#include "graph/two-edge-connected-components.hpp"
#pragma once #include "./graph-template.hpp" #include "./lowlink.hpp" template <typename G> struct TwoEdgeConnectedComponents { const G &g; LowLink<G> low; vector<int> comp; int k; vector<vector<int>> groups, tree; TwoEdgeConnectedComponents(const G &g_) : g(g_), low(g_), comp(g_.size(), -1), k(0) { for (int i = 0; i < (int)g.size(); i++) { if (comp[i] == -1) dfs(i, -1); } groups.resize(k); tree.resize(k); for (int i = 0; i < (int)g.size(); i++) { groups[comp[i]].push_back(i); } for (auto &e : low.bridge) { int u = comp[e.first], v = comp[e.second]; tree[u].push_back(v); } }; int operator[](const int &k) const { return comp[k]; } void dfs(int i, int p) { if (p >= 0 && low.ord[p] >= low.low[i]) comp[i] = comp[p]; else comp[i] = k++; for (auto &d : g[i]) { if (comp[d] == -1) dfs(d, i); } } };
#line 2 "graph/two-edge-connected-components.hpp" #line 2 "graph/graph-template.hpp" template <typename T> struct edge { int src, to; T cost; edge(int _to, T _cost) : src(-1), to(_to), cost(_cost) {} edge(int _src, int _to, T _cost) : src(_src), to(_to), cost(_cost) {} edge &operator=(const int &x) { to = x; return *this; } operator int() const { return to; } }; template <typename T> using Edges = vector<edge<T>>; template <typename T> using WeightedGraph = vector<Edges<T>>; using UnweightedGraph = vector<vector<int>>; // Input of (Unweighted) Graph UnweightedGraph graph(int N, int M = -1, bool is_directed = false, bool is_1origin = true) { UnweightedGraph g(N); if (M == -1) M = N - 1; for (int _ = 0; _ < M; _++) { int x, y; cin >> x >> y; if (is_1origin) x--, y--; g[x].push_back(y); if (!is_directed) g[y].push_back(x); } return g; } // Input of Weighted Graph template <typename T> WeightedGraph<T> wgraph(int N, int M = -1, bool is_directed = false, bool is_1origin = true) { WeightedGraph<T> g(N); if (M == -1) M = N - 1; for (int _ = 0; _ < M; _++) { int x, y; cin >> x >> y; T c; cin >> c; if (is_1origin) x--, y--; g[x].emplace_back(x, y, c); if (!is_directed) g[y].emplace_back(y, x, c); } return g; } // Input of Edges template <typename T> Edges<T> esgraph(int N, int M, int is_weighted = true, bool is_1origin = true) { Edges<T> es; for (int _ = 0; _ < M; _++) { int x, y; cin >> x >> y; T c; if (is_weighted) cin >> c; else c = 1; if (is_1origin) x--, y--; es.emplace_back(x, y, c); } return es; } // Input of Adjacency Matrix template <typename T> vector<vector<T>> adjgraph(int N, int M, T INF, int is_weighted = true, bool is_directed = false, bool is_1origin = true) { vector<vector<T>> d(N, vector<T>(N, INF)); for (int _ = 0; _ < M; _++) { int x, y; cin >> x >> y; T c; if (is_weighted) cin >> c; else c = 1; if (is_1origin) x--, y--; d[x][y] = c; if (!is_directed) d[y][x] = c; } return d; } /** * @brief グラフテンプレート * @docs docs/graph/graph-template.md */ #line 2 "graph/lowlink.hpp" #include <vector> using namespace std; #line 7 "graph/lowlink.hpp" // bridge ... 橋 (辺 (u, v) が u < v となるように格納) // articulation point ... 関節点 template <typename G> struct LowLink { const G &g; int N; vector<int> ord, low, articulation; vector<pair<int, int> > bridge; LowLink(const G &_g) : g(_g), N(g.size()), ord(N, -1), low(N, -1) { for (int i = 0, k = 0; i < N; i++) { if (ord[i] == -1) { k = dfs(i, k, -1); } } } int dfs(int idx, int k, int par) { low[idx] = (ord[idx] = k++); int cnt = 0; bool arti = false, second = false; for (auto &to : g[idx]) { if (ord[to] == -1) { cnt++; k = dfs(to, k, idx); low[idx] = min(low[idx], low[to]); arti |= (par != -1) && (low[to] >= ord[idx]); if (ord[idx] < low[to]) { bridge.emplace_back(minmax(idx, (int)to)); } } else if (to != par || second) { low[idx] = min(low[idx], ord[to]); } else { second = true; } } arti |= par == -1 && cnt > 1; if (arti) articulation.push_back(idx); return k; } }; #line 5 "graph/two-edge-connected-components.hpp" template <typename G> struct TwoEdgeConnectedComponents { const G &g; LowLink<G> low; vector<int> comp; int k; vector<vector<int>> groups, tree; TwoEdgeConnectedComponents(const G &g_) : g(g_), low(g_), comp(g_.size(), -1), k(0) { for (int i = 0; i < (int)g.size(); i++) { if (comp[i] == -1) dfs(i, -1); } groups.resize(k); tree.resize(k); for (int i = 0; i < (int)g.size(); i++) { groups[comp[i]].push_back(i); } for (auto &e : low.bridge) { int u = comp[e.first], v = comp[e.second]; tree[u].push_back(v); } }; int operator[](const int &k) const { return comp[k]; } void dfs(int i, int p) { if (p >= 0 && low.ord[p] >= low.low[i]) comp[i] = comp[p]; else comp[i] = k++; for (auto &d : g[i]) { if (comp[d] == -1) dfs(d, i); } } };