#include #include using namespace std; using int64 = long long; //const int mod = 1e9 + 7; const int mod = 998244353; const int64 infll = (1LL << 62) - 1; const int inf = (1 << 30) - 1; struct IoSetup { IoSetup() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(10); cerr << fixed << setprecision(10); } } iosetup; template< typename T1, typename T2 > ostream &operator<<(ostream &os, const pair< T1, T2 > &p) { os << p.first << " " << p.second; return os; } template< typename T1, typename T2 > istream &operator>>(istream &is, pair< T1, T2 > &p) { is >> p.first >> p.second; return is; } template< typename T > ostream &operator<<(ostream &os, const vector< T > &v) { for(int i = 0; i < (int) v.size(); i++) { os << v[i] << (i + 1 != v.size() ? " " : ""); } return os; } template< typename T > istream &operator>>(istream &is, vector< T > &v) { for(T &in: v) is >> in; return is; } template< typename T1, typename T2 > inline bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); } template< typename T1, typename T2 > inline bool chmin(T1 &a, T2 b) { return a > b && (a = b, true); } template< typename T = int64 > vector< T > make_v(size_t a) { return vector< T >(a); } template< typename T, typename... Ts > auto make_v(size_t a, Ts... ts) { return vector< decltype(make_v< T >(ts...)) >(a, make_v< T >(ts...)); } template< typename T, typename V > typename enable_if< is_class< T >::value == 0 >::type fill_v(T &t, const V &v) { t = v; } template< typename T, typename V > typename enable_if< is_class< T >::value != 0 >::type fill_v(T &t, const V &v) { for(auto &e: t) fill_v(e, v); } template< typename F > struct FixPoint : F { FixPoint(F &&f) : F(forward< F >(f)) {} template< typename... Args > decltype(auto) operator()(Args &&... args) const { return F::operator()(*this, forward< Args >(args)...); } }; template< typename F > inline decltype(auto) MFP(F &&f) { return FixPoint< F >{forward< F >(f)}; } #line 2 "graph/graph-template.hpp" #line 2 "graph/others/block-cut-tree.hpp" #line 2 "graph/graph-template.hpp" /** * @brief Graph Template(グラフテンプレート) */ template< typename T = int > struct Edge { int from, to; T cost; int idx; Edge() = default; Edge(int from, int to, T cost = 1, int idx = -1) : from(from), to(to), cost(cost), idx(idx) {} operator int() const { return to; } }; template< typename T = int > struct Graph { vector< vector< Edge< T > > > g; int es; Graph() = default; explicit Graph(int n) : g(n), es(0) {} size_t size() const { return g.size(); } void add_directed_edge(int from, int to, T cost = 1) { g[from].emplace_back(from, to, cost, es++); } void add_edge(int from, int to, T cost = 1) { g[from].emplace_back(from, to, cost, es); g[to].emplace_back(to, from, cost, es++); } void read(int M, int padding = -1, bool weighted = false, bool directed = false) { for(int i = 0; i < M; i++) { int a, b; cin >> a >> b; a += padding; b += padding; T c = T(1); if(weighted) cin >> c; if(directed) add_directed_edge(a, b, c); else add_edge(a, b, c); } } inline vector< Edge< T > > &operator[](const int &k) { return g[k]; } inline const vector< Edge< T > > &operator[](const int &k) const { return g[k]; } }; template< typename T = int > using Edges = vector< Edge< T > >; #line 2 "graph/others/low-link.hpp" #line 4 "graph/others/low-link.hpp" /** * @brief Low Link(橋/関節点) * @see http://kagamiz.hatenablog.com/entry/2013/10/05/005213 * @docs docs/low-link.md */ template< typename T = int > struct LowLink : Graph< T > { public: using Graph< T >::Graph; vector< int > ord, low, articulation; vector< Edge< T > > bridge; using Graph< T >::g; 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 < (int) g.size(); i++) { if(!used[i]) { k = dfs(i, k, -1); if(g[i].size() == 1) articulation.emplace_back(i); } } } explicit LowLink(const Graph< T > &g) : Graph< T >(g) {} private: vector< int > used; int dfs(int idx, int k, int par) { used[idx] = true; ord[idx] = k++; low[idx] = ord[idx]; bool is_articulation = false, beet = false; int cnt = 0; bool flag = true; for(auto &to: g[idx]) { if(to == par && !exchange(beet, true)) { continue; } flag = false; if(!used[to]) { ++cnt; k = dfs(to, k, idx); low[idx] = min(low[idx], low[to]); is_articulation |= par >= 0 && low[to] >= ord[idx]; if(ord[idx] < low[to]) bridge.emplace_back(to); } else { low[idx] = min(low[idx], ord[to]); } } is_articulation |= par == -1 && cnt > 1; if(is_articulation or flag) articulation.push_back(idx); return k; } }; #line 3 "graph/connected-components/bi-connected-components.hpp" /** * @brief Bi Connected Components(二重頂点連結成分分解) * @docs docs/bi-connected-components.md */ template< typename T = int > struct BiConnectedComponents : LowLink< T > { public: using LowLink< T >::LowLink; using LowLink< T >::g; using LowLink< T >::ord; using LowLink< T >::low; vector< vector< Edge< T > > > bc; void build() override { LowLink< T >::build(); used.assign(g.size(), 0); for(int i = 0; i < (int) used.size(); i++) { if(!used[i]) dfs(i, -1); } } explicit BiConnectedComponents(const Graph< T > &g) : Graph< T >(g) {} private: vector< int > used; vector< Edge< T > > tmp; void dfs(int idx, int par) { used[idx] = true; bool beet = false; for(auto &to: g[idx]) { if(to == par && !exchange(beet, true)) continue; if(!used[to] || ord[to] < ord[idx]) { tmp.emplace_back(to); } if(!used[to]) { dfs(to, idx); if(low[to] >= ord[idx]) { bc.emplace_back(); for(;;) { auto e = tmp.back(); bc.back().emplace_back(e); tmp.pop_back(); if(e.idx == to.idx) break; } } } } } }; #line 5 "graph/others/block-cut-tree.hpp" /** * @brief Block Cut Tree * @see https://ei1333.hateblo.jp/entry/2020/03/25/010057 */ template< typename T = int > struct BlockCutTree : BiConnectedComponents< T > { public: using BiConnectedComponents< T >::BiConnectedComponents; using BiConnectedComponents< T >::g; using BiConnectedComponents< T >::articulation; using BiConnectedComponents< T >::bc; vector< int > rev; vector< vector< int > > group; Graph< T > tree; explicit BlockCutTree(const Graph< T > &g) : Graph< T >(g) {} int operator[](const int &k) const { return rev[k]; } void build() override { BiConnectedComponents< T >::build(); rev.assign(g.size(), -1); int ptr = (int) bc.size(); for(auto &idx: articulation) { rev[idx] = ptr++; } vector< int > last(ptr, -1); tree = Graph< T >(ptr); for(int i = 0; i < (int) bc.size(); i++) { for(auto &e: bc[i]) { for(auto &ver: {e.from, e.to}) { if(rev[ver] >= (int) bc.size()) { if(exchange(last[rev[ver]], i) != i) { tree.add_edge(rev[ver], i, e.cost); } } else { rev[ver] = i; } } } } group.resize(ptr); for(int i = 0; i < (int) g.size(); i++) { group[rev[i]].emplace_back(i); } } }; /** * @brief Union-Find * @docs docs/union-find.md */ struct UnionFind { vector< int > data; UnionFind() = default; explicit UnionFind(size_t sz) : data(sz, -1) {} bool unite(int x, int y) { x = find(x), y = find(y); if(x == y) return false; if(data[x] > data[y]) swap(x, y); data[x] += data[y]; data[y] = x; return true; } int find(int k) { if(data[k] < 0) return (k); return data[k] = find(data[k]); } int size(int k) { return -data[find(k)]; } bool same(int x, int y) { return find(x) == find(y); } vector< vector< int > > groups() { int n = (int) data.size(); vector< vector< int > > ret(n); for(int i = 0; i < n; i++) { ret[find(i)].emplace_back(i); } ret.erase(remove_if(begin(ret), end(ret), [&](const vector< int > &v) { return v.empty(); })); return ret; } }; int main() { int N, M, Q; cin >> N >> M >> Q; vector< int > X(M), Y(M); vector< int > T(N); for(int i = 0; i < M; i++) { cin >> X[i] >> Y[i]; --X[i], --Y[i]; T[X[i]] = 1; T[Y[i]] = 1; } vector< int > conv(N, -1); int R = 0; for(int i = 0; i < N; i++) { if(T[i]) { conv[i] = R++; } } BlockCutTree<> g(R); for(int i = 0; i < M; i++) { X[i] = conv[X[i]]; Y[i] = conv[Y[i]]; g.add_edge(X[i], Y[i]); } g.build(); vector< int > ans(Q); UnionFind uf(g.tree.size()); for(int i = g.bc.size(); i < g.tree.size(); i++) { if(i >= g.bc.size()) { for(auto &j: g.tree[i]) { if(g.group[j].empty()) { for(auto &k: g.tree[j]) { uf.unite(i, k); } } } } } for(int i = 0; i < Q; i++) { int x, y; cin >> x >> y; --x, --y; if(~conv[x] and ~conv[y]) { x = conv[x]; y = conv[y]; x = g[x]; y = g[y]; ans[i] = uf.same(x, y); } } for(auto &p: ans) { if(p) cout << "Yes\n"; else cout << "No\n"; } }