From 3fe9e21881924ec5789d8e425788dfce7c9dddc0 Mon Sep 17 00:00:00 2001
From: Hromz <hromizz@gmail.com>
Date: Mon, 24 Jul 2023 19:14:49 +0300
Subject: [PATCH 01/40] - added DFS cycle detection for directed and undirected
 graph - added tests

---
 .gitignore                                    |   1 +
 include/graaflib/algorithm/cycle_detection.h  |  20 ++
 .../graaflib/algorithm/cycle_detection.tpp    |  96 ++++++++++
 .../algorithm/cycle_detection_test.cpp        | 172 ++++++++++++++++++
 4 files changed, 289 insertions(+)
 create mode 100644 include/graaflib/algorithm/cycle_detection.h
 create mode 100644 include/graaflib/algorithm/cycle_detection.tpp
 create mode 100644 test/graaflib/algorithm/cycle_detection_test.cpp

diff --git a/.gitignore b/.gitignore
index 8ee1efe7..ff15a5c4 100644
--- a/.gitignore
+++ b/.gitignore
@@ -4,3 +4,4 @@ build/
 # IDE
 .vscode/
 .cache/
+.vs/
diff --git a/include/graaflib/algorithm/cycle_detection.h b/include/graaflib/algorithm/cycle_detection.h
new file mode 100644
index 00000000..539843b7
--- /dev/null
+++ b/include/graaflib/algorithm/cycle_detection.h
@@ -0,0 +1,20 @@
+#pragma once
+
+#include <graaflib/graph.h>
+#include <graaflib/types.h>
+
+#include <concepts>
+
+namespace graaf::algorithm {
+
+/*
+ * @breif Traverses the graph and check for cycles.
+ *
+ * @param graph The graph to traverse.
+ */
+template <typename V, typename E, graph_spec S>
+bool has_cycle(const graph<V, E, S> &graph);
+
+}  // namespace graaf::algorithm
+
+#include "cycle_detection.tpp"
\ No newline at end of file
diff --git a/include/graaflib/algorithm/cycle_detection.tpp b/include/graaflib/algorithm/cycle_detection.tpp
new file mode 100644
index 00000000..53e1a29b
--- /dev/null
+++ b/include/graaflib/algorithm/cycle_detection.tpp
@@ -0,0 +1,96 @@
+#pragma once
+
+#include <algorithm>
+#include <unordered_map>
+
+namespace graaf::algorithm {
+
+namespace detail {
+
+enum vertex_color{WHITE, GREY, BLACK};
+
+template <typename V, typename E, graph_spec S>
+bool do_dfs_directed(const graph<V, E, S>& graph,
+                     std::unordered_map<vertex_id_t, int>& colored_vertices,
+                     vertex_id_t current) {
+  colored_vertices[current] = vertex_color::GREY;
+
+  for (const auto& neighbour_vertex : graph.get_neighbors(current)) {
+    if (colored_vertices[neighbour_vertex] == vertex_color::WHITE) {
+        if (do_dfs_directed(graph, colored_vertices, neighbour_vertex))
+            return true;
+    } 
+    else if (colored_vertices[neighbour_vertex] == vertex_color::GREY) {
+      return true;
+    }
+  }
+
+  colored_vertices[current] = vertex_color::BLACK;
+  return false;
+}
+
+template<typename V, typename E, graph_spec S>
+bool do_dfs_undirected(const graph<V,E,S> & graph, 
+    std::unordered_map<vertex_id_t, bool> & visited_vertices,
+    std::unordered_map<vertex_id_t, vertex_id_t> & parent_vertices,
+    vertex_id_t parent_vertex, vertex_id_t current) {
+
+    visited_vertices[current] = true;
+
+    for (const auto& neighbour_vertex : graph.get_neighbors(current)) {
+        if (neighbour_vertex == parent_vertex) 
+            continue;
+
+        if (visited_vertices[neighbour_vertex]) 
+            return true;
+
+        parent_vertices[neighbour_vertex] = parent_vertex;
+
+        if (do_dfs_undirected(graph, visited_vertices, parent_vertices, neighbour_vertex,
+                            parent_vertices[neighbour_vertex])) {
+                                     return true;
+        }
+    }
+
+    return false;
+}
+
+}  // namespace detail
+
+template <typename V, typename E, graph_spec S>
+bool has_cycle(const graph<V, E, S>& graph) {
+
+
+  if (graph.is_directed()) {
+        std::unordered_map<vertex_id_t, int> colored_vertices{};
+
+        for (const auto& vertex : graph.get_vertices()) {
+            if (!colored_vertices.contains(vertex.first) &&
+                detail::do_dfs_directed(graph, colored_vertices, vertex.first)) {
+                        return true;
+            }
+        }
+
+    return false;
+  }
+
+  if (graph.is_undirected()) {
+        std::unordered_map<vertex_id_t, bool> visited_vertices{};
+        std::unordered_map<vertex_id_t, vertex_id_t> parent_vertices{};
+
+        for (const auto& vertex : graph.get_vertices()) {
+            if (!visited_vertices.contains(vertex.first) &&
+                 detail::do_dfs_undirected(graph, visited_vertices, parent_vertices,
+                                      vertex.first, parent_vertices[vertex.first])) {
+                         return true;
+            }
+        }
+  }
+
+  return false;
+
+  // We should never reach this
+  std::abort();
+}
+
+}  // namespace graaf::algorithm
\ No newline at end of file
diff --git a/test/graaflib/algorithm/cycle_detection_test.cpp b/test/graaflib/algorithm/cycle_detection_test.cpp
new file mode 100644
index 00000000..4383a50b
--- /dev/null
+++ b/test/graaflib/algorithm/cycle_detection_test.cpp
@@ -0,0 +1,172 @@
+#include <graaflib/algorithm/cycle_detection.h>
+#include <graaflib/directed_graph.h>
+#include <graaflib/types.h>
+#include <graaflib/undirected_graph.h>
+#include <gtest/gtest.h>
+
+#include <unordered_map>
+#include <unordered_set>
+#include <utility>
+
+namespace graaf::algorithm {
+
+namespace {
+
+template <typename T>
+struct GraphCycleTest : public testing::Test {
+  using graph_t = T;
+};
+
+using graph_types =
+    testing::Types<directed_graph<int, int>, undirected_graph<int, int>>;
+TYPED_TEST_SUITE(GraphCycleTest, graph_types);
+
+}  // namespace
+
+TYPED_TEST(GraphCycleTest, GraphWithCycle) {
+  // GIVEN
+  directed_graph<int, int> graph{};
+
+  // graph vertices
+  const auto vertex_1{graph.add_vertex(10)};
+  const auto vertex_2{graph.add_vertex(20)};
+  const auto vertex_3{graph.add_vertex(30)};
+
+  // adding edges to our graph
+  graph.add_edge(vertex_1, vertex_2, 100);
+  graph.add_edge(vertex_2, vertex_3, 300);
+  graph.add_edge(vertex_3, vertex_1, 300);
+
+  // checking if graph contains cycles
+  bool cycle = has_cycle(graph);
+  ASSERT_TRUE(cycle);
+}
+
+TYPED_TEST(GraphCycleTest, DirectedGraphWithCycleMiddle) {
+  // GIVEN
+  directed_graph<int, int> graph{};
+
+  // graph vertices
+  const auto vertex_1{graph.add_vertex(10)};
+  const auto vertex_2{graph.add_vertex(20)};
+  const auto vertex_3{graph.add_vertex(30)};
+
+  // adding edges to our graph
+  graph.add_edge(vertex_1, vertex_2, 100);
+  graph.add_edge(vertex_2, vertex_3, 300);
+  graph.add_edge(vertex_2, vertex_1, 300);
+
+  // checking if graph contains cycle
+  bool cycle = has_cycle(graph);
+  ASSERT_TRUE(cycle);
+}
+
+TYPED_TEST(GraphCycleTest, GraphWithoutCycle) {
+  // GIVEN
+  directed_graph<int, int> graph{};
+
+  // graph vertices
+  const auto vertex_1{graph.add_vertex(10)};
+  const auto vertex_2{graph.add_vertex(20)};
+  const auto vertex_3{graph.add_vertex(30)};
+
+  // adding edges to our graph
+  graph.add_edge(vertex_1, vertex_2, 100);
+  graph.add_edge(vertex_2, vertex_3, 300);
+
+  // checking if graph contains cycle
+  bool cycle = has_cycle(graph);
+  ASSERT_FALSE(cycle);
+}
+
+TYPED_TEST(GraphCycleTest, UndirectedGraphWithoutCycle) {
+  // GIVEN
+  undirected_graph<int, int> graph{};
+
+  // graph vertices
+  const auto vertex_1{graph.add_vertex(10)};
+  const auto vertex_2{graph.add_vertex(20)};
+  const auto vertex_3{graph.add_vertex(30)};
+
+  // adding edges to our graph
+  graph.add_edge(vertex_1, vertex_2, 100);
+  graph.add_edge(vertex_2, vertex_3, 300);
+
+  // checking if graph contains cycle
+  bool cycle = has_cycle(graph);
+  ASSERT_FALSE(cycle);
+}
+
+TYPED_TEST(GraphCycleTest, UndirectedGraphWithCycle) {
+  // GIVEN
+  undirected_graph<int, int> graph{};
+
+  // graph vertices
+  const auto vertex_1{graph.add_vertex(10)};
+  const auto vertex_2{graph.add_vertex(20)};
+  const auto vertex_3{graph.add_vertex(30)};
+
+  // adding edges to our graph
+  graph.add_edge(vertex_1, vertex_2, 100);
+  graph.add_edge(vertex_2, vertex_3, 300);
+  graph.add_edge(vertex_3, vertex_1, 400);
+
+  // checking if graph contains cycle
+  bool cycle = has_cycle(graph);
+  ASSERT_TRUE(cycle);
+}
+
+TYPED_TEST(GraphCycleTest, EmptyGraphs) {
+  // GIVEN
+  directed_graph<int, int> directed_graph{};
+  undirected_graph<int, int> undirected_graph{};
+
+  // checking if graph contains cycles
+  bool cycle = has_cycle(directed_graph);
+  ASSERT_FALSE(cycle);
+
+  // checking  if graph contains cycles
+  cycle = has_cycle(undirected_graph);
+  ASSERT_FALSE(cycle);
+}
+
+TYPED_TEST(GraphCycleTest, DefaultGraphWithCycle) {
+  // GIVEN
+  using graph_t = typename TestFixture::graph_t;
+  graph_t graph{};
+
+  // graph vertices
+  const auto vertex_1{graph.add_vertex(10)};
+  const auto vertex_2{graph.add_vertex(20)};
+  const auto vertex_3{graph.add_vertex(30)};
+
+  // adding edges to our graph
+  graph.add_edge(vertex_1, vertex_2, 100);
+  graph.add_edge(vertex_2, vertex_3, 300);
+  graph.add_edge(vertex_3, vertex_1, 400);
+
+  // checking  if graph contains cycle
+  bool cycle = has_cycle(graph);
+  ASSERT_TRUE(cycle);
+}
+
+TYPED_TEST(GraphCycleTest, DefaultGraphWithoutCycle) {
+  // GIVEN
+  using graph_t = typename TestFixture::graph_t;
+  graph_t graph{};
+
+  // graph vertices
+  const auto vertex_1{graph.add_vertex(10)};
+  const auto vertex_2{graph.add_vertex(20)};
+  const auto vertex_3{graph.add_vertex(30)};
+
+  // adding edges to our graph
+  graph.add_edge(vertex_1, vertex_2, 100);
+  graph.add_edge(vertex_2, vertex_3, 300);
+
+  // checking if graph contains cycle
+  bool cycle = has_cycle(graph);
+  ASSERT_FALSE(cycle);
+}
+
+}  // namespace graaf::algorithm

