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#include "graph/find_odd_cycle.hpp"
#include "graph/strongly_connected_component.hpp" // (vs, es), size=(n+1,n) // https://yukicoder.me/problems/no/1436 template <typename GT> pair<vc<int>, vc<int>> find_odd_cycle(GT& G) { int N = G.N; vc<int> comp(N); if constexpr (GT::is_directed) { comp = strongly_connected_component<GT>(G).se; } vc<int> dist(2 * N, infty<int>); vc<int> par(2 * N, -1); // edge index deque<int> que; auto add = [&](int v, int d, int p) -> void { if (chmin(dist[v], d)) { que.eb(v), par[v] = p; } }; FOR(root, N) { if (dist[2 * root + 0] < infty<int>) continue; if (dist[2 * root + 1] < infty<int>) continue; add(2 * root, 0, -1); while (len(que)) { auto v = POP(que); auto [a, b] = divmod(v, 2); for (auto&& e: G[a]) { if (comp[e.frm] != comp[e.to]) continue; int w = 2 * e.to + (b ^ 1); add(w, dist[v] + 1, e.id); } } if (dist[2 * root + 1] == infty<int>) continue; // found vc<int> edges; vc<int> vs; vs.eb(root); int v = 2 * root + 1; while (par[v] != -1) { int i = par[v]; edges.eb(i); auto& e = G.edges[i]; v = 2 * (e.frm + e.to) + 1 - v; vs.eb(v / 2); } reverse(all(edges)); reverse(all(vs)); // walk -> cycle vc<int> used(N, -1); int l = -1, r = -1; FOR(i, len(vs)) { if (used[vs[i]] == -1) { used[vs[i]] = i; continue; } l = used[vs[i]]; r = i; break; } assert(l != -1); vs = {vs.begin() + l, vs.begin() + r}; edges = {edges.begin() + l, edges.begin() + r}; vs.eb(vs[0]); return {vs, edges}; } return {}; }
#line 2 "graph/base.hpp" template <typename T> struct Edge { int frm, to; T cost; int id; }; template <typename T = int, bool directed = false> struct Graph { static constexpr bool is_directed = directed; int N, M; using cost_type = T; using edge_type = Edge<T>; vector<edge_type> edges; vector<int> indptr; vector<edge_type> csr_edges; vc<int> vc_deg, vc_indeg, vc_outdeg; bool prepared; class OutgoingEdges { public: OutgoingEdges(const Graph* G, int l, int r) : G(G), l(l), r(r) {} const edge_type* begin() const { if (l == r) { return 0; } return &G->csr_edges[l]; } const edge_type* end() const { if (l == r) { return 0; } return &G->csr_edges[r]; } private: const Graph* G; int l, r; }; bool is_prepared() { return prepared; } Graph() : N(0), M(0), prepared(0) {} Graph(int N) : N(N), M(0), prepared(0) {} void build(int n) { N = n, M = 0; prepared = 0; edges.clear(); indptr.clear(); csr_edges.clear(); vc_deg.clear(); vc_indeg.clear(); vc_outdeg.clear(); } void add(int frm, int to, T cost = 1, int i = -1) { assert(!prepared); assert(0 <= frm && 0 <= to && to < N); if (i == -1) i = M; auto e = edge_type({frm, to, cost, i}); edges.eb(e); ++M; } #ifdef FASTIO // wt, off void read_tree(bool wt = false, int off = 1) { read_graph(N - 1, wt, off); } void read_graph(int M, bool wt = false, int off = 1) { for (int m = 0; m < M; ++m) { INT(a, b); a -= off, b -= off; if (!wt) { add(a, b); } else { T c; read(c); add(a, b, c); } } build(); } #endif void build() { assert(!prepared); prepared = true; indptr.assign(N + 1, 0); for (auto&& e: edges) { indptr[e.frm + 1]++; if (!directed) indptr[e.to + 1]++; } for (int v = 0; v < N; ++v) { indptr[v + 1] += indptr[v]; } auto counter = indptr; csr_edges.resize(indptr.back() + 1); for (auto&& e: edges) { csr_edges[counter[e.frm]++] = e; if (!directed) csr_edges[counter[e.to]++] = edge_type({e.to, e.frm, e.cost, e.id}); } } OutgoingEdges operator[](int v) const { assert(prepared); return {this, indptr[v], indptr[v + 1]}; } vc<int> deg_array() { if (vc_deg.empty()) calc_deg(); return vc_deg; } pair<vc<int>, vc<int>> deg_array_inout() { if (vc_indeg.empty()) calc_deg_inout(); return {vc_indeg, vc_outdeg}; } int deg(int v) { if (vc_deg.empty()) calc_deg(); return vc_deg[v]; } int in_deg(int v) { if (vc_indeg.empty()) calc_deg_inout(); return vc_indeg[v]; } int out_deg(int v) { if (vc_outdeg.empty()) calc_deg_inout(); return vc_outdeg[v]; } #ifdef FASTIO void debug() { print("Graph"); if (!prepared) { print("frm to cost id"); for (auto&& e: edges) print(e.frm, e.to, e.cost, e.id); } else { print("indptr", indptr); print("frm to cost id"); FOR(v, N) for (auto&& e: (*this)[v]) print(e.frm, e.to, e.cost, e.id); } } #endif vc<int> new_idx; vc<bool> used_e; // G における頂点 V[i] が、新しいグラフで i になるようにする // {G, es} // sum(deg(v)) の計算量になっていて、 // 新しいグラフの n+m より大きい可能性があるので注意 Graph<T, directed> rearrange(vc<int> V, bool keep_eid = 0) { if (len(new_idx) != N) new_idx.assign(N, -1); int n = len(V); FOR(i, n) new_idx[V[i]] = i; Graph<T, directed> G(n); vc<int> history; FOR(i, n) { for (auto&& e: (*this)[V[i]]) { if (len(used_e) <= e.id) used_e.resize(e.id + 1); if (used_e[e.id]) continue; int a = e.frm, b = e.to; if (new_idx[a] != -1 && new_idx[b] != -1) { history.eb(e.id); used_e[e.id] = 1; int eid = (keep_eid ? e.id : -1); G.add(new_idx[a], new_idx[b], e.cost, eid); } } } FOR(i, n) new_idx[V[i]] = -1; for (auto&& eid: history) used_e[eid] = 0; G.build(); return G; } Graph<T, true> to_directed_tree(int root = -1) { if (root == -1) root = 0; assert(!is_directed && prepared && M == N - 1); Graph<T, true> G1(N); vc<int> par(N, -1); auto dfs = [&](auto& dfs, int v) -> void { for (auto& e: (*this)[v]) { if (e.to == par[v]) continue; par[e.to] = v, dfs(dfs, e.to); } }; dfs(dfs, root); for (auto& e: edges) { int a = e.frm, b = e.to; if (par[a] == b) swap(a, b); assert(par[b] == a); G1.add(a, b, e.cost); } G1.build(); return G1; } private: void calc_deg() { assert(vc_deg.empty()); vc_deg.resize(N); for (auto&& e: edges) vc_deg[e.frm]++, vc_deg[e.to]++; } void calc_deg_inout() { assert(vc_indeg.empty()); vc_indeg.resize(N); vc_outdeg.resize(N); for (auto&& e: edges) { vc_indeg[e.to]++, vc_outdeg[e.frm]++; } } }; #line 3 "graph/strongly_connected_component.hpp" template <typename GT> pair<int, vc<int>> strongly_connected_component(GT& G) { static_assert(GT::is_directed); assert(G.is_prepared()); int N = G.N; int C = 0; vc<int> comp(N), low(N), ord(N, -1), path; int now = 0; auto dfs = [&](auto& dfs, int v) -> void { low[v] = ord[v] = now++; path.eb(v); for (auto&& [frm, to, cost, id]: G[v]) { if (ord[to] == -1) { dfs(dfs, to), chmin(low[v], low[to]); } else { chmin(low[v], ord[to]); } } if (low[v] == ord[v]) { while (1) { int u = POP(path); ord[u] = N, comp[u] = C; if (u == v) break; } ++C; } }; FOR(v, N) { if (ord[v] == -1) dfs(dfs, v); } FOR(v, N) comp[v] = C - 1 - comp[v]; return {C, comp}; } template <typename GT> Graph<int, 1> scc_dag(GT& G, int C, vc<int>& comp) { Graph<int, 1> DAG(C); vvc<int> edges(C); for (auto&& e: G.edges) { int x = comp[e.frm], y = comp[e.to]; if (x == y) continue; edges[x].eb(y); } FOR(c, C) { UNIQUE(edges[c]); for (auto&& to: edges[c]) DAG.add(c, to); } DAG.build(); return DAG; } #line 2 "graph/find_odd_cycle.hpp" // (vs, es), size=(n+1,n) // https://yukicoder.me/problems/no/1436 template <typename GT> pair<vc<int>, vc<int>> find_odd_cycle(GT& G) { int N = G.N; vc<int> comp(N); if constexpr (GT::is_directed) { comp = strongly_connected_component<GT>(G).se; } vc<int> dist(2 * N, infty<int>); vc<int> par(2 * N, -1); // edge index deque<int> que; auto add = [&](int v, int d, int p) -> void { if (chmin(dist[v], d)) { que.eb(v), par[v] = p; } }; FOR(root, N) { if (dist[2 * root + 0] < infty<int>) continue; if (dist[2 * root + 1] < infty<int>) continue; add(2 * root, 0, -1); while (len(que)) { auto v = POP(que); auto [a, b] = divmod(v, 2); for (auto&& e: G[a]) { if (comp[e.frm] != comp[e.to]) continue; int w = 2 * e.to + (b ^ 1); add(w, dist[v] + 1, e.id); } } if (dist[2 * root + 1] == infty<int>) continue; // found vc<int> edges; vc<int> vs; vs.eb(root); int v = 2 * root + 1; while (par[v] != -1) { int i = par[v]; edges.eb(i); auto& e = G.edges[i]; v = 2 * (e.frm + e.to) + 1 - v; vs.eb(v / 2); } reverse(all(edges)); reverse(all(vs)); // walk -> cycle vc<int> used(N, -1); int l = -1, r = -1; FOR(i, len(vs)) { if (used[vs[i]] == -1) { used[vs[i]] = i; continue; } l = used[vs[i]]; r = i; break; } assert(l != -1); vs = {vs.begin() + l, vs.begin() + r}; edges = {edges.begin() + l, edges.begin() + r}; vs.eb(vs[0]); return {vs, edges}; } return {}; }