Apply Copilot recommended changes to key algorithms

Dijkstrat & Bellman-Ford shortest paths

Author: pratzl

include/graph/algorithm/bellman_ford_shortest_paths.hpp

@@ -39,7 +39,7 @@ namespace graph {
  * 
  * @param g              The graph.
  * @param predecessor    The predecessor range.
- * @param cycle_vertex_id A vertex id in the negative weight cycle. IF no negative weight cycle exists 
+ * @param cycle_vertex_id A vertex id in the negative weight cycle. If no negative weight cycle exists 
  *                       then there will be no vertex id defined.
  * @param out_cycle      The output iterator that the vertex ids in the cycle are output to.
  */
@@ -84,9 +84,9 @@ void find_negative_cycle(G&                              g,
  * @tparam Predecessors The predecessor random access range.
  * @tparam WF           Edge weight function. Defaults to a function that returns 1.
  * @tparam Visitor      Visitor type with functions called for different events in the algorithm.
- *                      Function calls are removed by the optimizer if not uesd.
+ *                      Function calls are removed by the optimizer if not used.
  * @tparam Compare      Comparison function for Distance values. Defaults to less<DistanceValue>.
- * @tparam Combine      Combine function for Distance values. Defaults to plus<DistanctValue>.
+ * @tparam Combine      Combine function for Distance values. Defaults to plus<DistanceValue>.
  * 
  * @return optional<vertex_id_t<G>>, where no vertex id is returned if all edges were minimized.
  *         If an edge was not minimized, the on_edge_not_minimized event is called and a vertex id
@@ -120,7 +120,7 @@ requires convertible_to<range_value_t<Sources>, vertex_id_t<G>> &&      //
   using weight_type   = invoke_result_t<WF, edge_reference_t<G>>;
   using return_type   = optional<vertex_id_t<G>>;
 
-  // relxing the target is the function of reducing the distance from the source to the target
+  // relaxing the target is the function of reducing the distance from the source to the target
   auto relax_target = [&g, &predecessor, &distances, &compare, &combine] //
         (edge_reference_t<G> e, vertex_id_t<G> uid, const weight_type& w_e) -> bool {
     id_type             vid = target_id(g, e);
@@ -139,14 +139,14 @@ requires convertible_to<range_value_t<Sources>, vertex_id_t<G>> &&      //
 
   if (size(distances) < size(vertices(g))) {
     throw std::out_of_range(
-          std::format("bellman_ford_shortest_paths: size of distances is {} is less than the number of vertices {}",
+          std::format("bellman_ford_shortest_paths: size of distances of {} is less than the number of vertices {}",
                       size(distances), size(vertices(g))));
   }
 
   if constexpr (!is_same_v<Predecessors, _null_range_type>) {
     if (size(predecessor) < size(vertices(g))) {
       throw std::out_of_range(
-            std::format("bellman_ford_shortest_paths: size of predecessor is {} is less than the number of vertices {}",
+            std::format("bellman_ford_shortest_paths: size of predecessor of {} is less than the number of vertices {}",
                         size(predecessor), size(vertices(g))));
     }
   }
@@ -259,9 +259,9 @@ requires is_arithmetic_v<range_value_t<Distances>> &&                   //
  * @tparam Distances    The distance random access range.
  * @tparam WF           Edge weight function. Defaults to a function that returns 1.
  * @tparam Visitor      Visitor type with functions called for different events in the algorithm.
- *                      Function calls are removed by the optimizer if not uesd.
+ *                      Function calls are removed by the optimizer if not used.
  * @tparam Compare      Comparison function for Distance values. Defaults to less<DistanceValue>.
- * @tparam Combine      Combine function for Distance values. Defaults to plus<DistanctValue>.
+ * @tparam Combine      Combine function for Distance values. Defaults to plus<DistanceValue>.
  * 
  * @return optional<vertex_id_t<G>>, where no vertex id is returned if all edges were minimized.
  *         If an edge was not minimized, the on_edge_not_minimized event is called and a vertex id

include/graph/algorithm/dijkstra_clrs.hpp

@@ -11,11 +11,6 @@ template <class G, class F>
 concept edge_weight_function = // e.g. weight(uv)
       std::copy_constructible<F> && is_arithmetic_v<invoke_result_t<F, edge_reference_t<G>>>;
 
