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+#ifndef ENTT_GRAPH_ADJACENCY_MATRIX_HPP
+#define ENTT_GRAPH_ADJACENCY_MATRIX_HPP
+
+#include <cstddef>
+#include <iterator>
+#include <memory>
+#include <type_traits>
+#include <utility>
+#include <vector>
+#include "../config/config.h"
+#include "../core/iterator.hpp"
+#include "fwd.hpp"
+
+namespace entt {
+
+/*! @cond TURN_OFF_DOXYGEN */
+namespace internal {
+
+template<typename It>
+class edge_iterator {
+ using size_type = std::size_t;
+
+public:
+ using value_type = std::pair<size_type, size_type>;
+ using pointer = input_iterator_pointer<value_type>;
+ using reference = value_type;
+ using difference_type = std::ptrdiff_t;
+ using iterator_category = std::input_iterator_tag;
+ using iterator_concept = std::forward_iterator_tag;
+
+ constexpr edge_iterator() noexcept = default;
+
+ // NOLINTNEXTLINE(bugprone-easily-swappable-parameters)
+ constexpr edge_iterator(It base, const size_type vertices, const size_type from, const size_type to, const size_type step) noexcept
+ : it{std::move(base)},
+ vert{vertices},
+ pos{from},
+ last{to},
+ offset{step} {
+ for(; pos != last && !it[pos]; pos += offset) {}
+ }
+
+ constexpr edge_iterator &operator++() noexcept {
+ for(pos += offset; pos != last && !it[pos]; pos += offset) {}
+ return *this;
+ }
+
+ constexpr edge_iterator operator++(int) noexcept {
+ edge_iterator orig = *this;
+ return ++(*this), orig;
+ }
+
+ [[nodiscard]] constexpr reference operator*() const noexcept {
+ return *operator->();
+ }
+
+ [[nodiscard]] constexpr pointer operator->() const noexcept {
+ return std::make_pair<size_type>(pos / vert, pos % vert);
+ }
+
+ template<typename Type>
+ friend constexpr bool operator==(const edge_iterator<Type> &, const edge_iterator<Type> &) noexcept;
+
+private:
+ It it{};
+ size_type vert{};
+ size_type pos{};
+ size_type last{};
+ size_type offset{};
+};
+
+template<typename Container>
+[[nodiscard]] inline constexpr bool operator==(const edge_iterator<Container> &lhs, const edge_iterator<Container> &rhs) noexcept {
+ return lhs.pos == rhs.pos;
+}
+
+template<typename Container>
+[[nodiscard]] inline constexpr bool operator!=(const edge_iterator<Container> &lhs, const edge_iterator<Container> &rhs) noexcept {
+ return !(lhs == rhs);
+}
+
+} // namespace internal
+/*! @endcond */
+
+/**
+ * @brief Basic implementation of a directed adjacency matrix.
+ * @tparam Category Either a directed or undirected category tag.
+ * @tparam Allocator Type of allocator used to manage memory and elements.
+ */
+template<typename Category, typename Allocator>
+class adjacency_matrix {
+ using alloc_traits = std::allocator_traits<Allocator>;
+ static_assert(std::is_base_of_v<directed_tag, Category>, "Invalid graph category");
+ static_assert(std::is_same_v<typename alloc_traits::value_type, std::size_t>, "Invalid value type");
+ using container_type = std::vector<std::size_t, typename alloc_traits::template rebind_alloc<std::size_t>>;
+
+public:
+ /*! @brief Allocator type. */
+ using allocator_type = Allocator;
+ /*! @brief Unsigned integer type. */
+ using size_type = std::size_t;
+ /*! @brief Vertex type. */
+ using vertex_type = size_type;
+ /*! @brief Edge type. */
+ using edge_type = std::pair<vertex_type, vertex_type>;
+ /*! @brief Vertex iterator type. */
+ using vertex_iterator = iota_iterator<vertex_type>;
+ /*! @brief Edge iterator type. */
+ using edge_iterator = internal::edge_iterator<typename container_type::const_iterator>;
+ /*! @brief Out-edge iterator type. */
+ using out_edge_iterator = edge_iterator;
+ /*! @brief In-edge iterator type. */
+ using in_edge_iterator = edge_iterator;
+ /*! @brief Graph category tag. */
+ using graph_category = Category;
+
+ /*! @brief Default constructor. */
+ adjacency_matrix() noexcept(noexcept(allocator_type{}))
+ : adjacency_matrix{0u} {
+ }
+
+ /**
+ * @brief Constructs an empty container with a given allocator.
