YT-CPPGL-41: Implement the Prim's MST finding algorithm

- Added the implementation of the Prim's MST finding algorithm
- Moved/aligned the common algorithm types to be defined in the `gl::types` namespace
- Moved common graph utility to a dedicated header file

include/gl/algorithm/breadth_first_search.hpp

@@ -2,15 +2,16 @@
 
 #include "constants.hpp"
 #include "detail/bfs_impl.hpp"
+#include "types.hpp"
 
 namespace gl::algorithm {
 
 template <
-    type_traits::c_alg_return_graph SearchTreeType = no_return,
+    type_traits::c_alg_return_graph_type SearchTreeType = types::no_return,
     type_traits::c_graph GraphType,
-    type_traits::c_vertex_callback<GraphType, void> PreVisitCallback = empty_callback,
-    type_traits::c_vertex_callback<GraphType, void> PostVisitCallback = empty_callback>
-type_traits::alg_return_type<SearchTreeType> breadth_first_search(
+    type_traits::c_vertex_callback<GraphType, void> PreVisitCallback = types::empty_callback,
+    type_traits::c_vertex_callback<GraphType, void> PostVisitCallback = types::empty_callback>
+detail::alg_return_graph_type<SearchTreeType> breadth_first_search(
     const GraphType& graph,
     const std::optional<types::id_type>& root_vertex_id_opt = no_root_vertex,
     const PreVisitCallback& pre_visit = {},
@@ -48,7 +49,7 @@ type_traits::alg_return_type<SearchTreeType> breadth_first_search(
             );
     }
 
-    if constexpr (not type_traits::is_alg_no_return_type_v<SearchTreeType>)
+    if constexpr (not type_traits::c_alg_no_return_type<SearchTreeType>)
         return search_tree;
 }
 

include/gl/algorithm/coloring.hpp

@@ -9,8 +9,8 @@ using bicoloring_type = std::vector<types::binary_color>;
 
 template <
     type_traits::c_graph GraphType,
-    type_traits::c_vertex_callback<GraphType, void> PreVisitCallback = empty_callback,
-    type_traits::c_vertex_callback<GraphType, void> PostVisitCallback = empty_callback>
+    type_traits::c_vertex_callback<GraphType, void> PreVisitCallback = types::empty_callback,
+    type_traits::c_vertex_callback<GraphType, void> PostVisitCallback = types::empty_callback>
 [[nodiscard]] std::optional<bicoloring_type> bipartite_coloring(
     const GraphType& graph,
     const PreVisitCallback& pre_visit = {},

include/gl/algorithm/deapth_first_search.hpp

@@ -6,11 +6,11 @@
 namespace gl::algorithm {
 
 template <
-    type_traits::c_alg_return_graph SearchTreeType = no_return,
+    type_traits::c_alg_return_graph_type SearchTreeType = types::no_return,
     type_traits::c_graph GraphType,
-    type_traits::c_vertex_callback<GraphType, void> PreVisitCallback = empty_callback,
-    type_traits::c_vertex_callback<GraphType, void> PostVisitCallback = empty_callback>
-type_traits::alg_return_type<SearchTreeType> depth_first_search(
+    type_traits::c_vertex_callback<GraphType, void> PreVisitCallback = types::empty_callback,
+    type_traits::c_vertex_callback<GraphType, void> PostVisitCallback = types::empty_callback>
+detail::alg_return_graph_type<SearchTreeType> depth_first_search(
     const GraphType& graph,
     const std::optional<types::id_type>& root_vertex_id_opt = no_root_vertex,
     const PreVisitCallback& pre_visit = {},
@@ -48,16 +48,16 @@ type_traits::alg_return_type<SearchTreeType> depth_first_search(
             );
     }
 