From a6293523eac7b4e4d01b1e2b52af075d0a0d5d98 Mon Sep 17 00:00:00 2001
From: Hromz <hromizz@gmail.com>
Date: Tue, 25 Jul 2023 13:16:58 +0300
Subject: [PATCH 02/40] - corrected code according to comments

---
 include/graaflib/algorithm/cycle_detection.h  |  7 ++---
 .../graaflib/algorithm/cycle_detection.tpp    | 26 ++++++++++++-------
 .../algorithm/cycle_detection_test.cpp        |  4 +--
 3 files changed, 20 insertions(+), 17 deletions(-)

diff --git a/include/graaflib/algorithm/cycle_detection.h b/include/graaflib/algorithm/cycle_detection.h
index 539843b7..dc5889be 100644
--- a/include/graaflib/algorithm/cycle_detection.h
+++ b/include/graaflib/algorithm/cycle_detection.h
@@ -1,19 +1,16 @@
 #pragma once
 
 #include <graaflib/graph.h>
-#include <graaflib/types.h>
-
-#include <concepts>
 
 namespace graaf::algorithm {
 
 /*
- * @breif Traverses the graph and check for cycles.
+ * @breif Traverses the graph and checks for cycles.
  *
  * @param graph The graph to traverse.
  */
 template <typename V, typename E, graph_spec S>
-bool has_cycle(const graph<V, E, S> &graph);
+[[nodiscard]] bool has_cycle(const graph<V, E, S> &graph);
 
 }  // namespace graaf::algorithm
 
diff --git a/include/graaflib/algorithm/cycle_detection.tpp b/include/graaflib/algorithm/cycle_detection.tpp
index 53e1a29b..a1b25804 100644
--- a/include/graaflib/algorithm/cycle_detection.tpp
+++ b/include/graaflib/algorithm/cycle_detection.tpp
@@ -1,31 +1,32 @@
 #pragma once
 
+#include <graaflib/types.h>
+
 #include <algorithm>
 #include <unordered_map>
 
 namespace graaf::algorithm {
 
+enum vertex_color { UNVISITED, VISITED, NO_CYCLE };
 namespace detail {
 
-enum vertex_color{WHITE, GREY, BLACK};
-
 template <typename V, typename E, graph_spec S>
 bool do_dfs_directed(const graph<V, E, S>& graph,
-                     std::unordered_map<vertex_id_t, int>& colored_vertices,
+                     std::unordered_map<vertex_id_t, vertex_color>& colored_vertices,
                      vertex_id_t current) {
-  colored_vertices[current] = vertex_color::GREY;
+  colored_vertices[current] = vertex_color::VISITED;
 
   for (const auto& neighbour_vertex : graph.get_neighbors(current)) {
-    if (colored_vertices[neighbour_vertex] == vertex_color::WHITE) {
+    if (colored_vertices[neighbour_vertex] == vertex_color::UNVISITED) {
         if (do_dfs_directed(graph, colored_vertices, neighbour_vertex))
             return true;
     } 
-    else if (colored_vertices[neighbour_vertex] == vertex_color::GREY) {
+    else if (colored_vertices[neighbour_vertex] == vertex_color::VISITED) {
       return true;
     }
   }
 
-  colored_vertices[current] = vertex_color::BLACK;
+  colored_vertices[current] = vertex_color::NO_CYCLE;
   return false;
 }
 
@@ -60,12 +61,11 @@ bool do_dfs_undirected(const graph<V,E,S> & graph,
 template <typename V, typename E, graph_spec S>
 bool has_cycle(const graph<V, E, S>& graph) {
 
-
   if (graph.is_directed()) {
-        std::unordered_map<vertex_id_t, int> colored_vertices{};
+        std::unordered_map<vertex_id_t, vertex_color> colored_vertices{};
 
         for (const auto& vertex : graph.get_vertices()) {
-            if (!colored_vertices.contains(vertex.first) &&
+            if (colored_vertices[vertex.first] == UNVISITED &&
                 detail::do_dfs_directed(graph, colored_vertices, vertex.first)) {
                         return true;
             }
@@ -75,6 +75,11 @@ bool has_cycle(const graph<V, E, S>& graph) {
   }
 
   if (graph.is_undirected()) {
+    // Number of vertices cannot be zero (in case if graph is empty)
+    if (graph.edge_count() >= graph.vertex_count() && graph.vertex_count() > 0) {
+         return true;
+    }
+
         std::unordered_map<vertex_id_t, bool> visited_vertices{};
         std::unordered_map<vertex_id_t, vertex_id_t> parent_vertices{};
 
@@ -91,6 +96,7 @@ bool has_cycle(const graph<V, E, S>& graph) {
 
   // We should never reach this
   std::abort();
+  return false;
 }
 
 }  // namespace graaf::algorithm
\ No newline at end of file
diff --git a/test/graaflib/algorithm/cycle_detection_test.cpp b/test/graaflib/algorithm/cycle_detection_test.cpp
index 4383a50b..8c07e0b5 100644
--- a/test/graaflib/algorithm/cycle_detection_test.cpp
+++ b/test/graaflib/algorithm/cycle_detection_test.cpp
@@ -23,7 +23,7 @@ TYPED_TEST_SUITE(GraphCycleTest, graph_types);
 
 }  // namespace
 
-TYPED_TEST(GraphCycleTest, GraphWithCycle) {
+TYPED_TEST(GraphCycleTest, DirectedGraphWithCycle) {
   // GIVEN
   directed_graph<int, int> graph{};
 
@@ -61,7 +61,7 @@ TYPED_TEST(GraphCycleTest, DirectedGraphWithCycleMiddle) {
   ASSERT_TRUE(cycle);
 }
 
-TYPED_TEST(GraphCycleTest, GraphWithoutCycle) {
+TYPED_TEST(GraphCycleTest, DirectedGraphWithoutCycle) {
   // GIVEN
   directed_graph<int, int> graph{};
 

