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#define PROBLEM "https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=GRL_3_A" #include <bits/stdc++.h> #include "graph/read_graph.hpp" #include "graph/low_link.hpp" int main() { int N, M; std::cin >> N >> M; auto G = read_graph<int>(N, M, 0, 0, 0); LowLink llink(G); auto ans = llink.articulations; std::sort(ans.begin(), ans.end()); for (auto& v : ans) std::cout << v << '\n'; return 0; }
#line 1 "verify/aoj_grl/aoj_grl_3_a.test.cpp" #define PROBLEM "https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=GRL_3_A" #include <bits/stdc++.h> #line 2 "graph/read_graph.hpp" #line 2 "graph/graph_template.hpp" #line 4 "graph/graph_template.hpp" template <class T> struct Edge { int from, to; T cost; int id; Edge() = default; Edge(int from, int to, T cost = 1, int id = -1) : from(from), to(to), cost(cost), id(id) {} friend std::ostream &operator<<(std::ostream &os, const Edge<T> &e) { // output format: "{ id : from -> to, cost }" return os << "{ " << e.id << " : " << e.from << " -> " << e.to << ", " << e.cost << " }"; } }; template <class T> using Edges = std::vector<Edge<T>>; template <class T> using Graph = std::vector<std::vector<Edge<T>>>; #line 4 "graph/read_graph.hpp" template <class T> Graph<T> read_graph(const int n, const int m, const bool weight = false, const bool directed = false, const int offset = 1) { Graph<T> g(n); for (int i = 0; i < m; i++) { int a, b; std::cin >> a >> b; a -= offset, b -= offset; if (weight) { T c; std::cin >> c; if (!directed) g[b].push_back(Edge(b, a, c, i)); g[a].push_back(Edge(a, b, c, i)); } else { // c = 1 if (!directed) g[b].push_back(Edge(b, a, T(1), i)); g[a].push_back(Edge(a, b, T(1), i)); } } return g; } template <class T> Graph<T> read_parent(const int n, const bool weight = false, const bool directed = false, const int offset = 1) { Graph<T> g(n); for (int i = 1; i < n; i++) { int p; std::cin >> p; p -= offset; if (weight) { T c; std::cin >> c; if (!directed) g[i].push_back(Edge(i, p, c, i - 1)); g[p].push_back(Edge(p, i, c, i - 1)); } else { // c = 1 if (!directed) g[i].push_back(Edge(i, p, T(1), i - 1)); g[p].push_back(Edge(p, i, T(1), i - 1)); } } return g; } std::tuple<Graph<int>, std::vector<std::vector<int>>, std::vector<std::pair<int, int>>> read_grid(const int h, const int w, std::string rel = ".#") { std::vector<std::string> s(h); std::vector id(h, std::vector<int>(w, -1)); std::vector<std::pair<int, int>> loc; int n = 0; for (int i = 0; i < h; i++) { std::cin >> s[i]; for (int j = 0; j < w; j++) { if (s[i][j] == rel[1]) { id[i][j] = n++; loc.emplace_back(i, j); } } } int m = 0; Graph<int> g(n); for (int i = 0; i < h; i++) { for (int j = 0; j < w; j++) { if (s[i][j] == rel[1]) { if (i + 1 < h and s[i + 1][j] == rel[1]) { g[id[i][j]].push_back(Edge(id[i][j], id[i + 1][j], 1, m)); g[id[i + 1][j]].push_back(Edge(id[i + 1][j], id[i][j], 1, m++)); } if (j + 1 < w and s[i][j + 1] == rel[1]) { g[id[i][j]].push_back(Edge(id[i][j], id[i][j + 1], 1, m)); g[id[i][j + 1]].push_back(Edge(id[i][j + 1], id[i][j], 1, m++)); } } } } return {g, id, loc}; } #line 2 "graph/low_link.hpp" #line 4 "graph/low_link.hpp" template <class T> struct LowLink { int n; std::vector<int> ord, low; std::vector<int> articulations; std::vector<int> roots; std::vector<std::pair<int, int>> bridges; // edges {u, v} (u < v) std::vector<std::vector<int>> dfs_tree; LowLink(const Graph<T>& g) : n(int(g.size())) { ord.assign(n, -1); low.assign(n, -1); dfs_tree.resize(n); int ord_id = 0; auto dfs = [&](auto f, int cur, int par) -> void { low[cur] = ord[cur] = ord_id++; bool is_articulation = false; for (auto& e : g[cur]) { if (ord[e.to] == -1) { // DFS 木上の辺に対する処理 f(f, e.to, cur); dfs_tree[cur].push_back(e.to); // e が DFS 木に含まれているので後退辺をすでに通った low[e.to] を使って更新して良い low[cur] = std::min(low[cur], low[e.to]); is_articulation |= (par != -1) and (ord[cur] <= low[e.to]); if (ord[cur] < low[e.to]) { bridges.emplace_back(std::minmax(cur, e.to)); } } else if (e.to != par) { // 後退辺に対する処理 // Todo: multiple edges low[cur] = std::min(low[cur], ord[e.to]); } } is_articulation |= par == -1 and int(dfs_tree[cur].size()) > 1; if (is_articulation) articulations.push_back(cur); return; }; for (int i = 0; i < n; i++) { if (ord[i] == -1) { roots.push_back(i); dfs(dfs, i, -1); } } } // 連結成分数 int count_components() { return int(roots.size()); } // 頂点 x を取り除くともともと 1 つだった連結成分がいくつになるか int count_components_remove(int x) { if (std::binary_search(roots.begin(), roots.end(), x)) { int c = int(dfs_tree[x].size()); return c; } else { int c = 0; for (auto& e : dfs_tree[x]) { if (ord[x] <= low[e]) c++; } // 親の分で +1 return c + 1; } } }; #line 7 "verify/aoj_grl/aoj_grl_3_a.test.cpp" int main() { int N, M; std::cin >> N >> M; auto G = read_graph<int>(N, M, 0, 0, 0); LowLink llink(G); auto ans = llink.articulations; std::sort(ans.begin(), ans.end()); for (auto& v : ans) std::cout << v << '\n'; return 0; }