-    if constexpr (not type_traits::is_alg_no_return_type_v<SearchTreeType>)
+    if constexpr (not type_traits::c_alg_no_return_type<SearchTreeType>)
         return search_tree;
 }
 
 template <
-    type_traits::c_alg_return_graph SearchTreeType = no_return,
+    type_traits::c_alg_return_graph_type SearchTreeType = types::no_return,
     type_traits::c_graph GraphType,
-    type_traits::c_vertex_callback<GraphType, void> PreVisitCallback = empty_callback,
-    type_traits::c_vertex_callback<GraphType, void> PostVisitCallback = empty_callback>
-type_traits::alg_return_type<SearchTreeType> recursive_depth_first_search(
+    type_traits::c_vertex_callback<GraphType, void> PreVisitCallback = types::empty_callback,
+    type_traits::c_vertex_callback<GraphType, void> PostVisitCallback = types::empty_callback>
+detail::alg_return_graph_type<SearchTreeType> recursive_depth_first_search(
     const GraphType& graph,
     const std::optional<types::id_type>& root_vertex_id_opt = no_root_vertex,
     const PreVisitCallback& pre_visit = {},
@@ -98,7 +98,7 @@ type_traits::alg_return_type<SearchTreeType> recursive_depth_first_search(
             );
     }
 
-    if constexpr (not type_traits::is_alg_no_return_type_v<SearchTreeType>)
+    if constexpr (not type_traits::c_alg_no_return_type<SearchTreeType>)
         return search_tree;
 }
 

include/gl/algorithm/detail/bfs_impl.hpp

@@ -8,24 +8,26 @@ namespace gl::algorithm::detail {
 
 template <
     type_traits::c_graph GraphType,
-    type_traits::c_sized_range_of<vertex_info> InitQueueRangeType = std::vector<vertex_info>,
-    type_traits::c_vertex_callback<GraphType, void> PreVisitCallback = empty_callback,
-    type_traits::c_vertex_callback<GraphType, void> PostVisitCallback = empty_callback>
+    type_traits::c_sized_range_of<types::vertex_info> InitQueueRangeType =
+        std::vector<types::vertex_info>,
+    type_traits::c_vertex_callback<GraphType, void> PreVisitCallback = types::empty_callback,
+    type_traits::c_vertex_callback<GraphType, void> PostVisitCallback = types::empty_callback>
 bool bfs_impl(
     const GraphType& graph,
     const InitQueueRangeType& initial_queue_content,
-    const vertex_callback<GraphType, bool>& visit_vertex_pred,
-    const vertex_callback<GraphType, bool, types::id_type>& visit,
-    const vertex_callback<GraphType, std::optional<bool>, const typename GraphType::edge_type&>&
-        enque_vertex_pred,
+    const types::vertex_callback<GraphType, bool>& visit_vertex_pred,
+    const types::vertex_callback<GraphType, bool, types::id_type>& visit,
+    const types::
+        vertex_callback<GraphType, std::optional<bool>, const typename GraphType::edge_type&>&
+            enque_vertex_pred,
     const PreVisitCallback& pre_visit = {},
     const PostVisitCallback& post_visit = {}
 ) {
     if (initial_queue_content.size() == constants::default_size)
         return false;
 
     // prepare the vertex queue
-    using vertex_queue_type = std::queue<vertex_info>;
+    using vertex_queue_type = std::queue<types::vertex_info>;
     vertex_queue_type vertex_queue;
 
     // TODO [C++23]: replace with push_range
@@ -34,31 +36,31 @@ bool bfs_impl(
 
     // search the graph
     while (not vertex_queue.empty()) {
-        const vertex_info vi = vertex_queue.front();
+        const types::vertex_info vinfo = vertex_queue.front();
         vertex_queue.pop();
 
-        const auto& vertex = graph.get_vertex(vi.id);
+        const auto& vertex = graph.get_vertex(vinfo.id);
         if (not visit_vertex_pred(vertex))
             continue;
 
-        if constexpr (not type_traits::is_empty_callback_v<PreVisitCallback>)
+        if constexpr (not type_traits::c_empty_callback<PreVisitCallback>)
             pre_visit(vertex);
 
-        if (not visit(vertex, vi.source_id))
+        if (not visit(vertex, vinfo.source_id))
             return false;
 