From 99f77cd152e9990c52b85cf1b19632cd5928daca Mon Sep 17 00:00:00 2001
From: Bob Luppes <bobluppes@gmail.com>
Date: Tue, 25 Jul 2023 22:38:37 +0200
Subject: [PATCH 03/40] Apply suggestions from code review

---
 include/graaflib/algorithm/cycle_detection.h   |  2 +-
 include/graaflib/algorithm/cycle_detection.tpp | 10 ++++------
 2 files changed, 5 insertions(+), 7 deletions(-)

diff --git a/include/graaflib/algorithm/cycle_detection.h b/include/graaflib/algorithm/cycle_detection.h
index dc5889be..31522c93 100644
--- a/include/graaflib/algorithm/cycle_detection.h
+++ b/include/graaflib/algorithm/cycle_detection.h
@@ -5,7 +5,7 @@
 namespace graaf::algorithm {
 
 /*
- * @breif Traverses the graph and checks for cycles.
+ * @brief Traverses the graph and checks for cycles.
  *
  * @param graph The graph to traverse.
  */
diff --git a/include/graaflib/algorithm/cycle_detection.tpp b/include/graaflib/algorithm/cycle_detection.tpp
index a1b25804..7af5c12a 100644
--- a/include/graaflib/algorithm/cycle_detection.tpp
+++ b/include/graaflib/algorithm/cycle_detection.tpp
@@ -7,9 +7,10 @@
 
 namespace graaf::algorithm {
 
-enum vertex_color { UNVISITED, VISITED, NO_CYCLE };
 namespace detail {
 
+enum class vertex_color { UNVISITED, VISITED, NO_CYCLE };
+
 template <typename V, typename E, graph_spec S>
 bool do_dfs_directed(const graph<V, E, S>& graph,
                      std::unordered_map<vertex_id_t, vertex_color>& colored_vertices,
@@ -62,9 +63,10 @@ template <typename V, typename E, graph_spec S>
 bool has_cycle(const graph<V, E, S>& graph) {
 
   if (graph.is_directed()) {
-        std::unordered_map<vertex_id_t, vertex_color> colored_vertices{};
+        std::unordered_map<vertex_id_t, detail::vertex_color> colored_vertices{};
 
         for (const auto& vertex : graph.get_vertices()) {
+            using enum detail::vertex_color;
             if (colored_vertices[vertex.first] == UNVISITED &&
                 detail::do_dfs_directed(graph, colored_vertices, vertex.first)) {
                         return true;
@@ -93,10 +95,6 @@ bool has_cycle(const graph<V, E, S>& graph) {
   }
 
   return false;
-
-  // We should never reach this
-  std::abort();
-  return false;
 }
 
 }  // namespace graaf::algorithm
\ No newline at end of file

From 432b6b437212f4ebc50a8cb13d31bedb4cfad652 Mon Sep 17 00:00:00 2001
From: Hromz <hromizz@gmail.com>
Date: Tue, 1 Aug 2023 22:37:59 +0300
Subject: [PATCH 04/40] - First example of potential use of the library

---
 .../example-basics/transport-example.md       | 118 ++++++++++++++
 .../example_shortest_path_unweighted.png      | Bin 0 -> 56583 bytes
 .../example_shortest_path_weighted.png        | Bin 0 -> 56731 bytes
 .../examples/example_traversed_graph_BFS.png  | Bin 0 -> 53759 bytes
 docs/static/img/examples/example_usage.png    | Bin 0 -> 55425 bytes
 examples/CMakeLists.txt                       |   2 +-
 examples/transport/main.cpp                   | 154 ++++++++++++++++++
 7 files changed, 273 insertions(+), 1 deletion(-)
 create mode 100644 docs/docs/examples/example-basics/transport-example.md
 create mode 100644 docs/static/img/examples/example_shortest_path_unweighted.png
 create mode 100644 docs/static/img/examples/example_shortest_path_weighted.png
 create mode 100644 docs/static/img/examples/example_traversed_graph_BFS.png
 create mode 100644 docs/static/img/examples/example_usage.png
 create mode 100644 examples/transport/main.cpp

diff --git a/docs/docs/examples/example-basics/transport-example.md b/docs/docs/examples/example-basics/transport-example.md
new file mode 100644
index 00000000..cecac7f6
--- /dev/null
+++ b/docs/docs/examples/example-basics/transport-example.md
@@ -0,0 +1,118 @@
+---
+sidebar_position: 2
+---
+
+# Network Example
+The undirected_graph implemented in `graaf::undirected_graph`
+The shortest path algorithm implemented in `graaf::algorithm::get_shortest_path`
+The graph traversal implemented in `graaf::algorithm::graph_traversal`
+
+Using the following graph:
+
+<pre>
+<p align="center">
+    <img src={require("\static\img\examples\example_usage.png").default}></img>
+</p>
+</pre>
+
+Custom vertex and edge. In order to use Dijkstra, we should provide the get_weight() function for the edge.
+
+```c++
+struct station {
+    int id{};
+	std::string name{};
+    double gaz_capacity{};
+};
+
+struct road {
+	int length{};
+    int get_weight() { return length; }
+};
+```
+
+# Initializing graph, start and end vertecies
+First, we create data structure and initializing graph with vertices and edges
+
+```c++
+struct graph_with_start_and_target {
+    graaf::undirected_graph<station, road> graph{};
+    graaf::vertex_id_t start{};
+    graaf::vertex_id_t target{};
+};
+
+graph_with_start_and_target create_graph_with_start_and_target() {
+...
+}
+```
+
+## Visualizing graph traversal result
+For shortest path, colouring edges with red to indicate the shortest path for both weighted and unweighted graph
+
+Result of unweighted shortest path, chosen edges are coloured red
+<pre>
+<p align="center">
+    <img src={require("\static\img\examples\example_shortest_path_unweighted.png").default}></img>
+</p>
+</pre>
+
+Result of weighted shortest path, chosen edges are coloured red
+<pre>
+<p align="center">
+    <img src={require("\static\img\examples\example_shortest_path_weighted.png").default}></img>
+</p>
+</pre>
+
+
+```c++
+void print_shortest_path(const graaf::undirected_graph<station, road>& graph,
+                const std::optional<graaf::algorithm::GraphPath<int>>& path, const std::string & filepath) {
+...
+}
+
+void print_visited_vertices(const graaf::undirected_graph<station, road>& graph,
+                            seen_vertices_t& seen,
+                            const std::string& filepath) {
+...
+}
+```
+
+Creating a vertex callback structure that will be passed as an argument in the graph traverse function
+The function is needed in order to be called inside the traverse function; see graph.tpp file lines 15 and 45 for context.
+
+```c++
+using seen_vertices_t = std::unordered_multiset<graaf::vertex_id_t>;
+struct record_vertex_callback {
+    seen_vertices_t& seen_vertices;
+
+    record_vertex_callback(seen_vertices_t& seen_vertices)
+        : seen_vertices{seen_vertices} {}
+
+    void operator()(const graaf::vertex_id_t vertex) const {
+        seen_vertices.insert(vertex);
+    }
+};
+```
+
+### Graph example usage
+First code block: traversing a weighted graph for the shortest path (Dijkstra) and printing the result to *.dot file.
+Second code block: traversing an unweighted graph for the shortest path and printing the result to *.dot file.
+The last one is traversing the graph from a given vertex and printing the result to *.dot file.
+
+```c++
+ const auto [graph, start, target]{create_graph_with_start_and_target()};
+
+    const auto weighted_shortest_path{graaf::algorithm::get_shortest_path<
+            graaf::algorithm::edge_strategy::WEIGHTED, station, road,
+            graaf::graph_spec::UNDIRECTED, int>(graph, start, target)};
+    print_shortest_path(graph, weighted_shortest_path, "example_weighted_graph.dot");
+
+    const auto unweighted_shortest_path{graaf::algorithm::get_shortest_path<
+        graaf::algorithm::edge_strategy::UNWEIGHTED, station, road,
+        graaf::graph_spec::UNDIRECTED, int>(graph, start, target)};
+    print_shortest_path(graph, unweighted_shortest_path, "example_unwieghted_graph.dot");
+
+    seen_vertices_t seen_vertices{};
+    graaf::algorithm::traverse<graaf::algorithm::search_strategy::BFS>(
+        graph, start, record_vertex_callback{seen_vertices});
+    print_visited_vertices(graph, seen_vertices, "example_traverse_BFS_graph.dot");
+```
\ No newline at end of file
diff --git a/docs/static/img/examples/example_shortest_path_unweighted.png b/docs/static/img/examples/example_shortest_path_unweighted.png
new file mode 100644
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diff --git a/examples/CMakeLists.txt b/examples/CMakeLists.txt
index 6b5ca537..2654a56f 100644
--- a/examples/CMakeLists.txt
+++ b/examples/CMakeLists.txt
@@ -17,7 +17,7 @@ foreach (EXAMPLE ${EXAMPLES})
     add_executable(
         ${PROJECT_NAME}_${EXAMPLE_NAME}_example
         ${EXAMPLE}
-    )
+     )
 
