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#include "graph/cycle_detection.hpp"
グラフを与えてサイクルを検出する。サイクルが存在する場合、サイクルの $1$ つを返す。 $O(N+M)$
#pragma once #include <algorithm> #include <optional> #include <utility> #include <vector> #include "../graph/base.hpp" namespace ebi { template <class T> std::optional<std::pair<std::vector<int>, std::vector<int>>> cycle_detection_directed(const Graph<T> &g) { int n = g.node_number(); std::vector<int> used(n, -1); std::vector<int> par_idx(n, -1); std::vector<int> vs, es; auto dfs = [&](auto &&self, int v) -> void { used[v] = 1; for (auto e : g[v]) { if (!es.empty()) return; if (used[e.to] == -1) { used[e.to] = 1; par_idx[e.to] = e.id; self(self, e.to); } else if (used[e.to] == 1) { int now = v; vs.emplace_back(now); es.emplace_back(e.id); while (now != e.to) { es.emplace_back(par_idx[now]); now = g.get_edge(par_idx[now]).from; } std::reverse(vs.begin(), vs.end()); std::reverse(es.begin(), es.end()); return; } } used[v] = 2; }; for (auto v : std::views::iota(0, n)) { if (used[v] != -1) continue; dfs(dfs, v); if (!es.empty()) { return std::pair<std::vector<int>, std::vector<int>>{vs, es}; } } return std::nullopt; } template <class T> std::optional<std::pair<std::vector<int>, std::vector<int>>> cycle_detection_undirected(const Graph<T> &g) { int n = g.node_number(); int m = g.edge_number(); std::vector<bool> used_edge(m, false); std::vector<int> depth(n, -1); std::vector<int> par_idx(n, -1); auto dfs = [&](auto &&self, int v) -> int { for (auto e : g[v]) { if (used_edge[e.id]) continue; if (depth[e.to] != -1) return e.id; used_edge[e.id] = true; par_idx[e.to] = e.id; depth[e.to] = depth[v] + 1; int x = self(self, e.to); if (x != -1) return x; } return -1; }; for (auto v : std::views::iota(0, n)) { if (depth[v] != -1) continue; depth[v] = 0; int id = dfs(dfs, v); if (id == -1) continue; int s = -1; { auto e = g.get_edge(id); if (depth[e.to] < depth[e.from]) s = e.to; else s = e.from; } std::vector<int> vs, es; vs.emplace_back(s), es.emplace_back(id); while (1) { auto e = g.get_edge(es.back()); int u = e.from ^ e.to ^ vs.back(); if (u == s) break; vs.emplace_back(u), es.emplace_back(par_idx[u]); } return std::pair<std::vector<int>, std::vector<int>>{vs, es}; } return std::nullopt; } } // namespace ebi
#line 2 "graph/cycle_detection.hpp" #include <algorithm> #include <optional> #include <utility> #include <vector> #line 2 "graph/base.hpp" #include <cassert> #include <iostream> #include <ranges> #line 7 "graph/base.hpp" #line 2 "data_structure/simple_csr.hpp" #line 6 "data_structure/simple_csr.hpp" namespace ebi { template <class E> struct simple_csr { simple_csr() = default; simple_csr(int n, const std::vector<std::pair<int, E>>& elements) : start(n + 1, 0), elist(elements.size()) { for (auto e : elements) { start[e.first + 1]++; } for (auto i : std::views::iota(0, n)) { start[i + 1] += start[i]; } auto counter = start; for (auto [i, e] : elements) { elist[counter[i]++] = e; } } simple_csr(const std::vector<std::vector<E>>& es) : start(es.size() + 1, 0) { int n = es.size(); for (auto i : std::views::iota(0, n)) { start[i + 1] = (int)es[i].size() + start[i]; } elist.resize(start.back()); for (auto i : std::views::iota(0, n)) { std::copy(es[i].begin(), es[i].end(), elist.begin() + start[i]); } } int size() const { return (int)start.size() - 1; } const auto operator[](int i) const { return std::ranges::subrange(elist.begin() + start[i], elist.begin() + start[i + 1]); } auto operator[](int i) { return std::ranges::subrange(elist.begin() + start[i], elist.begin() + start[i + 1]); } const auto operator()(int i, int l, int r) const { return std::ranges::subrange(elist.begin() + start[i] + l, elist.begin() + start[i + 1] + r); } auto operator()(int i, int l, int r) { return std::ranges::subrange(elist.begin() + start[i] + l, elist.begin() + start[i + 1] + r); } private: std::vector<int> start; std::vector<E> elist; }; } // namespace