+ * @param allocator The allocator to use.
+ */
+ explicit adjacency_matrix(const allocator_type &allocator) noexcept
+ : adjacency_matrix{0u, allocator} {}
+
+ /**
+ * @brief Constructs an empty container with a given allocator and user
+ * supplied number of vertices.
+ * @param vertices Number of vertices.
+ * @param allocator The allocator to use.
+ */
+ adjacency_matrix(const size_type vertices, const allocator_type &allocator = allocator_type{})
+ : matrix{vertices * vertices, allocator},
+ vert{vertices} {}
+
+ /*! @brief Default copy constructor. */
+ adjacency_matrix(const adjacency_matrix &) = default;
+
+ /**
+ * @brief Allocator-extended copy constructor.
+ * @param other The instance to copy from.
+ * @param allocator The allocator to use.
+ */
+ adjacency_matrix(const adjacency_matrix &other, const allocator_type &allocator)
+ : matrix{other.matrix, allocator},
+ vert{other.vert} {}
+
+ /*! @brief Default move constructor. */
+ adjacency_matrix(adjacency_matrix &&) noexcept = default;
+
+ /**
+ * @brief Allocator-extended move constructor.
+ * @param other The instance to move from.
+ * @param allocator The allocator to use.
+ */
+ adjacency_matrix(adjacency_matrix &&other, const allocator_type &allocator)
+ : matrix{std::move(other.matrix), allocator},
+ vert{other.vert} {}
+
+ /*! @brief Default destructor. */
+ ~adjacency_matrix() noexcept = default;
+
+ /**
+ * @brief Default copy assignment operator.
+ * @return This container.
+ */
+ adjacency_matrix &operator=(const adjacency_matrix &) = default;
+
+ /**
+ * @brief Default move assignment operator.
+ * @return This container.
+ */
+ adjacency_matrix &operator=(adjacency_matrix &&) noexcept = default;
+
+ /**
+ * @brief Returns the associated allocator.
+ * @return The associated allocator.
+ */
+ [[nodiscard]] constexpr allocator_type get_allocator() const noexcept {
+ return matrix.get_allocator();
+ }
+
+ /*! @brief Clears the adjacency matrix. */
+ void clear() noexcept {
+ matrix.clear();
+ vert = {};
+ }
+
+ /**
+ * @brief Exchanges the contents with those of a given adjacency matrix.
+ * @param other Adjacency matrix to exchange the content with.
+ */
+ void swap(adjacency_matrix &other) {
+ using std::swap;
+ swap(matrix, other.matrix);
+ swap(vert, other.vert);
+ }
+
+ /**
+ * @brief Returns true if an adjacency matrix is empty, false otherwise.
+ *
+ * @warning
+ * Potentially expensive, try to avoid it on hot paths.
+ *
+ * @return True if the adjacency matrix is empty, false otherwise.
+ */
+ [[nodiscard]] bool empty() const noexcept {
+ const auto iterable = edges();
+ return (iterable.begin() == iterable.end());
+ }
+
+ /**
+ * @brief Returns the number of vertices.
+ * @return The number of vertices.
+ */
+ [[nodiscard]] size_type size() const noexcept {
+ return vert;
+ }
+
+ /**
+ * @brief Returns an iterable object to visit all vertices of a matrix.
+ * @return An iterable object to visit all vertices of a matrix.
+ */
+ [[nodiscard]] iterable_adaptor<vertex_iterator> vertices() const noexcept {
+ return {0u, vert};
+ }
+
+ /**
+ * @brief Returns an iterable object to visit all edges of a matrix.
+ * @return An iterable object to visit all edges of a matrix.
