Cycle Detection
(library/graph/cycle_detection.hpp)

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• Last update: 2022-10-30 21:38:10+09:00
• Include: #include "library/graph/cycle_detection.hpp"

Cycle Detection

Depends on

• Graph (CSR Format) (library/graph/csr_graph.hpp)

Verified with

• test/src/graph/cycle_detection/cycle_detection.test.cpp
• test/src/graph/cycle_detection/cycle_detection_undirected.test.cpp
• test/src/graph/cycle_detection/dummy.test.cpp

Code

#ifndef SUISEN_CYCLE_DETECTION
#define SUISEN_CYCLE_DETECTION

#include <optional>
#include <vector>

#include "library/graph/csr_graph.hpp"

namespace suisen {
    template <typename T>
    std::optional<std::vector<typename Graph<T>::edge_type>> get_cycle_undirected(Graph<T> &g) {
        using edge_type = typename Graph<T>::edge_type;
        using weight_type = typename Graph<T>::weight_type_or_1;

        const int n = g.size();

        std::vector<edge_type> res;

        std::vector<edge_type> stk(n);
        using iterator = typename std::vector<edge_type>::iterator;
        iterator ptr = stk.begin();
        std::vector<iterator> pos(n, stk.end());
        std::vector<int8_t> vis(n);
        auto dfs = [&](auto dfs, int u, int p = -1, const weight_type &w) -> bool {
            int c = 0;
            pos[u] = ptr;
            for (const auto &e : g[u]) {
                const int v = e;
                weight_type we = g.get_weight(e);
                if (v == p and we == w and ++c == 1) continue;
                if (not std::exchange(vis[v], true)) {
                    *ptr++ = e;
                    if (dfs(dfs, v, u, we)) return true;
                    --ptr;
                } else if (pos[v] != stk.end()) {
                    *ptr++ = e;
                    res.resize(ptr - pos[v]);
                    std::move(pos[v], ptr, res.begin());
                    return true;
                }
            }
            pos[u] = stk.end();
            return false;
        };
        for (int i = 0; i < n; ++i) if (not std::exchange(vis[i], true)) {
            if (dfs(dfs, i, -1, {})) return res;
        }
        return std::nullopt;
    }

    template <typename T>
    std::optional<std::vector<typename Graph<T>::edge_type>> get_cycle_directed(Graph<T> &g) {
        using edge_type = typename Graph<T>::edge_type;
        const int n = g.size();

        std::vector<edge_type> res;

        std::vector<edge_type> stk(n);
        using iterator = typename std::vector<edge_type>::iterator;
        iterator ptr = stk.begin();
        std::vector<iterator> pos(n, stk.end());
        std::vector<int8_t> vis(n);
        auto dfs = [&](auto dfs, int u) -> bool {
            pos[u] = ptr;
            for (const auto &e : g[u]) {
                const int v = e;
                if (not std::exchange(vis[v], true)) {
                    *ptr++ = e;
                    if (dfs(dfs, v)) return true;
                    --ptr;
                } else if (pos[v] != stk.end()) {
                    *ptr++ = e;
                    res.resize(ptr - pos[v]);
                    std::move(pos[v], ptr, res.begin());
                    return true;
                }
            }
            pos[u] = stk.end();
            return false;
        };
        for (int i = 0; i < n; ++i) if (not std::exchange(vis[i], true)) {
            if (dfs(dfs, i)) return res;
        }
        return std::nullopt;
    }
} // namespace suisen

#endif // SUISEN_CYCLE_DETECTION

#line 1 "library/graph/cycle_detection.hpp"



#include <optional>
#include <vector>

#line 1 "library/graph/csr_graph.hpp"



#include <algorithm>
#include <cassert>
#include <limits>
#line 8 "library/graph/csr_graph.hpp"
#include <type_traits>
#include <tuple>
#include <utility>
#line 12 "library/graph/csr_graph.hpp"

namespace suisen {
    namespace internal::csr_graph { struct graph_base_tag {}; }
    struct directed_graph_tag : internal::csr_graph::graph_base_tag {};
    struct undirected_graph_tag : internal::csr_graph::graph_base_tag {};
    template <typename T>
    struct is_graph_tag { static constexpr bool value = std::is_base_of_v<internal::csr_graph::graph_base_tag, T>; };
    template <typename T>
    constexpr bool is_graph_tag_v = is_graph_tag<T>::value;