-
-//edge_weight_function<G, WF> &&
-//strict_weak_order<Compare, range_value_t<Distance>, range_value_t<Distance>> &&
-//assignable_from <range_reference_t<Distance>, invoke_result_t <Combine, invoke_result_t<WF, edge_t<G>>,
-
 template <class G, class WF, class Distance, class Compare, class Combine>
 concept basic_edge_weight_function2 = // e.g. weight(uv)
       is_arithmetic_v<range_value_t<Distance>> &&
@@ -67,8 +62,8 @@ constexpr auto print_types(Ts...) {
  * @tparam Distance The distance range type.
  * @tparam Predecessor The predecessor range type.
  *
- * @param graph The graph.
- * @param source The source vertex.
+ * @param g The graph.
+ * @param seed The source vertex.
  * @param distance The distance vector.
  * @param predecessor The predecessor vector.
  * @param weight The edge weight function.
@@ -159,7 +154,7 @@ void dijkstra_clrs(
       WF&& weight = [](edge_identifier_t<G> uv) { return range_value_t<Distance>(1); }) // default weight(uv) -> 1
 {
   using id_type         = vertex_id_t<G>;
-  using weight_type     = invoke_result_t<WF, edge_identifer_t<G>>;
+  using weight_type     = invoke_result_t<WF, edge_identifier_t<G>>;
   const id_type seed_id = vertex_id(g, seed);
 
   size_t N(num_vertices(g));

include/graph/algorithm/dijkstra_shortest_paths.hpp

@@ -29,9 +29,9 @@ namespace graph {
 /**
  * @brief Dijkstra's single-source shortest paths algorithm with a visitor.
  * 
- * The implementation was taken from boost::graph dijkstra_shortes_paths_no_init.
+ * The implementation was taken from boost::graph dijkstra_shortest_paths_no_init.
  * 
- * Complexity: O(V * E)
+ * Complexity: O((V + E) log V)
  * 
  * Pre-conditions:
  *  - 0 <= source < num_vertices(g)
@@ -52,9 +52,9 @@ namespace graph {
  * @tparam Predecessors The predecessor random access range.
  * @tparam WF           Edge weight function. Defaults to a function that returns 1.
  * @tparam Visitor      Visitor type with functions called for different events in the algorithm.
- *                      Function calls are removed by the optimizer if not uesd.
+ *                      Function calls are removed by the optimizer if not used.
  * @tparam Compare      Comparison function for Distance values. Defaults to less<distance_type>.
- * @tparam Combine      Combine function for Distance values. Defaults to plus<DistanctValue>.
+ * @tparam Combine      Combine function for Distance values. Defaults to plus<DistanceValue>.
  */
 template <index_adjacency_list G,
           input_range          Sources,
@@ -83,7 +83,7 @@ constexpr void dijkstra_shortest_paths(
   using distance_type = range_value_t<Distances>;
   using weight_type   = invoke_result_t<WF, edge_reference_t<G>>;
 
-  // relxing the target is the function of reducing the distance from the source to the target
+  // relaxing the target is the function of reducing the distance from the source to the target
   auto relax_target = [&g, &predecessor, &distances, &compare, &combine] //
         (edge_reference_t<G> e, vertex_id_t<G> uid, const weight_type& w_e) -> bool {
     const id_type       vid = target_id(g, e);
@@ -233,7 +233,7 @@ constexpr void dijkstra_shortest_paths(
 }
 
 /**
- * @brief Shortest distnaces from a single source using Dijkstra's single-source shortest paths algorithm 
+ * @brief Shortest distances from a single source using Dijkstra's single-source shortest paths algorithm 
  *         with a visitor.
  * 
  * This is identical to dijkstra_shortest_paths() except that it does not require a predecessors range.
@@ -254,9 +254,9 @@ constexpr void dijkstra_shortest_paths(
  * @tparam Distances    The distance random access range.
  * @tparam WF           Edge weight function. Defaults to a function that returns 1.
  * @tparam Visitor      Visitor type with functions called for different events in the algorithm.
- *                      Function calls are removed by the optimizer if not uesd.
+ *                      Function calls are removed by the optimizer if not used.
  * @tparam Compare      Comparison function for Distance values. Defaults to less<distance_type>.
- * @tparam Combine      Combine function for Distance values. Defaults to plus<DistanctValue>.
+ * @tparam Combine      Combine function for Distance values. Defaults to plus<DistanceValue>.
  */
 template <index_adjacency_list G,
           input_range          Sources,