YT-CPPGL-56: Replace the usage of pointers for vertex storage to a simple composite type [Part 2]

- Modified the `edge_descriptor` class to store only the IDs of its incident vertices
- Aligned graph implementation to use vertex IDs instead of descriptor objects for internal operations
- Aligned algorithms to use vertex-ID-based callbacks

Author: SpectraL519

README.md

@@ -114,7 +114,7 @@ While the `gl::graph` class is the key element of the library, it's not the only
 - [The vertex and edge classes - representation of the graph's elements](/docs/graph_elements.md)
 - [I/O operations](/docs/io.md)
 - [Graph topology generators](/docs/topologies.md)
-- [Algorithms](/docs/algoithms.md)
+- [Algorithms](/docs/algorithms.md)
 - [Core utility types](/docs/core_util_types.md)
 - [Additional functionality](/docs/additional_functionality.md)
 

docs/algoithms.md docs/algorithms.mddocs/algoithms.md renamed to docs/algorithms.md

@@ -551,5 +551,5 @@ This section provides links to additional resources and documentation that can h
 - [The vertex and edge classes - representation of the graph's elements](/docs/graph_elements.md)
 - [I/O operations](/docs/io.md)
 - [Graph topology generators](/docs/topologies.md)
-- [Algorithms](/docs/algoithms.md)
+- [Algorithms](/docs/algorithms.md)
 - [Core utility types](/docs/core_util_types.md)

docs/graph.md

@@ -87,8 +87,6 @@ By default, the `edge_descriptor` class does not carry any properties and assume
 
 ### Template parameters
 
-- **`VertexType`**: The type of the vertex descriptors connected by this edge.
-  - *Constraints*: must satisfy the **`type_traits::c_instantiation_of<vertex_descriptor>`** concept
 - **`DirectionalTag`**: A tag type indicating whether the edge is directed or undirected.
   - *Default value*: `directed_t`
   - *Constraints*: must satisfy the **`type_traits::c_edge_directional_tag`** concept (either `directed_t` or `undirected_t`)
@@ -99,15 +97,14 @@ By default, the `edge_descriptor` class does not carry any properties and assume
 ### Member types
 
 - **`type`**: Alias for the `edge_descriptor` itself.
-- **`vertex_type`**: Type of the vertex descriptors connected by this edge.
 - **`directional_tag`**: The tag indicating whether the edge is directed or undirected.
 - **`properties_type`**: Type of the edge properties as defined by the `Properties` template parameter.
 
 ### Constructors
 
-- **`edge_descriptor(const vertex_type& first, const vertex_type& second)`**:
+- **`edge_descriptor(const types::id_type first, const types::id_type second)`**:
   - Constructs an edge between two vertices.
-- **`edge_descriptor(const vertex_type& first, const vertex_type& second, const properties_type& properties)`**:
+- **`edge_descriptor(const types::id_type first, const types::id_type second, const properties_type& properties)`**:
   - Constructs an edge between two vertices with specified properties.
   - *Constraints*: the `properties_type` must be non-default.
 - **Move constructor and assignment operator**: *default*
@@ -133,88 +130,48 @@ The destructor is *defaulted*, allowing proper cleanup of the `edge_descriptor`
 - **`incident_vertices() const`**:
   - *Description*: Returns a pair of references to the two vertices connected by the edge.
   - *Returned value*: $(u, v)$
-  - *Return type*: `types::homogeneous_pair<const vertex_type&>`
-
-- **`incident_vertex_ids() const`**:
-  - *Description*: Returns the unique IDs of the vertices connected by the edge.
-  - *Returned value*: $(u_{id}, v_{id})$
-  - *Return type*: `types::homogeneous_pair<types::id_type>`
+  - *Return type*: `types::homogeneous_pair<const types::id_type>`
 
 - **`first() const`**:
   - *Description*: Returns a reference to the first vertex of the edge.
   - *Returned value*: $u$
-  - *Return type*: `const vertex_type&`
+  - *Return type*: `types::id_type`
 
 - **`second() const`**:
   - *Description*: Returns a reference to the second vertex of the edge.
   - *Returned value*: $v$
-  - *Return type*: `const vertex_type&`
+  - *Return type*: `const types::id_type`
 