ebi #line 9 "graph/base.hpp" namespace ebi { template <class T> struct Edge { int from, to; T cost; int id; }; template <class E> struct Graph { using cost_type = E; using edge_type = Edge<cost_type>; Graph(int n_) : n(n_) {} Graph() = default; void add_edge(int u, int v, cost_type c) { buff.emplace_back(u, edge_type{u, v, c, m}); edges.emplace_back(edge_type{u, v, c, m++}); } void add_undirected_edge(int u, int v, cost_type c) { buff.emplace_back(u, edge_type{u, v, c, m}); buff.emplace_back(v, edge_type{v, u, c, m}); edges.emplace_back(edge_type{u, v, c, m}); m++; } void read_tree(int offset = 1, bool is_weighted = false) { read_graph(n - 1, offset, false, is_weighted); } void read_parents(int offset = 1) { for (auto i : std::views::iota(1, n)) { int p; std::cin >> p; p -= offset; add_undirected_edge(p, i, 1); } build(); } void read_graph(int e, int offset = 1, bool is_directed = false, bool is_weighted = false) { for (int i = 0; i < e; i++) { int u, v; std::cin >> u >> v; u -= offset; v -= offset; if (is_weighted) { cost_type c; std::cin >> c; if (is_directed) { add_edge(u, v, c); } else { add_undirected_edge(u, v, c); } } else { if (is_directed) { add_edge(u, v, 1); } else { add_undirected_edge(u, v, 1); } } } build(); } void build() { assert(!prepared); csr = simple_csr<edge_type>(n, buff); buff.clear(); prepared = true; } int size() const { return n; } int node_number() const { return n; } int edge_number() const { return m; } edge_type get_edge(int i) const { return edges[i]; } std::vector<edge_type> get_edges() const { return edges; } const auto operator[](int i) const { return csr[i]; } auto operator[](int i) { return csr[i]; } private: int n, m = 0; std::vector<std::pair<int,edge_type>> buff; std::vector<edge_type> edges; simple_csr<edge_type> csr; bool prepared = false; }; } // namespace ebi #line 9 "graph/cycle_detection.hpp" namespace ebi { template <class T> std::optional<std::pair<std::vector<int>, std::vector<int>>> cycle_detection_directed(const Graph<T> &g) { int n = g.node_number(); std::vector<int> used(n, -1); std::vector<int> par_idx(n, -1); std::vector<int> vs, es; auto dfs = [&](auto &&self, int v) -> void { used[v] = 1; for (auto e : g[v]) { if (!es.empty()) return; if (used[e.to] == -1) { used[e.to] = 1; par_idx[e.to] = e.id; self(self, e.to); } else if (used[e.to] == 1) { int now = v; vs.emplace_back(now); es.emplace_back(e.id); while (now != e.to) { es.emplace_back(par_idx[now]); now = g.get_edge(par_idx[now]).from; } std::reverse(vs.begin(), vs.end()); std::reverse(es.begin(), es.end()); return; } } used[v] = 2; }; for (auto v : std::views::iota(0, n)) { if (used[v] != -1) continue; dfs(dfs, v); if (!es.empty()) { return std::pair<std::vector<int>, std::vector<int>>{vs, es}; } } return std::nullopt; } template <class T> std::optional<std::pair<std::vector<int>, std::vector<int>>> cycle_detection_undirected(const Graph<T> &g) { int n = g.node_number(); int m = g.edge_number(); std::vector<bool> used_edge(m, false); std::vector<int> depth(n, -1); std::vector<int> par_idx(n, -1); auto dfs = [&](auto &&self, int v) -> int { for (auto e : g[v]) { if (used_edge[e.id]) continue; if (depth[e.to] != -1) return e.id; used_edge[e.id] = true; par_idx[e.to] = e.id; depth[e.to] = depth[v] + 1; int x = self(self, e.to); if (x != -1) return x; } return -1; }; for (auto v : std::views::iota(0, n)) { if (depth[v] != -1) continue; depth[v] = 0; int id = dfs(dfs, v); if (id == -1) continue; int s = -1; { auto e = g.get_edge(id); if (depth[e.to] < depth[e.from]) s = e.to; else s = e.from; } std::vector<int> vs, es; vs.emplace_back(s), es.emplace_back(id); while (1) { auto e = g.get_edge(es.back()); int u = e.from ^ e.to ^ vs.back(); if (u == s) break; vs.emplace_back(u), es.emplace_back(par_idx[u]); } return std::pair<std::vector<int>, std::vector<int>>{vs, es}; } return std::nullopt; } } // namespace ebi