-        for (const auto& edge : graph.adjacent_edges(vi.id)) {
+        for (const auto& edge : graph.adjacent_edges(vinfo.id)) {
             const auto& incident_vertex = edge.incident_vertex(vertex);
 
             const auto enqueue = enque_vertex_pred(incident_vertex, edge);
             if (not enqueue.has_value())
                 return false;
 
             if (enqueue.value())
-                vertex_queue.emplace(incident_vertex.id(), vi.id);
+                vertex_queue.emplace(incident_vertex.id(), vinfo.id);
         }
 
-        if constexpr (not type_traits::is_empty_callback_v<PostVisitCallback>)
+        if constexpr (not type_traits::c_empty_callback<PostVisitCallback>)
             post_visit(vertex);
     }
 
@@ -67,26 +69,29 @@ bool bfs_impl(
 
 template <
     type_traits::c_graph GraphType,
-    std::predicate<vertex_info, vertex_info> PQCompare,
-    type_traits::c_sized_range_of<vertex_info> InitQueueRangeType = std::vector<vertex_info>,
-    type_traits::c_vertex_callback<GraphType, void> PreVisitCallback = empty_callback,
-    type_traits::c_vertex_callback<GraphType, void> PostVisitCallback = empty_callback>
+    std::predicate<types::vertex_info, types::vertex_info> PQCompare,
+    type_traits::c_sized_range_of<types::vertex_info> InitQueueRangeType =
+        std::vector<types::vertex_info>,
+    type_traits::c_vertex_callback<GraphType, void> PreVisitCallback = types::empty_callback,
+    type_traits::c_vertex_callback<GraphType, void> PostVisitCallback = types::empty_callback>
 bool pq_bfs_impl(
     const GraphType& graph,
     const PQCompare pq_compare,
     const InitQueueRangeType& initial_queue_content,
-    const vertex_callback<GraphType, bool>& visit_vertex_pred,
-    const vertex_callback<GraphType, bool, types::id_type>& visit,
-    const vertex_callback<GraphType, std::optional<bool>, const typename GraphType::edge_type&>&
-        enque_vertex_pred,
+    const types::vertex_callback<GraphType, bool>& visit_vertex_pred,
+    const types::vertex_callback<GraphType, bool, types::id_type>& visit,
+    const types::
+        vertex_callback<GraphType, std::optional<bool>, const typename GraphType::edge_type&>&
+            enque_vertex_pred,
     const PreVisitCallback& pre_visit = {},
     const PostVisitCallback& post_visit = {}
 ) {
     if (initial_queue_content.size() == constants::default_size)
         return false;
 
     // prepare the vertex queue
-    using vertex_queue_type = std::priority_queue<vertex_info, std::vector<vertex_info>, PQCompare>;
+    using vertex_queue_type =
+        std::priority_queue<types::vertex_info, std::vector<types::vertex_info>, PQCompare>;
     vertex_queue_type vertex_queue(pq_compare);
 
     // TODO [C++23]: replace with push_range
@@ -95,30 +100,30 @@ bool pq_bfs_impl(
 
     // search the graph
     while (not vertex_queue.empty()) {
-        const vertex_info vi = vertex_queue.top();
+        const auto vinfo = vertex_queue.top();
         vertex_queue.pop();
 
-        const auto& vertex = graph.get_vertex(vi.id);
+        const auto& vertex = graph.get_vertex(vinfo.id);
         if (not visit_vertex_pred(vertex))
             continue;
 
-        if constexpr (not type_traits::is_empty_callback_v<PreVisitCallback>)
+        if constexpr (not type_traits::c_empty_callback<PreVisitCallback>)
             pre_visit(vertex);
 
-        if (not visit(vertex, vi.source_id))
+        if (not visit(vertex, vinfo.source_id))
             return false;
 