     # Include src such that we can #include <graaflib/*> in the sources
     target_include_directories(${PROJECT_NAME}_${EXAMPLE_NAME}_example PUBLIC ${CMAKE_CURRENT_SOURCE_DIR}/../include)
diff --git a/examples/transport/main.cpp b/examples/transport/main.cpp
new file mode 100644
index 00000000..ef7a6445
--- /dev/null
+++ b/examples/transport/main.cpp
@@ -0,0 +1,154 @@
+#include <fmt/core.h>
+#include <graaflib/algorithm/graph_traversal.h>
+#include <graaflib/algorithm/shortest_path.h>
+#include <graaflib/io/dot.h>
+#include <graaflib/types.h>
+#include <graaflib/undirected_graph.h>
+
+struct station {
+  std::string name{};
+  double gaz_capacity{};
+};
+
+struct road {
+  int length{};
+  int get_weight() { return length; }
+};
+
+struct graph_with_start_and_target {
+  graaf::undirected_graph<station, road> graph{};
+  graaf::vertex_id_t start{};
+  graaf::vertex_id_t target{};
+};
+
+graph_with_start_and_target create_graph_with_start_and_target() {
+  graaf::undirected_graph<station, road> my_stations{};
+
+  const auto station_1{my_stations.add_vertex(station{"Road 66", 13.5})};
+  const auto station_2{my_stations.add_vertex(station{"Long road", 7.3})};
+  const auto station_3{my_stations.add_vertex(station{"Stop & Buy", 25.4})};
+  const auto station_4{my_stations.add_vertex(station{"GAZilla", 11.3})};
+  const auto station_5{my_stations.add_vertex(station{"Station 32", 73.12})};
+  const auto station_6{my_stations.add_vertex(station{"Last stop", 0.5})};
+  const auto station_7{my_stations.add_vertex(station{"You won't reach it", 55.5})};
+  const auto station_8{my_stations.add_vertex(station{"Went for lunch break", 66.5})};
+
+  my_stations.add_edge(station_1, station_2, road{125});
+  my_stations.add_edge(station_2, station_4, road{205});
+  my_stations.add_edge(station_4, station_5, road{325});
+  my_stations.add_edge(station_5, station_3, road{1725});
+  my_stations.add_edge(station_6, station_3, road{88});
+  my_stations.add_edge(station_1, station_5, road{77});
+  my_stations.add_edge(station_5, station_2, road{93});
+  my_stations.add_edge(station_5, station_6, road{193});
+  my_stations.add_edge(station_7, station_8, road{5});
+
+  return {my_stations, station_1, station_3};
+}
+
+void print_shortest_path(const graaf::undirected_graph<station, road>& graph,
+        const std::optional<graaf::algorithm::GraphPath<int>>& path,
+        const std::string& filepath) {
+
+    auto shortest_path{path.value()};
+    std::unordered_set<graaf::edge_id_t, graaf::edge_id_hash>
+        edges_on_shortest_path{};
+
+    graaf::vertex_id_t prev{shortest_path.vertices.front()};
+    shortest_path.vertices.pop_front();
+    for (const auto current : shortest_path.vertices) {
+         edges_on_shortest_path.insert(std::make_pair(prev, current));
+         prev = current;
+    }
+
+    const auto vertex_writer{
+        [](graaf::vertex_id_t vertex_id, station vertex) -> std::string {
+        const auto style{"solid"};
+        return fmt::format("label=\"{}: {}\", style={}, color=black, fontcolor=black",
+                            vertex.name, style);
+    }};
+
+    const auto edge_writer{[&edges_on_shortest_path](
+                                const graaf::edge_id_t& edge_id,
+                                const auto& edge) -> std::string {
+        const auto style{"solid"};
+        if (edges_on_shortest_path.contains({edge_id.first, edge_id.second}) ||
+            edges_on_shortest_path.contains({edge_id.second, edge_id.first})) {
+            return fmt::format("label=\"{}\", style={}, color=red, fontcolor=black",
+                                edge->length, style);
+        }
+        return fmt::format("label=\"{}\", style={}, color=black, fontcolor=black",
+                       edge->length, style);
+    }};
+
+  const std::filesystem::path output{filepath};
+  graaf::io::to_dot(graph, output, vertex_writer, edge_writer);
+}
+
+using seen_vertices_t = std::unordered_multiset<graaf::vertex_id_t>;
+struct record_vertex_callback {
+  seen_vertices_t& seen_vertices;
+
+  record_vertex_callback(seen_vertices_t& seen_vertices)
+      : seen_vertices{seen_vertices} {}
+
+  void operator()(const graaf::vertex_id_t vertex) const {
+    seen_vertices.insert(vertex);
+  }
+};
+
+void print_visited_vertices(const graaf::undirected_graph<station, road>& graph,
+                            seen_vertices_t& seen,
+                            const std::string& filepath) {
+  std::unordered_set<graaf::edge_id_t, graaf::edge_id_hash> seen_edges{};
+
+  for (const auto current : graph.get_edges()) {
+    const auto from = current.first.first;
+    const auto to = current.first.second;
+    if (seen.contains(from) && seen.contains(to)) 
+        seen_edges.insert({from, to});
+  }
+
+  const auto vertex_writer{
+      [](graaf::vertex_id_t vertex_id, station vertex) -> std::string {
+        const auto style{"solid"};
+
+        return fmt::format(
+            "label=\"{}: {}\", style={}, color=gray, fontcolor=black",
+            vertex.name, style);
+  }};
+
+  const auto edge_writer{[&seen_edges](const graaf::edge_id_t& edge_id,
+                                       const auto& edge) -> std::string {
+    const auto style{"solid"};
+
+    if (seen_edges.contains({edge_id.first, edge_id.second}) ||
+        seen_edges.contains({edge_id.second, edge_id.first}))
+            return fmt::format("label=\"{}\", style={}, color=red, fontcolor=black",
+                            edge->length, style);
+    return fmt::format("label=\"{}\", style={}, color=black, fontcolor=black",
+                       edge->length, style);
+  }};
+
+  const std::filesystem::path output{filepath};
+  graaf::io::to_dot(graph, output, vertex_writer, edge_writer);
+}
+
+int main() {
+  const auto [graph, start, target]{create_graph_with_start_and_target()};
+
+  const auto weighted_shortest_path{graaf::algorithm::get_shortest_path<
+      graaf::algorithm::edge_strategy::WEIGHTED, station, road,
+      graaf::graph_spec::UNDIRECTED, int>(graph, start, target)};
+  print_shortest_path(graph, weighted_shortest_path, "example_weighted_graph.dot");
+
+  const auto unweighted_shortest_path{graaf::algorithm::get_shortest_path<
+      graaf::algorithm::edge_strategy::UNWEIGHTED, station, road,
+      graaf::graph_spec::UNDIRECTED, int>(graph, start, target)};
+  print_shortest_path(graph, unweighted_shortest_path, "example_unwieghted_graph.dot");
+
+  seen_vertices_t seen_vertices{};
+  graaf::algorithm::traverse<graaf::algorithm::search_strategy::BFS>(
+      graph, start, record_vertex_callback{seen_vertices});
+  print_visited_vertices(graph, seen_vertices, "example_traverse_BFS_graph.dot");
+}

From 97ccea70f449122d20d2a6773033d64a03f6d978 Mon Sep 17 00:00:00 2001
From: Hromz <hromizz@gmail.com>
Date: Tue, 1 Aug 2023 23:20:15 +0300
Subject: [PATCH 05/40] - small fixes

---
 .../example_shortest_path_unweighted.png      | Bin 56583 -> 60414 bytes
 .../example_shortest_path_weighted.png        | Bin 56731 -> 60187 bytes
 .../examples/example_traversed_graph_BFS.png  | Bin 53759 -> 59640 bytes
 docs/static/img/examples/example_usage.png    | Bin 55425 -> 60003 bytes
 examples/CMakeLists.txt                       |   2 +-
 examples/transport/main.cpp                   |   8 ++++----
 6 files changed, 5 insertions(+), 5 deletions(-)

diff --git a/docs/static/img/examples/example_shortest_path_unweighted.png b/docs/static/img/examples/example_shortest_path_unweighted.png
index 850ffe90197319e4533cdca2cd26d54b7cdc3063..f2d45591fea0f1b85b7dc812e6746af5fbd74f04 100644
GIT binary patch
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diff --git a/docs/static/img/examples/example_shortest_path_weighted.png b/docs/static/img/examples/example_shortest_path_weighted.png
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diff --git a/docs/static/img/examples/example_usage.png b/docs/static/img/examples/example_usage.png
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diff --git a/examples/CMakeLists.txt b/examples/CMakeLists.txt
index 2654a56f..6b5ca537 100644
--- a/examples/CMakeLists.txt
+++ b/examples/CMakeLists.txt
@@ -17,7 +17,7 @@ foreach (EXAMPLE ${EXAMPLES})
     add_executable(
         ${PROJECT_NAME}_${EXAMPLE_NAME}_example
         ${EXAMPLE}
-     )
+    )
 
