This documentation is automatically generated by online-judge-tools/verification-helper
View the Project on GitHub ei1333/library
#define PROBLEM "https://judge.yosupo.jp/problem/three_edge_connected_components" #include "../../template/template.hpp" #include "../../graph/connected-components/three-edge-connected-components.hpp" int main() { int N, M; cin >> N >> M; ThreeEdgeConnectedComponents<> g(N); g.read(M, 0); g.build(); cout << g.group.size() << "\n"; for(auto &p : g.group) { cout << p.size() << " " << p << "\n"; } }
#line 1 "test/verify/yosupo-three-edge-connected-components.test.cpp" #define PROBLEM "https://judge.yosupo.jp/problem/three_edge_connected_components" #line 1 "template/template.hpp" #include<bits/stdc++.h> using namespace std; using int64 = long long; const int mod = 1e9 + 7; 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 { explicit 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 4 "test/verify/yosupo-three-edge-connected-components.test.cpp" #line 2 "graph/connected-components/three-edge-connected-components.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/connected-components/incremental-bridge-connectivity.hpp" #line 2 "structure/union-find/union-find.hpp" 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(); }), end(ret)); return ret; } }; #line 4 "graph/connected-components/incremental-bridge-connectivity.hpp" struct IncrementalBridgeConnectivity { private: UnionFind cc, bcc; vector< int > bbf; size_t bridge; int size() { return bbf.size(); } int par(int x) { return bbf[x] == size() ? size() : bcc.find(bbf[x]); } int lca(int x, int y) { unordered_set< int > used; for(;;) { if(x != size()) { if(!used.insert(x).second) return x; x = par(x); } swap(x, y); } } void compress(int x, int y) { while(bcc.find(x) != bcc.find(y)) { int nxt = par(x); bbf[x] = bbf[y]; bcc.unite(x, y); x = nxt; --bridge; } } void link(int x, int y) { int v = x, pre = y; while(v != size()) { int nxt = par(v); bbf[v] = pre; pre = v; v = nxt; } } public: IncrementalBridgeConnectivity() = default; explicit IncrementalBridgeConnectivity(int sz) : cc(sz), bcc(sz), bbf(sz, sz), bridge(0) {} int find(int k) { return bcc.find(k); } size_t bridge_size() const { return bridge; } void add_edge(int x, int y) { x = bcc.find(x); y = bcc.find(y); if(cc.find(x) == cc.find(y)) { int w = lca(x, y); compress(x, w); compress(y, w); } else { if(cc.size(x) > cc.size(y)) swap(x, y); link(x, y); cc.unite(x, y); ++bridge; } } }; #line 5 "graph/connected-components/three-edge-connected-components.hpp" template< typename T = int > struct ThreeEdgeConnectedComponents : Graph< T > { public: using Graph< T >::Graph; using Graph< T >::g; vector< vector< int > > group; void build() { uf = UnionFind(g.size()); bcc = IncrementalBridgeConnectivity(g.size()); used.assign(g.size(), 0); in.assign(g.size(), 0); out.assign(g.size(), 0); deg.assign(g.size(), 0); low.assign(g.size(), g.size()); for(size_t from = 0; from < g.size(); from++) { for(auto &to : g[from]) { if((T)from < to) bcc.add_edge(from, to); } } int cnt = 0; for(size_t i = 0; i < g.size(); i++) { if(used[i]) continue; vector< int > tmp; dfs(i, -1, tmp, cnt); cnt++; } vector< int > id(g.size(), -1); cnt = 0; for(size_t i = 0; i < g.size(); i++) { if(id[uf.find(i)] == -1) id[uf.find(i)] = cnt++; } group.resize(cnt); for(size_t i = 0; i < g.size(); i++) { group[id[uf.find(i)]].emplace_back(i); } } int operator[](const int &k) { return uf.find(k); } private: vector< int > used; vector< int > in, out, low, deg; IncrementalBridgeConnectivity bcc; UnionFind uf; void absorb(vector< int > &path, int v, int w = -1) { while(!path.empty()) { int x = path.back(); if(w != -1 && (in[x] > in[w] or in[w] >= out[x])) break; path.pop_back(); uf.unite(v, x); deg[v] += deg[x] - 2; } } void dfs(int idx, int p, vector< int > &path, int &k) { used[idx] = 1; in[idx] = low[idx] = k++; for(auto &to : g[idx]) { if(idx == to || bcc.find(idx) != bcc.find(to)) continue; deg[idx]++; if(to == p) { p = -1; continue; } if(used[to]) { if(in[idx] > in[to]) { if(in[to] < low[idx]) { low[idx] = in[to]; absorb(path, idx); } } else { deg[idx] -= 2; absorb(path, idx, to); } } else { vector< int > ps; dfs(to, idx, ps, k); if(deg[to] == 2) ps.pop_back(); if(low[to] < low[idx]) { low[idx] = low[to]; absorb(path, idx); path = ps; } else { absorb(ps, idx); } } } out[idx] = k; path.push_back(idx); } }; #line 6 "test/verify/yosupo-three-edge-connected-components.test.cpp" int main() { int N, M; cin >> N >> M; ThreeEdgeConnectedComponents<> g(N); g.read(M, 0); g.build(); cout << g.group.size() << "\n"; for(auto &p : g.group) { cout << p.size() << " " << p << "\n"; } }