#include //#include using namespace std; // using namespace atcoder; // using mint = modint1000000007; // const int mod = 1000000007; // using mint = modint998244353; // const int mod = 998244353; // const int INF = 1e9; // const long long LINF = 1e18; #define rep(i, n) for (int i = 0; i < (n); ++i) #define rep2(i, l, r) for (int i = (l); i < (r); ++i) #define rrep(i, n) for (int i = (n)-1; i >= 0; --i) #define rrep2(i, l, r) for (int i = (r)-1; i >= (l); --i) #define all(x) (x).begin(), (x).end() #define allR(x) (x).rbegin(), (x).rend() #define P pair template inline bool chmax(A& a, const B& b) { if (a < b) { a = b; return true; } return false; } template inline bool chmin(A& a, const B& b) { if (a > b) { a = b; return true; } return false; } #ifndef KWM_T_GRAPH_BIPARTITE_COLORING_HPP #define KWM_T_GRAPH_BIPARTITE_COLORING_HPP #include namespace kwm_t::graph::bipartite { /** * @brief 二部グラフ判定 + 2色塗り * * 典型用途: * - グラフが二部グラフか判定 * - 頂点を 0/1 に色分け * - 連結成分数の取得 * * 計算量: * - O(N + M) * * @param n 頂点数 * * 制約 / 注意: * - 無向グラフを想定 * * 使用例: * vector graph(n, vector()); * BipartiteColoring bc(n,graph); * auto col = bc.get_color; // 0 or 1 * * verified: * - https://atcoder.jp/contests/awc0071/submissions/75933094 */ class BipartiteColoring { public: explicit BipartiteColoring(int n, const std::vector>& graph) : n(n), graph(graph), color(n, -1), components(0) { execute(); } bool is_bipartite() const { return bipartite; } int get_components() const { return components; } int get_color(int i) const { return color[i]; } const std::vector& get_color() const { return color; } private: int n; bool bipartite; std::vector> graph; std::vector color; int components; bool dfs(int v) { bool ok = true; for (int nv : graph[v]) { if (color[nv] != -1) { if (color[nv] == color[v]) ok = false; } else { color[nv] = 1 - color[v]; if (!dfs(nv)) ok = false; } } return ok; } void execute() { bipartite = true; components = 0; for (int i = 0; i < n; ++i) { if (color[i] != -1) continue; color[i] = 0; components++; if (!dfs(i)) bipartite = false; } } }; } // namespace kwm_t::graph::bipartite #endif // KWM_T_GRAPH_BIPARTITE_COLORING_HPP int main() { std::ios::sync_with_stdio(false); std::cin.tie(nullptr); int n, m; cin >> n >> m; vector g(n, vector()); rep(i, m) { int a, b; cin >> a >> b; a--, b--; g[a].push_back(b); g[b].push_back(a); } kwm_t::graph::bipartite::BipartiteColoring bc(n, g); cout << (bc.is_bipartite() ? "Yes" : "No") << endl; return 0; }