-- **`incident_vertex(vertex) const`**:
+- **`incident_vertex(vertex_id) const`**:
   - *Description*: Returns the vertex on the other end of the edge relative to the provided vertex. Throws an error if the provided vertex is not incident with the edge.
   - *Returned value*:
-    - $v$ if $\text{vertex} = u$
-    - $u$ if $\text{vertex} = v$
+    - $v$ if $\text{vertex-id} = u$
+    - $u$ if $\text{vertex-id} = v$
     - error otherwise
   - *Parameters*:
-    - `vertex: const vertex_type&` – the vertex for which the opposite vertex is requested.
-  - *Return type*: `const vertex_type&`
-
-- **`incident_vertex(vertex_id) const`**:
-  - *Description*: Returns the vertex on the other end of the edge relative to the provided vertex ID. Throws an error if the provided vertex ID is invalid.
-  - *Returned value*:
-    - $v$ if $\text{vertex-id} = u_{id}$
-    - $u$ if $\text{vertex-id} = v_{id}$
-    - error otherwise
-  - *Parameters*:
-    - `vertex_id: const types::id_type` – the vertex ID for which the opposite vertex ID is requested.
-  - *Return type*: `types::id_type`
-
-- **`is_incident_with(vertex) const`**:
-  - *Description*: Returns `true` if the provided vertex is connected to the edge.
-  - *Returned value*: $\text{vertex} \in {u, v}$
-  - *Parameters*:
-    - `vertex: const vertex_type&` – the vertex to check for incidence with the edge.
-  - *Return type*: `bool`
+    - `vertex_id: const types::id_type` – the vertex for which the opposite vertex is requested.
+  - *Return type*: `const types::id_type`
 
 - **`is_incident_with(vertex_id) const`**:
   - *Description*: Returns `true` if a vertex with the given ID is connected to the edge.
-  - *Returned value*: $\text{vertex-id} \in {u_{id}, v_{id}}$
+  - *Returned value*: $\text{vertex-id} \in {u, v}$
   - *Parameters*:
     - `vertex_id: const types::id_type` – the vertex ID to check for incidence with the edge.
   - *Return type*: `bool`
 
-- **`is_incident_from(vertex) const`**:
-  - *Description*: Returns `true` if the provided vertex is the source of the edge (for directed edges).
-  - *Returned value*:
-    - For directed edges: $\text{vertex} = u$
-    - For undirected edges: `is_incident_with(vertex)`
-  - *Parameters*:
-    - `vertex: const vertex_type&` – the vertex to check if it is the source.
-  - *Return type*: `bool`
-
 - **`is_incident_from(vertex_id) const`**:
   - *Description*: Returns `true` if a vertex with the given ID is the source of the edge.
   - *Returned value*:
-    - For directed edges: $\text{vertex-id} = u_{id}$
-    - For undirected edges: `is_incident_with(vertex)`
+    - For directed edges: $\text{vertex-id} = u$
+    - For undirected edges: `is_incident_with(vertex_id)`
   - *Parameters*:
     - `vertex_id: const types::id_type` – the vertex ID to check if it is the source.
   - *Return type*: `bool`
 
-- **`is_incident_to(vertex) const`**:
-  - *Description*: Returns `true` if the provided vertex is the target vertex of the edge (for directed edges).
-  - *Returned value*:
-    - For directed edges: $\text{vertex} = v$
-    - For undirected edges: `is_incident_with(vertex)`
-  - *Parameters*:
-    - `vertex: const vertex_type&` – the vertex to check if it is the target.
-  - *Return type*: `bool`
-
 - **`is_incident_to(vertex_id) const`**:
   - *Description*: Returns `true` if a vertex with the given ID is the target of the edge.
   - *Returned value*:
-    - For directed edges: $\text{vertex-id} = v_{id}$
+    - For directed edges: $\text{vertex-id} = v$
     - For undirected edges: `is_incident_with(vertex)`
   - *Parameters*:
     - `vertex_id: const types::id_type` – the vertex ID to check if it is the target.
@@ -231,28 +188,23 @@ The destructor is *defaulted*, allowing proper cleanup of the `edge_descriptor`
 
   ```cpp
   template <
-      type_traits::c_instantiation_of<vertex_descriptor> VertexType,
       type_traits::c_edge_directional_tag DirectionalTag = directed_t,
       type_traits::c_properties Properties = types::empty_properties>
-  using edge = edge_descriptor<VertexType, DirectionalTag, Properties>;
+  using edge = edge_descriptor<DirectionalTag, Properties>;
   ```
 
 - `directed_edge`: An alias for `edge_descriptor` specifically for directed edges.
 
