_pos[u], m_list.begin() + m_pos[u+1] }; } int size() const { return m_n; } int fullSize() const { return (int)m_list.size(); } }; } // namespace nachia namespace nachia{ struct Graph { public: struct Edge{ int from, to; void reverse(){ std::swap(from, to); } int xorval() const { return from ^ to; } }; Graph(int n = 0, bool undirected = false, int m = 0) : m_n(n), m_e(m), m_isUndir(undirected) {} Graph(int n, const std::vector>& edges, bool undirected = false) : m_n(n), m_isUndir(undirected){ m_e.resize(edges.size()); for(std::size_t i=0; i static Graph Input(Cin& cin, int n, bool undirected, int m, bool offset = 0){ Graph res(n, undirected, m); for(int i=0; i> u >> v; res[i].from = u - offset; res[i].to = v - offset; } return res; } int numVertices() const noexcept { return m_n; } int numEdges() const noexcept { return int(m_e.size()); } int addNode() noexcept { return m_n++; } int addEdge(int from, int to){ m_e.push_back({ from, to }); return numEdges() - 1; } Edge& operator[](int ei) noexcept { return m_e[ei]; } const Edge& operator[](int ei) const noexcept { return m_e[ei]; } Edge& at(int ei) { return m_e.at(ei); } const Edge& at(int ei) const { return m_e.at(ei); } auto begin(){ return m_e.begin(); } auto end(){ return m_e.end(); } auto begin() const { return m_e.begin(); } auto end() const { return m_e.end(); } bool isUndirected() const noexcept { return m_isUndir; } void reverseEdges() noexcept { for(auto& e : m_e) e.reverse(); } void contract(int newV, const std::vector& mapping){ assert(numVertices() == int(mapping.size())); for(int i=0; i induce(int num, const std::vector& mapping) const { int n = numVertices(); assert(n == int(mapping.size())); for(int i=0; i indexV(n), newV(num); for(int i=0; i= 0) indexV[i] = newV[mapping[i]]++; std::vector res; res.reserve(num); for(int i=0; i= 0) res[mapping[e.to]].addEdge(indexV[e.from], indexV[e.to]); return res; } CsrArray getEdgeIndexArray(bool undirected) const { std::vector> src; src.reserve(numEdges() * (undirected ? 2 : 1)); for(int i=0; i::Construct(numVertices(), src); } CsrArray getEdgeIndexArray() const { return getEdgeIndexArray(isUndirected()); } CsrArray getAdjacencyArray(bool undirected) const { std::vector> src; src.reserve(numEdges() * (undirected ? 2 : 1)); for(auto e : m_e){ src.emplace_back(e.from, e.to); if(undirected) src.emplace_back(e.to, e.from); } return CsrArray::Construct(numVertices(), src); } CsrArray getAdjacencyArray() const { return getAdjacencyArray(isUndirected()); } private: int m_n; std::vector m_e; bool m_isUndir; }; } // namespace nachia namespace nachia{ struct StronglyConnectedComponents{ private: int m_n; CsrArray induce; int componentNum; public: StronglyConnectedComponents() : m_n(0), induce(), componentNum(0) {} StronglyConnectedComponents(Graph E) { int n = E.numVertices(); m_n = n; std::vector O(n); { auto adj = E.getAdjacencyArray(); int Oi = n; std::vector P(n, -1), EI(n, 0); for(int s=0; s= 0){ if(EI[p] == adj[p].size()){ O[--Oi] = p; p = P[p]; continue; } int q = adj[p][EI[p]++]; if(P[q] == -1){ P[q] = p; p = q; } } } } E.reverseEdges(); auto adj = E.getAdjacencyArray(); std::vector sep = {0}, csr(n), vis(n,0); int p1 = 0, p2 = 0; for(int s : O) if(!vis[s]){ csr[p2++] = s; vis[s] = 1; for(; p1::FromRaw(std::move(csr), std::move(sep)); componentNum = induce.size(); } int numComponents() const noexcept { return componentNum; } const CsrArray& getCsr() const noexcept { return induce; } std::vector getMapping() const { std::vector res(m_n); for(int i=0; i> N; auto graph = nachia::Graph(N, false); rep(i,N){ int a; cin >> a; rep(t,a){ int b; cin >> b; graph.addEdge(i,b-1); } } auto scc = nachia::StronglyConnectedComponents(graph); graph.contract(scc.numComponents(), scc.getMapping()); auto adj = graph.getAdjacencyArray(); bool ans = scc.getMapping()[0] == 0; rep(i,adj.size()-1){ bool ok = false; for(int j : adj[i]) if(j == i+1) ok = true; if(!ok) ans = false; } cout << yn(ans) << endl; return 0; }