     # Include src such that we can #include <graaflib/*> in the sources
     target_include_directories(${PROJECT_NAME}_${EXAMPLE_NAME}_example PUBLIC ${CMAKE_CURRENT_SOURCE_DIR}/../include)
diff --git a/examples/transport/main.cpp b/examples/transport/main.cpp
index ef7a6445..e242bbfd 100644
--- a/examples/transport/main.cpp
+++ b/examples/transport/main.cpp
@@ -63,8 +63,8 @@ void print_shortest_path(const graaf::undirected_graph<station, road>& graph,
 
     const auto vertex_writer{
         [](graaf::vertex_id_t vertex_id, station vertex) -> std::string {
-        const auto style{"solid"};
-        return fmt::format("label=\"{}: {}\", style={}, color=black, fontcolor=black",
+        const auto style{"filled"};
+        return fmt::format("label=\"{}\", style={}, color=black, fontcolor=black, fillcolor=mediumspringgreen",
                             vertex.name, style);
     }};
 
@@ -111,10 +111,10 @@ void print_visited_vertices(const graaf::undirected_graph<station, road>& graph,
 
   const auto vertex_writer{
       [](graaf::vertex_id_t vertex_id, station vertex) -> std::string {
-        const auto style{"solid"};
+        const auto style{"filled"};
 
         return fmt::format(
-            "label=\"{}: {}\", style={}, color=gray, fontcolor=black",
+            "label=\"{}\", style={}, color=black, fontcolor=black, fillcolor=mediumspringgreen",
             vertex.name, style);
   }};
 

From 3e55e23289ff626af36168d33926f23103331670 Mon Sep 17 00:00:00 2001
From: Aleksandr <hromizz@gmail.com>
Date: Wed, 2 Aug 2023 14:53:45 +0300
Subject: [PATCH 06/40] Update transport-example.md

Corrected trailling slashes
---
 docs/docs/examples/example-basics/transport-example.md | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/docs/docs/examples/example-basics/transport-example.md b/docs/docs/examples/example-basics/transport-example.md
index cecac7f6..e49a7226 100644
--- a/docs/docs/examples/example-basics/transport-example.md
+++ b/docs/docs/examples/example-basics/transport-example.md
@@ -11,7 +11,7 @@ Using the following graph:
 
 <pre>
 <p align="center">
-    <img src={require("\static\img\examples\example_usage.png").default}></img>
+    <img src={require("/static/img/examples/example_usage.png").default}></img>
 </p>
 </pre>
 
@@ -51,14 +51,14 @@ For shortest path, colouring edges with red to indicate the shortest path for bo
 Result of unweighted shortest path, chosen edges are coloured red
 <pre>
 <p align="center">
-    <img src={require("\static\img\examples\example_shortest_path_unweighted.png").default}></img>
+    <img src={require("/static/img/examples/example_shortest_path_unweighted.png").default}></img>
 </p>
 </pre>
 
 Result of weighted shortest path, chosen edges are coloured red
 <pre>
 <p align="center">
-    <img src={require("\static\img\examples\example_shortest_path_weighted.png").default}></img>
+    <img src={require("/static/img/examples/example_shortest_path_weighted.png").default}></img>
 </p>
 </pre>
 
@@ -115,4 +115,4 @@ The last one is traversing the graph from a given vertex and printing the result
     graaf::algorithm::traverse<graaf::algorithm::search_strategy::BFS>(
         graph, start, record_vertex_callback{seen_vertices});
     print_visited_vertices(graph, seen_vertices, "example_traverse_BFS_graph.dot");
-```
\ No newline at end of file
+```

From 419b6630ba462c0554d24051eaf3febeb59db56b Mon Sep 17 00:00:00 2001
From: Bob Luppes <bobluppes@gmail.com>
Date: Sat, 5 Aug 2023 15:07:47 +0200
Subject: [PATCH 07/40] clang format fix

---
 examples/transport/main.cpp | 89 ++++++++++++++++++++-----------------
 1 file changed, 48 insertions(+), 41 deletions(-)

diff --git a/examples/transport/main.cpp b/examples/transport/main.cpp
index e242bbfd..bff2f8e3 100644
--- a/examples/transport/main.cpp
+++ b/examples/transport/main.cpp
@@ -30,8 +30,10 @@ graph_with_start_and_target create_graph_with_start_and_target() {
   const auto station_4{my_stations.add_vertex(station{"GAZilla", 11.3})};
   const auto station_5{my_stations.add_vertex(station{"Station 32", 73.12})};
   const auto station_6{my_stations.add_vertex(station{"Last stop", 0.5})};
-  const auto station_7{my_stations.add_vertex(station{"You won't reach it", 55.5})};
-  const auto station_8{my_stations.add_vertex(station{"Went for lunch break", 66.5})};
+  const auto station_7{
+      my_stations.add_vertex(station{"You won't reach it", 55.5})};
+  const auto station_8{
+      my_stations.add_vertex(station{"Went for lunch break", 66.5})};
 
   my_stations.add_edge(station_1, station_2, road{125});
   my_stations.add_edge(station_2, station_4, road{205});
@@ -46,40 +48,42 @@ graph_with_start_and_target create_graph_with_start_and_target() {
   return {my_stations, station_1, station_3};
 }
 
-void print_shortest_path(const graaf::undirected_graph<station, road>& graph,
-        const std::optional<graaf::algorithm::GraphPath<int>>& path,
-        const std::string& filepath) {
+void print_shortest_path(
+    const graaf::undirected_graph<station, road>& graph,
+    const std::optional<graaf::algorithm::GraphPath<int>>& path,
+    const std::string& filepath) {
+  auto shortest_path{path.value()};
+  std::unordered_set<graaf::edge_id_t, graaf::edge_id_hash>
+      edges_on_shortest_path{};
+
+  graaf::vertex_id_t prev{shortest_path.vertices.front()};
+  shortest_path.vertices.pop_front();
+  for (const auto current : shortest_path.vertices) {
+    edges_on_shortest_path.insert(std::make_pair(prev, current));
+    prev = current;
+  }
 
-    auto shortest_path{path.value()};
-    std::unordered_set<graaf::edge_id_t, graaf::edge_id_hash>
-        edges_on_shortest_path{};
+  const auto vertex_writer{
+      [](graaf::vertex_id_t vertex_id, station vertex) -> std::string {
+        const auto style{"filled"};
+        return fmt::format(
+            "label=\"{}\", style={}, color=black, fontcolor=black, "
+            "fillcolor=mediumspringgreen",
+            vertex.name, style);
+      }};
 
-    graaf::vertex_id_t prev{shortest_path.vertices.front()};
-    shortest_path.vertices.pop_front();
-    for (const auto current : shortest_path.vertices) {
-         edges_on_shortest_path.insert(std::make_pair(prev, current));
-         prev = current;
+  const auto edge_writer{[&edges_on_shortest_path](
+                             const graaf::edge_id_t& edge_id,
+                             const auto& edge) -> std::string {
+    const auto style{"solid"};
+    if (edges_on_shortest_path.contains({edge_id.first, edge_id.second}) ||
+        edges_on_shortest_path.contains({edge_id.second, edge_id.first})) {
+      return fmt::format("label=\"{}\", style={}, color=red, fontcolor=black",
+                         edge->length, style);
     }
-
-    const auto vertex_writer{
-        [](graaf::vertex_id_t vertex_id, station vertex) -> std::string {
-        const auto style{"filled"};
-        return fmt::format("label=\"{}\", style={}, color=black, fontcolor=black, fillcolor=mediumspringgreen",
-                            vertex.name, style);
-    }};
-
-    const auto edge_writer{[&edges_on_shortest_path](
-                                const graaf::edge_id_t& edge_id,
-                                const auto& edge) -> std::string {
-        const auto style{"solid"};
-        if (edges_on_shortest_path.contains({edge_id.first, edge_id.second}) ||
-            edges_on_shortest_path.contains({edge_id.second, edge_id.first})) {
-            return fmt::format("label=\"{}\", style={}, color=red, fontcolor=black",
-                                edge->length, style);
-        }
-        return fmt::format("label=\"{}\", style={}, color=black, fontcolor=black",
+    return fmt::format("label=\"{}\", style={}, color=black, fontcolor=black",
                        edge->length, style);
-    }};
+  }};
 