   ```cpp
-  template <
-      type_traits::c_instantiation_of<vertex_descriptor> VertexType,
-      type_traits::c_properties Properties = types::empty_properties>
-  using directed_edge = edge_descriptor<VertexType, directed_t, Properties>;
+  template <type_traits::c_properties Properties = types::empty_properties>
+  using directed_edge = edge_descriptor<directed_t, Properties>;
   ```
 
 - `undirected_edge`: An alias for `edge_descriptor` specifically for undirected edges.
 
   ```cpp
-  template <
-      type_traits::c_instantiation_of<vertex_descriptor> VertexType,
-      type_traits::c_properties Properties = types::empty_properties>
-  using undirected_edge = edge_descriptor<VertexType, undirected_t, Properties>;
+  template <type_traits::c_properties Properties = types::empty_properties>
+  using undirected_edge = edge_descriptor<undirected_t, Properties>;
   ```
 
 <br />

docs/graph_elements.md

@@ -13,10 +13,8 @@ namespace gl::algorithm {
 template <
     result_discriminator ResultDiscriminator = algorithm::ret,
     type_traits::c_graph GraphType,
-    type_traits::c_optional_vertex_callback<GraphType, void> PreVisitCallback =
-        algorithm::empty_callback,
-    type_traits::c_optional_vertex_callback<GraphType, void> PostVisitCallback =
-        algorithm::empty_callback>
+    type_traits::c_optional_id_callback<void> PreVisitCallback = algorithm::empty_callback,
+    type_traits::c_optional_id_callback<void> PostVisitCallback = algorithm::empty_callback>
 impl::alg_return_type<ResultDiscriminator, predecessors_descriptor> breadth_first_search(
     const GraphType& graph,
     const std::optional<types::id_type>& root_vertex_id_opt = no_root_vertex,
@@ -35,8 +33,8 @@ impl::alg_return_type<ResultDiscriminator, predecessors_descriptor> breadth_firs
         impl::bfs(
             graph,
             impl::init_range(root_vertex_id_opt.value()),
-            impl::default_visit_vertex_predicate<GraphType>(visited),
-            impl::default_visit_callback<GraphType, ResultDiscriminator>(visited, pd),
+            impl::default_visit_vertex_predicate(visited),
+            impl::default_visit_callback<ResultDiscriminator>(visited, pd),
             impl::default_enqueue_vertex_predicate<GraphType, true>(visited),
             pre_visit,
             post_visit
@@ -47,8 +45,8 @@ impl::alg_return_type<ResultDiscriminator, predecessors_descriptor> breadth_firs
             impl::bfs(
                 graph,
                 impl::init_range(root_id),
-                impl::default_visit_vertex_predicate<GraphType>(visited),
-                impl::default_visit_callback<GraphType, ResultDiscriminator>(visited, pd),
+                impl::default_visit_vertex_predicate(visited),
+                impl::default_visit_callback<ResultDiscriminator>(visited, pd),
                 impl::default_enqueue_vertex_predicate<GraphType, true>(visited),
                 pre_visit,
                 post_visit

include/gl/algorithm/breadth_first_search.hpp

@@ -12,10 +12,8 @@ using bicoloring_type = std::vector<types::binary_color>;
 
 template <
     type_traits::c_graph GraphType,
-    type_traits::c_optional_vertex_callback<GraphType, void> PreVisitCallback =
-        algorithm::empty_callback,
-    type_traits::c_optional_vertex_callback<GraphType, void> PostVisitCallback =
-        algorithm::empty_callback>
+    type_traits::c_optional_id_callback<void> PreVisitCallback = algorithm::empty_callback,
+    type_traits::c_optional_id_callback<void> PostVisitCallback = algorithm::empty_callback>
 [[nodiscard]] std::optional<bicoloring_type> bipartite_coloring(
     const GraphType& graph,
     const PreVisitCallback& pre_visit = {},
@@ -28,8 +26,7 @@ template <
     coloring_opt.emplace(graph.n_vertices(), bin_color_value::unset);
     auto& coloring = coloring_opt.value();
 
