#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #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) { return m < q ? (m = q, true) : false; } template bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; } int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); } 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 sort_unique(vector vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; } template int arglb(const std::vector &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); } template int argub(const std::vector &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); } 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; } template ostream &operator<<(ostream &os, const array &arr) { os << '['; for (auto v : arr) 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) { os << '('; 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 const string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m"; #define dbg(x) cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl #define dbgif(cond, x) ((cond) ? cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl : cerr) #else #define dbg(x) 0 #define dbgif(cond, x) 0 #endif #include #include #include #include #include struct lowlink { 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 lowlink(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) continue; 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 (e == nxt.second) break; } tvcc_num++; } } } } void build() { for (int v = 0; v < V; ++v) { if (order[v] < 0) dfs_lowlink(v); } // Find all bridges // Complexity: O(V + E) for (int i = 0; i < E; i++) { int v1 = edges[i].first, v2 = edges[i].second; if (order[v1] > order[v2]) std::swap(v1, v2); is_bridge[i] = order[v1] < lowlink_[v2]; } } // Find two-edge-connected components and classify all vertices // Complexity: O(V + E) std::vector> two_edge_connected_components() { build(); tecc_num = 0; tecc_id.assign(V, -1); std::vector st; for (int i = 0; i < V; i++) { if (tecc_id[i] != -1) continue; tecc_id[i] = tecc_num; st.push_back(i); while (!st.empty()) { int now = st.back(); st.pop_back(); 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; st.push_back(nxt); } } ++tecc_num; } std::vector> ret(tecc_num); for (int i = 0; i < V; ++i) ret[tecc_id[i]].push_back(i); return ret; } // Find biconnected components and classify all edges // Complexity: O(V + E) std::vector> biconnected_components() { build(); std::vector> ret(tvcc_num); for (int i = 0; i < E; ++i) ret[tvcc_id[i]].push_back(i); return ret; } }; #include #include #include #include // UnionFind Tree (0-indexed), based on size of each disjoint set struct UnionFind { std::vector par, cou; UnionFind(int N = 0) : par(N), cou(N, 1) { iota(par.begin(), par.end(), 0); } int find(int x) { return (par[x] == x) ? x : (par[x] = find(par[x])); } bool unite(int x, int y) { x = find(x), y = find(y); if (x == y) return false; if (cou[x] < cou[y]) std::swap(x, y); par[y] = x, cou[x] += cou[y]; return true; } int count(int x) { return cou[find(x)]; } bool same(int x, int y) { return find(x) == find(y); } std::vector> groups() { std::vector> ret(par.size()); for (int i = 0; i < int(par.size()); ++i) ret[find(i)].push_back(i); ret.erase(std::remove_if(ret.begin(), ret.end(), [&](const std::vector &v) { return v.empty(); }), ret.end()); return ret; } }; int main() { int N, M, Q; cin >> N >> M >> Q; vector edges(M); lowlink graph(N); for (auto &[s, t] : edges) { cin >> s >> t; --s, --t; graph.add_edge(s, t); } graph.build(); UnionFind uf(N); REP(e, M) { if (graph.is_bridge.at(e)) { auto [s, t] = edges[e]; uf.unite(s, t); } } while (Q--) { int x, y; cin >> x >> y; --x, --y; cout << (uf.same(x, y) ? "Yes" : "No") << '\n'; } }