+ */
+ [[nodiscard]] iterable_adaptor<edge_iterator> edges() const noexcept {
+ const auto it = matrix.cbegin();
+ const auto sz = matrix.size();
+ return {{it, vert, 0u, sz, 1u}, {it, vert, sz, sz, 1u}};
+ }
+
+ /**
+ * @brief Returns an iterable object to visit all out-edges of a vertex.
+ * @param vertex The vertex of which to return all out-edges.
+ * @return An iterable object to visit all out-edges of a vertex.
+ */
+ [[nodiscard]] iterable_adaptor<out_edge_iterator> out_edges(const vertex_type vertex) const noexcept {
+ const auto it = matrix.cbegin();
+ const auto from = vertex * vert;
+ const auto to = from + vert;
+ return {{it, vert, from, to, 1u}, {it, vert, to, to, 1u}};
+ }
+
+ /**
+ * @brief Returns an iterable object to visit all in-edges of a vertex.
+ * @param vertex The vertex of which to return all in-edges.
+ * @return An iterable object to visit all in-edges of a vertex.
+ */
+ [[nodiscard]] iterable_adaptor<in_edge_iterator> in_edges(const vertex_type vertex) const noexcept {
+ const auto it = matrix.cbegin();
+ const auto from = vertex;
+ const auto to = vert * vert + from;
+ return {{it, vert, from, to, vert}, {it, vert, to, to, vert}};
+ }
+
+ /**
+ * @brief Resizes an adjacency matrix.
+ * @param vertices The new number of vertices.
+ */
+ void resize(const size_type vertices) {
+ adjacency_matrix other{vertices, get_allocator()};
+
+ for(auto [lhs, rhs]: edges()) {
+ other.insert(lhs, rhs);
+ }
+
+ other.swap(*this);
+ }
+
+ /**
+ * @brief Inserts an edge into the adjacency matrix, if it does not exist.
+ * @param lhs The left hand vertex of the edge.
+ * @param rhs The right hand vertex of the edge.
+ * @return A pair consisting of an iterator to the inserted element (or to
+ * the element that prevented the insertion) and a bool denoting whether the
+ * insertion took place.
+ */
+ std::pair<edge_iterator, bool> insert(const vertex_type lhs, const vertex_type rhs) {
+ const auto pos = lhs * vert + rhs;
+
+ if constexpr(std::is_same_v<graph_category, undirected_tag>) {
+ const auto rev = rhs * vert + lhs;
+ ENTT_ASSERT(matrix[pos] == matrix[rev], "Something went really wrong");
+ matrix[rev] = 1u;
+ }
+
+ const auto inserted = !std::exchange(matrix[pos], 1u);
+ return {edge_iterator{matrix.cbegin(), vert, pos, matrix.size(), 1u}, inserted};
+ }
+
+ /**
+ * @brief Removes the edge associated with a pair of given vertices.
+ * @param lhs The left hand vertex of the edge.
+ * @param rhs The right hand vertex of the edge.
+ * @return Number of elements removed (either 0 or 1).
+ */
+ size_type erase(const vertex_type lhs, const vertex_type rhs) {
+ const auto pos = lhs * vert + rhs;
+
+ if constexpr(std::is_same_v<graph_category, undirected_tag>) {
+ const auto rev = rhs * vert + lhs;
+ ENTT_ASSERT(matrix[pos] == matrix[rev], "Something went really wrong");
+ matrix[rev] = 0u;
+ }
+
+ return std::exchange(matrix[pos], 0u);
+ }
+
+ /**
+ * @brief Checks if an adjacency matrix contains a given edge.
+ * @param lhs The left hand vertex of the edge.
+ * @param rhs The right hand vertex of the edge.
+ * @return True if there is such an edge, false otherwise.
+ */
+ [[nodiscard]] bool contains(const vertex_type lhs, const vertex_type rhs) const {
+ const auto pos = lhs * vert + rhs;
+ return pos < matrix.size() && matrix[pos];
+ }
+
+private:
+ container_type matrix;
+ size_type vert;
+};
+
+} // namespace entt
+
+#endif