-    for (const auto root_vertex : graph.vertices()) {
-        const auto root_id = root_vertex.id();
+    for (const auto root_id : graph.vertex_ids()) {
         if (coloring[root_id].is_set())
             continue;
 
@@ -41,19 +38,18 @@ template <
             impl::init_range(root_id),
             algorithm::empty_callback{}, // visit predicate
             algorithm::empty_callback{}, // visit callback
-            [&coloring](const vertex_type& vertex, const edge_type& in_edge)
+            [&coloring](const types::id_type vertex_id, const edge_type& in_edge)
                 -> predicate_result { // enqueue predicate
                 if (in_edge.is_loop())
                     return false;
 
-                const auto vertex_id = vertex.id();
-                const auto source_id = in_edge.incident_vertex(vertex).id();
+                const auto pred_id = in_edge.incident_vertex(vertex_id);
 
-                if (coloring[vertex_id] == coloring[source_id])
+                if (coloring[vertex_id] == coloring[pred_id])
                     return predicate_result::unknown; // graph is not bipartite
 
-                if (not coloring[vertex.id()].is_set()) {
-                    coloring[vertex.id()] = coloring[source_id].next();
+                if (not coloring[vertex_id].is_set()) {
+                    coloring[vertex_id] = coloring[pred_id].next();
                     return true;
                 }
 

include/gl/algorithm/coloring.hpp

@@ -12,10 +12,8 @@ namespace gl::algorithm {
 template <
     result_discriminator ResultDiscriminator = algorithm::ret,
     type_traits::c_graph GraphType,
-    type_traits::c_optional_vertex_callback<GraphType, void> PreVisitCallback =
-        algorithm::empty_callback,
-    type_traits::c_optional_vertex_callback<GraphType, void> PostVisitCallback =
-        algorithm::empty_callback>
+    type_traits::c_optional_id_callback<void> PreVisitCallback = algorithm::empty_callback,
+    type_traits::c_optional_id_callback<void> PostVisitCallback = algorithm::empty_callback>
 impl::alg_return_type<ResultDiscriminator, predecessors_descriptor> depth_first_search(
     const GraphType& graph,
     const std::optional<types::id_type>& root_vertex_id_opt = no_root_vertex,
@@ -33,21 +31,21 @@ impl::alg_return_type<ResultDiscriminator, predecessors_descriptor> depth_first_
     if (root_vertex_id_opt) {
         impl::dfs(
             graph,
-            graph.get_vertex(root_vertex_id_opt.value()),
-            impl::default_visit_vertex_predicate<GraphType>(visited),
-            impl::default_visit_callback<GraphType, ResultDiscriminator>(visited, pd),
+            root_vertex_id_opt.value(),
+            impl::default_visit_vertex_predicate(visited),
+            impl::default_visit_callback<ResultDiscriminator>(visited, pd),
             impl::default_enqueue_vertex_predicate<GraphType>(visited),
             pre_visit,
             post_visit
         );
     }
     else {
-        for (const auto& root_vertex : graph.vertices())
+        for (const auto root_vertex_id : graph.vertex_ids())
             impl::dfs(
                 graph,
-                root_vertex,
-                impl::default_visit_vertex_predicate<GraphType>(visited),
-                impl::default_visit_callback<GraphType, ResultDiscriminator>(visited, pd),
+                root_vertex_id,
+                impl::default_visit_vertex_predicate(visited),
+                impl::default_visit_callback<ResultDiscriminator>(visited, pd),
                 impl::default_enqueue_vertex_predicate<GraphType>(visited),
                 pre_visit,
                 post_visit
@@ -61,10 +59,8 @@ impl::alg_return_type<ResultDiscriminator, predecessors_descriptor> depth_first_
 template <
     result_discriminator ResultDiscriminator = algorithm::ret,
     type_traits::c_graph GraphType,
-    type_traits::c_optional_vertex_callback<GraphType, void> PreVisitCallback =
-        algorithm::empty_callback,
-    type_traits::c_optional_vertex_callback<GraphType, void> PostVisitCallback =
-        algorithm::empty_callback>
+    type_traits::c_optional_id_callback<void> PreVisitCallback = algorithm::empty_callback,
+    type_traits::c_optional_id_callback<void> PostVisitCallback = algorithm::empty_callback>
 impl::alg_return_type<ResultDiscriminator, predecessors_descriptor> recursive_depth_first_search(
     const GraphType& graph,
     const std::optional<types::id_type>& root_vertex_id_opt = no_root_vertex,
@@ -83,23 +79,23 @@ impl::alg_return_type<ResultDiscriminator, predecessors_descriptor> recursive_de
         const auto root_id = root_vertex_id_opt.value();
         impl::r_dfs(
             graph,
-            graph.get_vertex(root_id),
             root_id,
-            impl::default_visit_vertex_predicate<GraphType>(visited),
-            impl::default_visit_callback<GraphType, ResultDiscriminator>(visited, pd),
+            root_id, // pred_id
+            impl::default_visit_vertex_predicate(visited),
+            impl::default_visit_callback<ResultDiscriminator>(visited, pd),
             impl::default_enqueue_vertex_predicate<GraphType>(visited),
             pre_visit,
             post_visit
         );
     }
     else {
-        for (const auto& root_vertex : graph.vertices())
+        for (const auto& root_id : graph.vertex_ids())
             impl::r_dfs(
                 graph,
-                root_vertex,
-                root_vertex.id(),
-                impl::default_visit_vertex_predicate<GraphType>(visited),
-                impl::default_visit_callback<GraphType, ResultDiscriminator>(visited, pd),
+                root_id,
+                root_id, // pred_id
+                impl::default_visit_vertex_predicate(visited),
+                impl::default_visit_callback<ResultDiscriminator>(visited, pd),
                 impl::default_enqueue_vertex_predicate<GraphType>(visited),
                 pre_visit,
                 post_visit