   const std::filesystem::path output{filepath};
   graaf::io::to_dot(graph, output, vertex_writer, edge_writer);
@@ -105,8 +109,7 @@ void print_visited_vertices(const graaf::undirected_graph<station, road>& graph,
   for (const auto current : graph.get_edges()) {
     const auto from = current.first.first;
     const auto to = current.first.second;
-    if (seen.contains(from) && seen.contains(to)) 
-        seen_edges.insert({from, to});
+    if (seen.contains(from) && seen.contains(to)) seen_edges.insert({from, to});
   }
 
   const auto vertex_writer{
@@ -114,9 +117,10 @@ void print_visited_vertices(const graaf::undirected_graph<station, road>& graph,
         const auto style{"filled"};
 
         return fmt::format(
-            "label=\"{}\", style={}, color=black, fontcolor=black, fillcolor=mediumspringgreen",
+            "label=\"{}\", style={}, color=black, fontcolor=black, "
+            "fillcolor=mediumspringgreen",
             vertex.name, style);
-  }};
+      }};
 
   const auto edge_writer{[&seen_edges](const graaf::edge_id_t& edge_id,
                                        const auto& edge) -> std::string {
@@ -124,8 +128,8 @@ void print_visited_vertices(const graaf::undirected_graph<station, road>& graph,
 
     if (seen_edges.contains({edge_id.first, edge_id.second}) ||
         seen_edges.contains({edge_id.second, edge_id.first}))
-            return fmt::format("label=\"{}\", style={}, color=red, fontcolor=black",
-                            edge->length, style);
+      return fmt::format("label=\"{}\", style={}, color=red, fontcolor=black",
+                         edge->length, style);
     return fmt::format("label=\"{}\", style={}, color=black, fontcolor=black",
                        edge->length, style);
   }};
@@ -140,15 +144,18 @@ int main() {
   const auto weighted_shortest_path{graaf::algorithm::get_shortest_path<
       graaf::algorithm::edge_strategy::WEIGHTED, station, road,
       graaf::graph_spec::UNDIRECTED, int>(graph, start, target)};
-  print_shortest_path(graph, weighted_shortest_path, "example_weighted_graph.dot");
+  print_shortest_path(graph, weighted_shortest_path,
+                      "example_weighted_graph.dot");
 
   const auto unweighted_shortest_path{graaf::algorithm::get_shortest_path<
       graaf::algorithm::edge_strategy::UNWEIGHTED, station, road,
       graaf::graph_spec::UNDIRECTED, int>(graph, start, target)};
-  print_shortest_path(graph, unweighted_shortest_path, "example_unwieghted_graph.dot");
+  print_shortest_path(graph, unweighted_shortest_path,
+                      "example_unwieghted_graph.dot");
 
   seen_vertices_t seen_vertices{};
   graaf::algorithm::traverse<graaf::algorithm::search_strategy::BFS>(
       graph, start, record_vertex_callback{seen_vertices});
-  print_visited_vertices(graph, seen_vertices, "example_traverse_BFS_graph.dot");
+  print_visited_vertices(graph, seen_vertices,
+                         "example_traverse_BFS_graph.dot");
 }

From 7e459bffc2213f56c7de0b3e126d82a00c208049 Mon Sep 17 00:00:00 2001
From: Bob Luppes <bobluppes@gmail.com>
Date: Sat, 5 Aug 2023 23:28:13 +0200
Subject: [PATCH 08/40] reflect breaking changes on main

---
 .../example-basics/transport-example.md       | 14 +++++-------
 examples/transport/main.cpp                   | 22 ++++++++-----------
 2 files changed, 14 insertions(+), 22 deletions(-)

diff --git a/docs/docs/examples/example-basics/transport-example.md b/docs/docs/examples/example-basics/transport-example.md
index e49a7226..bb8ee5b3 100644
--- a/docs/docs/examples/example-basics/transport-example.md
+++ b/docs/docs/examples/example-basics/transport-example.md
@@ -4,7 +4,7 @@ sidebar_position: 2
 
 # Network Example
 The undirected_graph implemented in `graaf::undirected_graph`
-The shortest path algorithm implemented in `graaf::algorithm::get_shortest_path`
+The shortest path algorithms implemented in `graaf::algorithm::bfs_shortest_path` and `graaf::algorithm::dijkstra_shortest_path`
 The graph traversal implemented in `graaf::algorithm::graph_traversal`
 
 Using the following graph:
@@ -65,7 +65,7 @@ Result of weighted shortest path, chosen edges are coloured red
 
 ```c++
 void print_shortest_path(const graaf::undirected_graph<station, road>& graph,
-                const std::optional<graaf::algorithm::GraphPath<int>>& path, const std::string & filepath) {
+                const std::optional<graaf::algorithm::graph_path<int>>& path, const std::string & filepath) {
 ...
 }
 
@@ -101,18 +101,14 @@ The last one is traversing the graph from a given vertex and printing the result
 ```c++
  const auto [graph, start, target]{create_graph_with_start_and_target()};
 
-    const auto weighted_shortest_path{graaf::algorithm::get_shortest_path<
-            graaf::algorithm::edge_strategy::WEIGHTED, station, road,
-            graaf::graph_spec::UNDIRECTED, int>(graph, start, target)};
+    const auto weighted_shortest_path{graaf::algorithm::dijkstra_shortest_path(graph, start, target)};
     print_shortest_path(graph, weighted_shortest_path, "example_weighted_graph.dot");
 
-    const auto unweighted_shortest_path{graaf::algorithm::get_shortest_path<
-        graaf::algorithm::edge_strategy::UNWEIGHTED, station, road,
-        graaf::graph_spec::UNDIRECTED, int>(graph, start, target)};
+    const auto unweighted_shortest_path{graaf::algorithm::bfs_shortest_path(graph, start, target)};
     print_shortest_path(graph, unweighted_shortest_path, "example_unwieghted_graph.dot");
 