    template <typename WeightType = void>
    struct Graph {
        template <typename GraphTag, typename, std::enable_if_t<is_graph_tag_v<GraphTag>, std::nullptr_t>>
        friend struct GraphBuilder;

        using weight_type = WeightType;
        static constexpr bool weighted = std::negation_v<std::is_same<weight_type, void>>;

        using weight_type_or_1 = std::conditional_t<weighted, weight_type, int>;

        using input_edge_type = std::conditional_t<weighted, std::tuple<int, int, weight_type>, std::pair<int, int>>;
    private:
        using internal_edge_type = std::conditional_t<weighted, std::pair<int, weight_type>, int>;
        struct Edge : public internal_edge_type {
            using internal_edge_type::internal_edge_type;
            operator int() const { return std::get<0>(*this); }
        };
    public:
        using edge_type = std::conditional_t<weighted, Edge, int>;
    private:
        struct AdjacentList {
            friend struct Graph;

            using value_type = edge_type;
            using iterator = typename std::vector<value_type>::iterator;
            using const_iterator = typename std::vector<value_type>::const_iterator;
            using reverse_iterator = typename std::vector<value_type>::reverse_iterator;
            using const_reverse_iterator = typename std::vector<value_type>::const_reverse_iterator;

            AdjacentList() = default;

            int size() const { return _siz; }
            bool empty() const { return _siz == 0; }
            int capacity() const { return _cap; }

            value_type& operator[](int i) { return *(begin() + i); }
            const value_type& operator[](int i) const { return *(cbegin() + i); }
            value_type& at(uint32_t i) { assert(i < _siz); return *(begin() + i); }
            const value_type& at(uint32_t i) const { assert(i < _siz); return *(cbegin() + i); }

            value_type* data() { return _g->_edges.data() + _offset; }
            const value_type* data() const { return _g->_edges.data() + _offset; }

            iterator begin() const { return _g->_edges.begin() + _offset; }
            iterator end() const { return begin() + _siz; }
            const_iterator cbegin() const { return _g->_edges.cbegin() + _offset; }
            const_iterator cend() const { return cbegin() + _siz; }
            reverse_iterator rbegin() const { return _g->_edges.rbegin() + (_g->_edges.size() - (_offset + _siz)); }
            reverse_iterator rend() const { return rbegin() + _siz; }
            const_reverse_iterator crbegin() const { return _g->_edges.crbegin() + (_g->_edges.size() - (_offset + _siz)); }
            const_reverse_iterator crend() const { return crbegin() + _siz; }

            void erase(const_iterator pos) {
                erase(pos, std::next(pos));
            }
            void erase(const_iterator first, const_iterator last) {
                const int num = last - first, k = first - cbegin();
                assert(num >= 0);
                if (num == 0) return;
                assert(0 <= k and k <= _siz - num);
                std::move(begin() + k + num, end(), begin() + k);
                _siz -= num;
            }
            void pop_back() {
                assert(_siz);
                --_siz;
            }
            void clear() { _siz = 0; }

            const value_type& back() const { return *--cend(); }
            value_type& back() { return *--end(); }
            const value_type& front() const { return *cbegin(); }
            value_type& front() { return *begin(); }

            void push_back(const value_type& x) {
                ++_siz;
                assert(_siz <= _cap);
                back() = x;
            }
            template <typename ...Args>
            void emplace_back(Args &&...args) {
                ++_siz;
                assert(_siz <= _cap);
                back() = value_type(std::forward<Args>(args)...);
            }

            void insert(const_iterator pos, const value_type& x) {
                emplace(pos, x);
            }
            void insert(const_iterator pos, int num, const value_type& x) {
                const int k = pos - cbegin();
                assert(0 <= k and k <= _siz);
                std::fill(begin() + k, shift_back(begin() + k, num), x);
            }
            template <class RandomAccessIterator>
            auto insert(const_iterator pos, RandomAccessIterator first, RandomAccessIterator last) -> decltype(*first++, last - first, void()) {
                const int num = last - first, k = pos - cbegin();
                assert(0 <= k and k <= _siz);
                shift_back(begin() + k, num);
                std::copy(first, last, begin() + k);
            }
            void insert(const_iterator pos, std::initializer_list<value_type> il) { insert(pos, il.begin(), il.end()); }
            template <typename ...Args>
            void emplace(const_iterator pos, Args &&...args) {
                const int k = pos - cbegin();
                assert(0 <= k and k <= _siz);
                *--shift_back(begin() + k) = value_type(std::forward<Args>(args)...);
            }
        private:
            mutable Graph* _g;
            int _cap;
            int _offset;
            int _siz;

            iterator shift_back(iterator pos, int num = 1) {
                _siz += num;
                assert(_siz <= _cap);
                return std::move_backward(pos, end() - num, end());
            }
        };
    public:
        using adjacent_list = AdjacentList;