-        for (const auto& edge : graph.adjacent_edges(vi.id)) {
+        for (const auto& edge : graph.adjacent_edges(vinfo.id)) {
             const auto& incident_vertex = edge.incident_vertex(vertex);
 
             const auto enqueue = enque_vertex_pred(incident_vertex, edge);
             if (not enqueue.has_value())
                 return false;
 
             if (enqueue.value())
-                vertex_queue.emplace(incident_vertex.id(), vi.id);
+                vertex_queue.emplace(incident_vertex.id(), vinfo.id);
         }
-        if constexpr (not type_traits::is_empty_callback_v<PostVisitCallback>)
+        if constexpr (not type_traits::c_empty_callback<PostVisitCallback>)
             post_visit(vertex);
     }
 

include/gl/algorithm/detail/common.hpp

@@ -5,27 +5,21 @@
 
 namespace gl::algorithm::detail {
 
-template <type_traits::c_alg_return_graph SearchTreeType, type_traits::c_graph GraphType>
+// --- common functions ---
+
+template <type_traits::c_alg_return_graph_type SearchTreeType, type_traits::c_graph GraphType>
 [[nodiscard]] gl_attr_force_inline SearchTreeType init_search_tree(const GraphType& graph) {
-    if constexpr (type_traits::is_alg_no_return_type_v<SearchTreeType>)
+    if constexpr (type_traits::c_alg_no_return_type<SearchTreeType>)
         return SearchTreeType{};
     else
         return SearchTreeType(graph.n_vertices());
 }
 
-struct vertex_info {
-    vertex_info(types::id_type id) : id(id), source_id(id) {}
-
-    vertex_info(types::id_type id, types::id_type source_id) : id(id), source_id(source_id) {}
-
-    // if id == source_id then vertex_id is the id of the starting vertex
-    types::id_type id;
-    types::id_type source_id;
-};
-
-template <type_traits::c_sized_range_of<vertex_info> InitRangeType = std::vector<vertex_info>>
+template <
+    type_traits::c_sized_range_of<types::vertex_info> InitRangeType =
+        std::vector<types::vertex_info>>
 [[nodiscard]] gl_attr_force_inline InitRangeType init_range(types::id_type root_vertex_id) {
-    return InitRangeType{vertex_info{root_vertex_id}};
+    return InitRangeType{types::vertex_info{root_vertex_id}};
 }
 
 template <bool B>
@@ -45,14 +39,14 @@ template <type_traits::c_graph GraphType>
     };
 }
 
-template <type_traits::c_graph GraphType, type_traits::c_alg_return_graph SearchTreeType>
+template <type_traits::c_graph GraphType, type_traits::c_alg_return_graph_type SearchTreeType>
 [[nodiscard]] gl_attr_force_inline auto default_visit_callback(
     std::vector<bool>& visited, SearchTreeType& search_tree
 ) {
     return [&](const typename GraphType::vertex_type& vertex, const types::id_type source_id) {
         const auto vertex_id = vertex.id();
         visited[vertex_id] = true;
-        if constexpr (not type_traits::is_alg_no_return_type_v<SearchTreeType>) {
+        if constexpr (not type_traits::c_alg_no_return_type<SearchTreeType>) {
             if (source_id != vertex_id)
                 search_tree.add_edge(source_id, vertex_id);
         }

include/gl/algorithm/detail/dfs_impl.hpp

@@ -8,18 +8,19 @@ namespace gl::algorithm::detail {
 
 template <
     type_traits::c_graph GraphType,
-    type_traits::c_vertex_callback<GraphType, void> PreVisitCallback = empty_callback,
-    type_traits::c_vertex_callback<GraphType, void> PostVisitCallback = empty_callback>
+    type_traits::c_vertex_callback<GraphType, void> PreVisitCallback = types::empty_callback,
+    type_traits::c_vertex_callback<GraphType, void> PostVisitCallback = types::empty_callback>
 void dfs_impl(
     const GraphType& graph,
     const typename GraphType::vertex_type& root_vertex,
-    const vertex_callback<GraphType, bool>& visit_vertex_pred,
-    const vertex_callback<GraphType, void, types::id_type>& visit,
-    const vertex_callback<GraphType, bool, const typename GraphType::edge_type&>& enque_vertex_pred,
+    const types::vertex_callback<GraphType, bool>& visit_vertex_pred,
+    const types::vertex_callback<GraphType, void, types::id_type>& visit,
+    const types::vertex_callback<GraphType, bool, const typename GraphType::edge_type&>&
+        enque_vertex_pred,
     const PreVisitCallback& pre_visit = {},
     const PostVisitCallback& post_visit = {}
 ) {
-    using vertex_stack_type = std::stack<vertex_info>;
+    using vertex_stack_type = std::stack<types::vertex_info>;
 