     seen_vertices_t seen_vertices{};
-    graaf::algorithm::traverse<graaf::algorithm::search_strategy::BFS>(
+    graaf::algorithm::breadth_first_traverse(
         graph, start, record_vertex_callback{seen_vertices});
     print_visited_vertices(graph, seen_vertices, "example_traverse_BFS_graph.dot");
 ```
diff --git a/examples/transport/main.cpp b/examples/transport/main.cpp
index bff2f8e3..f40abae1 100644
--- a/examples/transport/main.cpp
+++ b/examples/transport/main.cpp
@@ -3,7 +3,7 @@
 #include <graaflib/algorithm/shortest_path.h>
 #include <graaflib/io/dot.h>
 #include <graaflib/types.h>
-#include <graaflib/undirected_graph.h>
+#include <graaflib/graph.h>
 
 struct station {
   std::string name{};
@@ -50,7 +50,7 @@ graph_with_start_and_target create_graph_with_start_and_target() {
 
 void print_shortest_path(
     const graaf::undirected_graph<station, road>& graph,
-    const std::optional<graaf::algorithm::GraphPath<int>>& path,
+    const std::optional<graaf::algorithm::graph_path<int>>& path,
     const std::string& filepath) {
   auto shortest_path{path.value()};
   std::unordered_set<graaf::edge_id_t, graaf::edge_id_hash>
@@ -79,10 +79,10 @@ void print_shortest_path(
     if (edges_on_shortest_path.contains({edge_id.first, edge_id.second}) ||
         edges_on_shortest_path.contains({edge_id.second, edge_id.first})) {
       return fmt::format("label=\"{}\", style={}, color=red, fontcolor=black",
-                         edge->length, style);
+                         edge.length, style);
     }
     return fmt::format("label=\"{}\", style={}, color=black, fontcolor=black",
-                       edge->length, style);
+                       edge.length, style);
   }};
 
   const std::filesystem::path output{filepath};
@@ -129,9 +129,9 @@ void print_visited_vertices(const graaf::undirected_graph<station, road>& graph,
     if (seen_edges.contains({edge_id.first, edge_id.second}) ||
         seen_edges.contains({edge_id.second, edge_id.first}))
       return fmt::format("label=\"{}\", style={}, color=red, fontcolor=black",
-                         edge->length, style);
+                         edge.length, style);
     return fmt::format("label=\"{}\", style={}, color=black, fontcolor=black",
-                       edge->length, style);
+                       edge.length, style);
   }};
 
   const std::filesystem::path output{filepath};
@@ -141,20 +141,16 @@ void print_visited_vertices(const graaf::undirected_graph<station, road>& graph,
 int main() {
   const auto [graph, start, target]{create_graph_with_start_and_target()};
 
-  const auto weighted_shortest_path{graaf::algorithm::get_shortest_path<
-      graaf::algorithm::edge_strategy::WEIGHTED, station, road,
-      graaf::graph_spec::UNDIRECTED, int>(graph, start, target)};
+  const auto weighted_shortest_path{graaf::algorithm::dijkstra_shortest_path(graph, start, target)};
   print_shortest_path(graph, weighted_shortest_path,
                       "example_weighted_graph.dot");
 
-  const auto unweighted_shortest_path{graaf::algorithm::get_shortest_path<
-      graaf::algorithm::edge_strategy::UNWEIGHTED, station, road,
-      graaf::graph_spec::UNDIRECTED, int>(graph, start, target)};
+  const auto unweighted_shortest_path{graaf::algorithm::bfs_shortest_path(graph, start, target)};
   print_shortest_path(graph, unweighted_shortest_path,
                       "example_unwieghted_graph.dot");
 
   seen_vertices_t seen_vertices{};
-  graaf::algorithm::traverse<graaf::algorithm::search_strategy::BFS>(
+  graaf::algorithm::breadth_first_traverse(
       graph, start, record_vertex_callback{seen_vertices});
   print_visited_vertices(graph, seen_vertices,
                          "example_traverse_BFS_graph.dot");

From 6fc3af0678bce37e3bd4e38b16dad5bfce8b8489 Mon Sep 17 00:00:00 2001
From: Bob Luppes <bobluppes@gmail.com>
Date: Sat, 5 Aug 2023 23:30:06 +0200
Subject: [PATCH 09/40] clang format fix

---
 examples/transport/main.cpp | 8 +++++---
 1 file changed, 5 insertions(+), 3 deletions(-)

diff --git a/examples/transport/main.cpp b/examples/transport/main.cpp
index f40abae1..332a64f0 100644
--- a/examples/transport/main.cpp
+++ b/examples/transport/main.cpp
@@ -1,9 +1,9 @@
 #include <fmt/core.h>
 #include <graaflib/algorithm/graph_traversal.h>
 #include <graaflib/algorithm/shortest_path.h>
+#include <graaflib/graph.h>
 #include <graaflib/io/dot.h>
 #include <graaflib/types.h>
-#include <graaflib/graph.h>
 
 struct station {
   std::string name{};
@@ -141,11 +141,13 @@ void print_visited_vertices(const graaf::undirected_graph<station, road>& graph,
 int main() {
   const auto [graph, start, target]{create_graph_with_start_and_target()};
 
-  const auto weighted_shortest_path{graaf::algorithm::dijkstra_shortest_path(graph, start, target)};
+  const auto weighted_shortest_path{
+      graaf::algorithm::dijkstra_shortest_path(graph, start, target)};
   print_shortest_path(graph, weighted_shortest_path,
                       "example_weighted_graph.dot");
 
-  const auto unweighted_shortest_path{graaf::algorithm::bfs_shortest_path(graph, start, target)};
+  const auto unweighted_shortest_path{
+      graaf::algorithm::bfs_shortest_path(graph, start, target)};
   print_shortest_path(graph, unweighted_shortest_path,
                       "example_unwieghted_graph.dot");
 

From 767a532d655b99fc7fb8799fa4ed37c89931c04a Mon Sep 17 00:00:00 2001
From: Hromz <hromizz@gmail.com>
Date: Sat, 12 Aug 2023 23:02:42 +0300
Subject: [PATCH 10/40] - corrected according to git comments - relative
 railway example - corrected png files

---
 .../example-basics/transport-example.md       |  20 ++--
 .../example_shortest_path_unweighted.png      | Bin 60414 -> 100225 bytes
 .../example_shortest_path_weighted.png        | Bin 60187 -> 100463 bytes
 .../examples/example_traversed_graph_BFS.png  | Bin 59640 -> 98355 bytes
 docs/static/img/examples/example_usage.png    | Bin 60003 -> 99841 bytes
 examples/transport/main.cpp                   |  99 +++++++++++-------
 6 files changed, 75 insertions(+), 44 deletions(-)

diff --git a/docs/docs/examples/example-basics/transport-example.md b/docs/docs/examples/example-basics/transport-example.md
index bb8ee5b3..05d758ff 100644
--- a/docs/docs/examples/example-basics/transport-example.md
+++ b/docs/docs/examples/example-basics/transport-example.md
@@ -1,11 +1,12 @@
 ---
-sidebar_position: 2
+sidebar_position: 3
 ---
 
 # Network Example
-The undirected_graph implemented in `graaf::undirected_graph`
-The shortest path algorithms implemented in `graaf::algorithm::bfs_shortest_path` and `graaf::algorithm::dijkstra_shortest_path`
-The graph traversal implemented in `graaf::algorithm::graph_traversal`
+This example showcases graph traversal and shortest path algorithms in an undirected graph network. As such, it demonstrates the usage of the following classes and algorithms:
+- The undirected_graph implemented in `graaf::undirected_graph`
+- The shortest path algorithm implemented in `graaf::algorithm::get_shortest_path`
+- The graph traversal implemented in `graaf::algorithm::graph_traversal`
 
 Using the following graph:
 
@@ -47,6 +48,7 @@ graph_with_start_and_target create_graph_with_start_and_target() {
 
 ## Visualizing graph traversal result
 For shortest path, colouring edges with red to indicate the shortest path for both weighted and unweighted graph
+We need to specify the start and end vertices in order to find the shortest path between the start and end vertices.
 
 Result of unweighted shortest path, chosen edges are coloured red
 <pre>
@@ -62,7 +64,6 @@ Result of weighted shortest path, chosen edges are coloured red
 </p>
 </pre>
 
-
 ```c++
 void print_shortest_path(const graaf::undirected_graph<station, road>& graph,
                 const std::optional<graaf::algorithm::graph_path<int>>& path, const std::string & filepath) {
@@ -77,7 +78,7 @@ void print_visited_vertices(const graaf::undirected_graph<station, road>& graph,
 ```
 
 Creating a vertex callback structure that will be passed as an argument in the graph traverse function
-The function is needed in order to be called inside the traverse function; see graph.tpp file lines 15 and 45 for context.
+The function is needed in order to be called inside the traverse function; see graph.tpp for context.
 