        Graph() = default;

        template <typename GraphTag, std::enable_if_t<is_graph_tag_v<GraphTag>, std::nullptr_t> = nullptr>
        Graph(const int n, const std::vector<input_edge_type>& edges, GraphTag, std::vector<int> cap = {}) : _n(n), _adj(_n) {
            static constexpr bool undirected = std::is_same_v<undirected_graph_tag, GraphTag>;

            for (const auto& e : edges) {
                const int u = std::get<0>(e);
                ++_adj[u]._siz;
                if constexpr (undirected) {
                    const int v = std::get<1>(e);
                    ++_adj[v]._siz;
                }
            }
            if (cap.empty()) cap.resize(_n, std::numeric_limits<int>::max());
            int edge_num = 0;
            for (int i = 0; i < _n; ++i) {
                _adj[i]._g = this;
                _adj[i]._cap = std::min(_adj[i]._siz, cap[i]);
                _adj[i]._offset = edge_num;
                edge_num += _adj[i]._siz;
            }
            _edges.resize(edge_num);
            std::vector<typename std::vector<edge_type>::iterator> ptr(_n);
            for (int i = 0; i < _n; ++i) ptr[i] = _adj[i].begin();
            for (const auto& e : edges) {
                const int u = std::get<0>(e);
                const int v = std::get<1>(e);
                if constexpr (weighted) {
                    const weight_type& w = std::get<2>(e);
                    *ptr[u]++ = { v, w };
                    if constexpr (undirected) *ptr[v]++ = { u, w };
                } else {
                    *ptr[u]++ = v;
                    if constexpr (undirected) *ptr[v]++ = u;
                }
            }
        }
        Graph(const std::vector<std::vector<edge_type>>& g) : Graph(g.size(), make_edges(g), directed_graph_tag{}) {}

        static Graph create_directed_graph(const int n, const std::vector<input_edge_type>& edges, const std::vector<int>& cap = {}) {
            return Graph(n, edges, directed_graph_tag{}, cap);
        }
        static Graph create_undirected_graph(const int n, const std::vector<input_edge_type>& edges, const std::vector<int>& cap = {}) {
            return Graph(n, edges, undirected_graph_tag{}, cap);
        }

        adjacent_list& operator[](int i) {
            _adj[i]._g = this;
            return _adj[i];
        }
        const adjacent_list& operator[](int i) const {
            _adj[i]._g = const_cast<Graph*>(this);
            return _adj[i];
        }

        int size() const {
            return _n;
        }

        void shrink_to_fit() {
            int edge_num = 0;
            for (const auto& l : _adj) edge_num += l.size();

            std::vector<edge_type> new_edges(edge_num);
            auto it = new_edges.begin();
            for (int i = 0; i < _n; ++i) {
                int nl = it - new_edges.begin();
                it = std::move(_adj[i].begin(), _adj[i].end(), it);
                _adj[i]._offset = nl;
                _adj[i]._cap = _adj[i]._siz;
            }
            _edges.swap(new_edges);
        }

        static weight_type_or_1 get_weight(const edge_type& edge) {
            if constexpr (weighted) return std::get<1>(edge);
            else return 1;
        }

        Graph reversed(const std::vector<int>& cap = {}) const {
            std::vector<input_edge_type> edges;
            for (int i = 0; i < _n; ++i) {
                for (const auto& edge : (*this)[i]) {
                    if constexpr (weighted) edges.emplace_back(std::get<0>(edge), i, std::get<1>(edge));
                    else edges.emplace_back(edge, i);
                }
            }
            return Graph(_n, std::move(edges), directed_graph_tag{}, cap);
        }

        struct DFSTree {
            std::vector<int> par;
            std::vector<int> pre_ord, pst_ord;
            Graph tree, back;
        };