     if (not visit_vertex_pred(root_vertex))
         return;
@@ -28,47 +29,48 @@ void dfs_impl(
     vertex_stack.emplace(root_vertex.id());
 
     while (not vertex_stack.empty()) {
-        const vertex_info vi = vertex_stack.top();
+        const auto vinfo = vertex_stack.top();
         vertex_stack.pop();
 
-        const auto& vertex = graph.get_vertex(vi.id);
+        const auto& vertex = graph.get_vertex(vinfo.id);
         if (not visit_vertex_pred(vertex))
             continue;
 
-        if constexpr (not type_traits::is_empty_callback_v<PreVisitCallback>)
+        if constexpr (not type_traits::c_empty_callback<PreVisitCallback>)
             pre_visit(vertex);
 
-        visit(vertex, vi.source_id);
+        visit(vertex, vinfo.source_id);
 
-        for (const auto& edge : graph.adjacent_edges(vi.id)) {
+        for (const auto& edge : graph.adjacent_edges(vinfo.id)) {
             const auto& incident_vertex = edge.incident_vertex(vertex);
             if (enque_vertex_pred(incident_vertex, edge))
-                vertex_stack.emplace(incident_vertex.id(), vi.id);
+                vertex_stack.emplace(incident_vertex.id(), vinfo.id);
         }
 
-        if constexpr (not type_traits::is_empty_callback_v<PostVisitCallback>)
+        if constexpr (not type_traits::c_empty_callback<PostVisitCallback>)
             post_visit(vertex);
     }
 }
 
 template <
     type_traits::c_graph GraphType,
-    type_traits::c_vertex_callback<GraphType, void> PreVisitCallback = empty_callback,
-    type_traits::c_vertex_callback<GraphType, void> PostVisitCallback = empty_callback>
+    type_traits::c_vertex_callback<GraphType, void> PreVisitCallback = types::empty_callback,
+    type_traits::c_vertex_callback<GraphType, void> PostVisitCallback = types::empty_callback>
 void rdfs_impl(
     const GraphType& graph,
     const typename GraphType::vertex_type& vertex,
     const types::id_type source_id,
-    const vertex_callback<GraphType, bool>& visit_vertex_pred,
-    const vertex_callback<GraphType, void, types::id_type>& visit,
-    const vertex_callback<GraphType, bool, const typename GraphType::edge_type&>& enque_vertex_pred,
+    const types::vertex_callback<GraphType, bool>& visit_vertex_pred,
+    const types::vertex_callback<GraphType, void, types::id_type>& visit,
+    const types::vertex_callback<GraphType, bool, const typename GraphType::edge_type&>&
+        enque_vertex_pred,
     const PreVisitCallback& pre_visit = {},
     const PostVisitCallback& post_visit = {}
 ) {
     if (not visit_vertex_pred(vertex))
         return;
 
-    if constexpr (not type_traits::is_empty_callback_v<PreVisitCallback>)
+    if constexpr (not type_traits::c_empty_callback<PreVisitCallback>)
         pre_visit(vertex);
 
     visit(vertex, source_id);
@@ -89,7 +91,7 @@ void rdfs_impl(
             );
     }
 
-    if constexpr (not type_traits::is_empty_callback_v<PostVisitCallback>)
+    if constexpr (not type_traits::c_empty_callback<PostVisitCallback>)
         post_visit(vertex);
 }