include/gl/algorithm/depth_first_search.hpp

@@ -65,10 +65,8 @@ template <type_traits::c_graph GraphType>
 
 template <
     type_traits::c_graph GraphType,
-    type_traits::c_optional_vertex_callback<GraphType, void> PreVisitCallback =
-        algorithm::empty_callback,
-    type_traits::c_optional_vertex_callback<GraphType, void> PostVisitCallback =
-        algorithm::empty_callback>
+    type_traits::c_optional_id_callback<void> PreVisitCallback = algorithm::empty_callback,
+    type_traits::c_optional_id_callback<void> PostVisitCallback = algorithm::empty_callback>
 [[nodiscard]] paths_descriptor_type<GraphType> dijkstra_shortest_paths(
     const GraphType& graph,
     const types::id_type source_id,
@@ -94,22 +92,21 @@ template <
         impl::init_range(source_id),
         algorithm::empty_callback{}, // visit predicate
         algorithm::empty_callback{}, // visit callback
-        [&paths, &negative_edge](const vertex_type& vertex, const edge_type& in_edge)
+        [&paths, &negative_edge](const types::id_type vertex_id, const edge_type& in_edge)
             -> predicate_result { // enqueue predicate
-            const auto vertex_id = vertex.id();
-            const auto source_id = in_edge.incident_vertex(vertex).id();
+            const auto pred_id = in_edge.incident_vertex(vertex_id);
 
             const auto edge_weight = get_weight<GraphType>(in_edge);
             if (edge_weight < constants::zero) {
                 negative_edge = std::cref(in_edge);
                 return predicate_result::unknown;
             }
 
-            const auto new_distance = paths.distances[source_id] + edge_weight;
+            const auto new_distance = paths.distances[pred_id] + edge_weight;
             if (not paths.predecessors[vertex_id].has_value()
                 or new_distance < paths.distances[vertex_id]) {
                 paths.distances[vertex_id] = new_distance;
-                paths.predecessors[vertex_id].emplace(source_id);
+                paths.predecessors[vertex_id].emplace(pred_id);
                 return true;
             }
 
@@ -121,8 +118,8 @@ template <
         const auto& edge = negative_edge.value().get();
         throw std::invalid_argument(std::format(
             "[alg::dijkstra_shortest_paths] Found an edge with a negative weight: [{}, {} | w={}]",
-            edge.first().id(),
-            edge.second().id(),
+            edge.first(),
+            edge.second(),
             get_weight<GraphType>(edge)
         ));
     }