        DFSTree dfs_tree(int start = 0) const {
            std::vector<input_edge_type> tree_edge, back_edge;

            std::vector<int> pre(_n), pst(_n);
            auto pre_it = pre.begin(), pst_it = pst.begin();

            std::vector<int> eid(_n, -1), par(_n, -2);
            std::vector<std::optional<weight_type_or_1>> par_w(_n, std::nullopt);
            for (int i = 0; i < _n; ++i) {
                int cur = (start + i) % _n;
                if (par[cur] != -2) continue;
                par[cur] = -1;
                while (cur >= 0) {
                    ++eid[cur];
                    if (eid[cur] == 0) *pre_it++ = cur;
                    if (eid[cur] == _adj[cur].size()) {
                        *pst_it++ = cur;
                        cur = par[cur];
                    } else {
                        const auto &e = _adj[cur][eid[cur]];
                        weight_type_or_1 w = get_weight(e);
                        int nxt = e;
                        if (par[nxt] == -2) {
                            tree_edge.emplace_back(make_edge(cur, e));
                            par[nxt] = cur;
                            par_w[nxt] = std::move(w);
                            cur = nxt;
                        } else if (eid[nxt] != _adj[nxt].size()) {
                            if (par[cur] != nxt or par_w[cur] != w or not std::exchange(par_w[cur], std::nullopt).has_value()) {
                                back_edge.emplace_back(make_edge(cur, e));
                            }
                        }
                    }
                }
            }
            Graph tree = create_directed_graph(_n, tree_edge);
            Graph back = create_directed_graph(_n, back_edge);
            return DFSTree{ std::move(par), std::move(pre), std::move(pst), std::move(tree), std::move(back) };
        }

    private:
        int _n;
        std::vector<adjacent_list> _adj;
        std::vector<edge_type> _edges;

        static std::vector<input_edge_type> make_edges(const std::vector<std::vector<edge_type>>& g) {
            const int n = g.size();
            std::vector<input_edge_type> edges;
            for (int i = 0; i < n; ++i) for (const auto& e : g[i]) {
                edges.emplace_back(make_edge(i, e));
            }
            return edges;
        }
        static input_edge_type make_edge(int i, const edge_type& e) {
            if constexpr (weighted) return { i, std::get<0>(e), std::get<1>(e) };
            else return { i, e };
        }
    };

    template <typename GraphTag>
    Graph(int, std::vector<std::pair<int, int>>, GraphTag, std::vector<int> = {})->Graph<void>;
    template <typename WeightType, typename GraphTag>
    Graph(int, std::vector<std::tuple<int, int, WeightType>>, GraphTag, std::vector<int> = {})->Graph<WeightType>;

    Graph(std::vector<std::vector<int>>)->Graph<void>;
    template <typename WeightType>
    Graph(std::vector<std::vector<std::pair<int, WeightType>>>)->Graph<WeightType>;

    template <typename GraphTag, typename WeightType = void,
        std::enable_if_t<is_graph_tag_v<GraphTag>, std::nullptr_t> = nullptr>
    struct GraphBuilder {
        using graph_tag = GraphTag;
        using weight_type = WeightType;
        using edge_type = typename Graph<weight_type>::input_edge_type;

        GraphBuilder(int n = 0) : _n(n) {}

        void add_edge(const edge_type& edge) {
            check_not_moved();
            _edges.push_back(edge);
        }
        template <typename ...Args>
        void emplace_edge(Args &&...args) {
            check_not_moved();
            _edges.emplace_back(std::forward<Args>(args)...);
        }
        template <typename EdgeContainer, std::enable_if_t<std::is_constructible_v<edge_type, typename EdgeContainer::value_type>, std::nullptr_t> = nullptr>
        void add_edges(const EdgeContainer& edges) {
            for (const auto& edge : edges) add_edge(edge);
        }

        template <bool move_edges = true>
        Graph<weight_type> build() {
            if constexpr (move_edges) {
                _moved = true;
                return Graph<weight_type>(_n, std::move(_edges), graph_tag{});
            } else {
                return Graph<weight_type>(_n, _edges, graph_tag{});
            }
        }
        Graph<weight_type> build_without_move() {
            return build<false>();
        }

        static Graph<weight_type> build(const int n, const std::vector<edge_type>& edges) {
            GraphBuilder builder(n);
            builder.add_edges(edges);
            return builder.build();
        }
    private:
        int _n;
        std::vector<edge_type> _edges;
        bool _moved = false;

        void check_not_moved() {
            if (not _moved) return;
            std::cerr << "[\033[31mERROR\033[m] Edges are already moved. If you want to add edges after calling build() and build another graph, you should use build_without_move() instead." << std::endl;
            assert(false);
        }
    };
    template <typename WeightType = void>
    using DirectedGraphBuilder = GraphBuilder<directed_graph_tag, WeightType>;
    template <typename WeightType = void>
    using UndirectedGraphBuilder = GraphBuilder<undirected_graph_tag, WeightType>;

    template <typename Weight, std::enable_if_t<std::negation_v<std::is_same<Weight, void>>, std::nullptr_t> = nullptr>
    using WeightedGraph = Graph<Weight>;
    using UnweightedGraph = Graph<void>;

    template <typename T>
    struct is_weighted_graph { static constexpr bool value = false; };
    template <typename WeightType>
    struct is_weighted_graph<Graph<WeightType>> { static constexpr bool value = Graph<WeightType>::weighted; };
    template <typename T>
    constexpr bool is_weighted_graph_v = is_weighted_graph<T>::value;

    template <typename T>
    struct is_unweighted_graph { static constexpr bool value = false; };
    template <typename WeightType>
    struct is_unweighted_graph<Graph<WeightType>> { static constexpr bool value = not Graph<WeightType>::weighted; };
    template <typename T>
    constexpr bool is_unweighted_graph_v = is_unweighted_graph<T>::value;
} // namespace suisen


#line 8 "library/graph/cycle_detection.hpp"

namespace suisen {
    template <typename T>
    std::optional<std::vector<typename Graph<T>::edge_type>> get_cycle_undirected(Graph<T> &g) {
        using edge_type = typename Graph<T>::edge_type;
        using weight_type = typename Graph<T>::weight_type_or_1;

        const int n = g.size();

        std::vector<edge_type> res;

        std::vector<edge_type> stk(n);
        using iterator = typename std::vector<edge_type>::iterator;
        iterator ptr = stk.begin();
        std::vector<iterator> pos(n, stk.end());
        std::vector<int8_t> vis(n);
        auto dfs = [&](auto dfs, int u, int p = -1, const weight_type &w) -> bool {
            int c = 0;
            pos[u] = ptr;
            for (const auto &e : g[u]) {
                const int v = e;
                weight_type we = g.get_weight(e);
                if (v == p and we == w and ++c == 1) continue;
                if (not std::exchange(vis[v], true)) {
                    *ptr++ = e;
                    if (dfs(dfs, v, u, we)) return true;
                    --ptr;
                } else if (pos[v] != stk.end()) {
                    *ptr++ = e;
                    res.resize(ptr - pos[v]);
                    std::move(pos[v], ptr, res.begin());
                    return true;
                }
            }
            pos[u] = stk.end();
            return false;
        };
        for (int i = 0; i < n; ++i) if (not std::exchange(vis[i], true)) {
            if (dfs(dfs, i, -1, {})) return res;
        }
        return std::nullopt;
    }

    template <typename T>
    std::optional<std::vector<typename Graph<T>::edge_type>> get_cycle_directed(Graph<T> &g) {
        using edge_type = typename Graph<T>::edge_type;
        const int n = g.size();

        std::vector<edge_type> res;

        std::vector<edge_type> stk(n);
        using iterator = typename std::vector<edge_type>::iterator;
        iterator ptr = stk.begin();
        std::vector<iterator> pos(n, stk.end());
        std::vector<int8_t> vis(n);
        auto dfs = [&](auto dfs, int u) -> bool {
            pos[u] = ptr;
            for (const auto &e : g[u]) {
                const int v = e;
                if (not std::exchange(vis[v], true)) {
                    *ptr++ = e;
                    if (dfs(dfs, v)) return true;
                    --ptr;
                } else if (pos[v] != stk.end()) {
                    *ptr++ = e;
                    res.resize(ptr - pos[v]);
                    std::move(pos[v], ptr, res.begin());
                    return true;
                }
            }
            pos[u] = stk.end();
            return false;
        };
        for (int i = 0; i < n; ++i) if (not std::exchange(vis[i], true)) {
            if (dfs(dfs, i)) return res;
        }
        return std::nullopt;
    }
} // namespace suisen

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