 ```c++
 using seen_vertices_t = std::unordered_multiset<graaf::vertex_id_t>;
@@ -93,6 +94,13 @@ struct record_vertex_callback {
 };
 ```
 
+Result of shortest path BFS, visited edges are coloured red
+<pre>
+<p align="center">
+    <img src={require("/static/img/examples/example_traversed_graph_BFS.png").default}></img>
+</p>
+</pre>
+
 ### Graph example usage
 First code block: traversing a weighted graph for the shortest path (Dijkstra) and printing the result to *.dot file.
 Second code block: traversing an unweighted graph for the shortest path and printing the result to *.dot file.
diff --git a/docs/static/img/examples/example_shortest_path_unweighted.png b/docs/static/img/examples/example_shortest_path_unweighted.png
index f2d45591fea0f1b85b7dc812e6746af5fbd74f04..a52e77a698f1c488714cb86c435250b21aadc807 100644
GIT binary patch
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diff --git a/docs/static/img/examples/example_shortest_path_weighted.png b/docs/static/img/examples/example_shortest_path_weighted.png
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diff --git a/docs/static/img/examples/example_traversed_graph_BFS.png b/docs/static/img/examples/example_traversed_graph_BFS.png
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diff --git a/docs/static/img/examples/example_usage.png b/docs/static/img/examples/example_usage.png
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diff --git a/examples/transport/main.cpp b/examples/transport/main.cpp
index 332a64f0..057e0ee8 100644
--- a/examples/transport/main.cpp
+++ b/examples/transport/main.cpp
@@ -7,50 +7,72 @@
 
 struct station {
   std::string name{};
-  double gaz_capacity{};
 };
 
-struct road {
-  int length{};
-  int get_weight() { return length; }
+struct railroad : public graaf::weighted_edge<double> {
+  double kilometers{};
+  [[nodiscard]] double get_weight() const noexcept override { return kilometers; }
+  railroad(double distance) : kilometers(distance) {}
 };
 
 struct graph_with_start_and_target {
-  graaf::undirected_graph<station, road> graph{};
+  graaf::undirected_graph<station, railroad> graph{};
   graaf::vertex_id_t start{};
   graaf::vertex_id_t target{};
 };
 
 graph_with_start_and_target create_graph_with_start_and_target() {
-  graaf::undirected_graph<station, road> my_stations{};
-
-  const auto station_1{my_stations.add_vertex(station{"Road 66", 13.5})};
-  const auto station_2{my_stations.add_vertex(station{"Long road", 7.3})};
-  const auto station_3{my_stations.add_vertex(station{"Stop & Buy", 25.4})};
-  const auto station_4{my_stations.add_vertex(station{"GAZilla", 11.3})};
-  const auto station_5{my_stations.add_vertex(station{"Station 32", 73.12})};
-  const auto station_6{my_stations.add_vertex(station{"Last stop", 0.5})};
-  const auto station_7{
-      my_stations.add_vertex(station{"You won't reach it", 55.5})};
-  const auto station_8{
-      my_stations.add_vertex(station{"Went for lunch break", 66.5})};
-
-  my_stations.add_edge(station_1, station_2, road{125});
-  my_stations.add_edge(station_2, station_4, road{205});
-  my_stations.add_edge(station_4, station_5, road{325});
-  my_stations.add_edge(station_5, station_3, road{1725});
-  my_stations.add_edge(station_6, station_3, road{88});
-  my_stations.add_edge(station_1, station_5, road{77});
-  my_stations.add_edge(station_5, station_2, road{93});
-  my_stations.add_edge(station_5, station_6, road{193});
-  my_stations.add_edge(station_7, station_8, road{5});
-
-  return {my_stations, station_1, station_3};
+  graaf::undirected_graph<station, railroad> my_stations{};
+
+  // Germany
+  const auto station_13{my_stations.add_vertex(station{"Hamburg"})};
+  const auto station_12{my_stations.add_vertex(station{"Bremen"})};
+  const auto station_3{my_stations.add_vertex(station{"Berlin Central Station"})};
+  const auto station_4{my_stations.add_vertex(station{"Hannover Hauptbahnhof"})};
+  const auto station_11{my_stations.add_vertex(station{"Dortmund"})};
+  const auto station_5{my_stations.add_vertex(station{"Kassel Hbf"})};
+  const auto station_2{my_stations.add_vertex(station{"Leipzig Central Station"})}; 
+  const auto station_1{my_stations.add_vertex(station{"Dresden Central Station"})};
+  const auto station_10{my_stations.add_vertex(station{"Cologne Hauptbahnhof"})};
+  const auto station_9{my_stations.add_vertex(station{"Frankfurt Hauptbahnhof"})};
+  const auto station_6{my_stations.add_vertex(station{"Nurnberg Central Station"})};
+  const auto station_8{my_stations.add_vertex(station{"Stuttgart Central Station"})};
+  const auto station_7{my_stations.add_vertex(station{"Munchen Hbf"})};
+  
+  // Canada
+  const auto station_14{my_stations.add_vertex(station{"Edmonton central station"})};
+  const auto station_15{my_stations.add_vertex(station{"Toronto Union Station"})};
+
+  my_stations.add_edge(station_1, station_2, railroad{357.3});
+  my_stations.add_edge(station_1, station_3, railroad{730.67});
+  my_stations.add_edge(station_3, station_4, railroad{533.3});
+  my_stations.add_edge(station_2, station_5, railroad{693.3});
+  my_stations.add_edge(station_2, station_4, railroad{1152});
+  my_stations.add_edge(station_4, station_5, railroad{288});
+  my_stations.add_edge(station_2, station_6, railroad{741.3});
+  my_stations.add_edge(station_5, station_6, railroad{1464});
+  my_stations.add_edge(station_7, station_6, railroad{432});
+  my_stations.add_edge(station_7, station_8, railroad{930});
+  my_stations.add_edge(station_8, station_6, railroad{1236});
+  my_stations.add_edge(station_9, station_6, railroad{840});
+  my_stations.add_edge(station_9, station_10, railroad{498});
+  my_stations.add_edge(station_10, station_11, railroad{462});
+  my_stations.add_edge(station_13, station_4, railroad{480});
+  my_stations.add_edge(station_11, station_5, railroad{822});
+  my_stations.add_edge(station_11, station_4, railroad{582});
+  my_stations.add_edge(station_11, station_12, railroad{720});
+  my_stations.add_edge(station_12, station_13, railroad{330});
+  my_stations.add_edge(station_12, station_4, railroad{486});
+  my_stations.add_edge(station_13, station_3, railroad{732});
+
+  my_stations.add_edge(station_14, station_15, railroad{9920});
+
+  return {my_stations, station_13, station_6};
 }
 
 void print_shortest_path(
-    const graaf::undirected_graph<station, road>& graph,
-    const std::optional<graaf::algorithm::graph_path<int>>& path,
+    const graaf::undirected_graph<station, railroad>& graph,
+    const std::optional<graaf::algorithm::graph_path<double>>& path,
     const std::string& filepath) {
   auto shortest_path{path.value()};
   std::unordered_set<graaf::edge_id_t, graaf::edge_id_hash>
@@ -67,7 +89,7 @@ void print_shortest_path(
       [](graaf::vertex_id_t vertex_id, station vertex) -> std::string {
         const auto style{"filled"};
         return fmt::format(
-            "label=\"{}\", style={}, color=black, fontcolor=black, "
+            "label=\"{}\", style={}, color=black, fontcolor=black, shape=rectangle,"
             "fillcolor=mediumspringgreen",
             vertex.name, style);
       }};
@@ -79,10 +101,10 @@ void print_shortest_path(
     if (edges_on_shortest_path.contains({edge_id.first, edge_id.second}) ||
         edges_on_shortest_path.contains({edge_id.second, edge_id.first})) {
       return fmt::format("label=\"{}\", style={}, color=red, fontcolor=black",
-                         edge.length, style);
+                         edge.kilometers, style);
     }
     return fmt::format("label=\"{}\", style={}, color=black, fontcolor=black",
-                       edge.length, style);
+                       edge.kilometers, style);
   }};
 
   const std::filesystem::path output{filepath};
@@ -101,7 +123,8 @@ struct record_vertex_callback {
   }
 };
 
-void print_visited_vertices(const graaf::undirected_graph<station, road>& graph,
+void print_visited_vertices(
+    const graaf::undirected_graph<station, railroad>& graph,
                             seen_vertices_t& seen,
                             const std::string& filepath) {
   std::unordered_set<graaf::edge_id_t, graaf::edge_id_hash> seen_edges{};
@@ -117,7 +140,7 @@ void print_visited_vertices(const graaf::undirected_graph<station, road>& graph,
         const auto style{"filled"};
 
         return fmt::format(
-            "label=\"{}\", style={}, color=black, fontcolor=black, "
+            "label=\"{}\", style={}, color=black, fontcolor=black, shape=rectangle,"
             "fillcolor=mediumspringgreen",
             vertex.name, style);
       }};
@@ -129,9 +152,9 @@ void print_visited_vertices(const graaf::undirected_graph<station, road>& graph,
     if (seen_edges.contains({edge_id.first, edge_id.second}) ||
         seen_edges.contains({edge_id.second, edge_id.first}))
       return fmt::format("label=\"{}\", style={}, color=red, fontcolor=black",
-                         edge.length, style);
+                         edge.kilometers, style);
     return fmt::format("label=\"{}\", style={}, color=black, fontcolor=black",
-                       edge.length, style);
+                       edge.kilometers, style);
   }};
 
   const std::filesystem::path output{filepath};

From 8ebb5f4aa992eff84c1b0f5773f5c34dcfb16081 Mon Sep 17 00:00:00 2001
From: Hromz <hromizz@gmail.com>
Date: Sat, 12 Aug 2023 23:31:48 +0300
Subject: [PATCH 11/40] small fixes

---
 examples/transport/main.cpp | 5 +++--
 1 file changed, 3 insertions(+), 2 deletions(-)

diff --git a/examples/transport/main.cpp b/examples/transport/main.cpp
index 057e0ee8..7bb01bc9 100644
--- a/examples/transport/main.cpp
+++ b/examples/transport/main.cpp
@@ -13,6 +13,7 @@ struct railroad : public graaf::weighted_edge<double> {
   double kilometers{};
   [[nodiscard]] double get_weight() const noexcept override { return kilometers; }
   railroad(double distance) : kilometers(distance) {}
+  ~railroad() {}
 };
 
 struct graph_with_start_and_target {
@@ -24,7 +25,7 @@ struct graph_with_start_and_target {
 graph_with_start_and_target create_graph_with_start_and_target() {
   graaf::undirected_graph<station, railroad> my_stations{};
 
-  // Germany
+  // Germany railway stations
   const auto station_13{my_stations.add_vertex(station{"Hamburg"})};
   const auto station_12{my_stations.add_vertex(station{"Bremen"})};
   const auto station_3{my_stations.add_vertex(station{"Berlin Central Station"})};
@@ -39,7 +40,7 @@ graph_with_start_and_target create_graph_with_start_and_target() {
   const auto station_8{my_stations.add_vertex(station{"Stuttgart Central Station"})};
   const auto station_7{my_stations.add_vertex(station{"Munchen Hbf"})};
   
-  // Canada
+  // Canada stations
   const auto station_14{my_stations.add_vertex(station{"Edmonton central station"})};
   const auto station_15{my_stations.add_vertex(station{"Toronto Union Station"})};
 

From ffe4553e0eeedca643dfe398981773b67726fcae Mon Sep 17 00:00:00 2001
From: Hromz <hromizz@gmail.com>
Date: Sun, 13 Aug 2023 00:03:31 +0300
Subject: [PATCH 12/40] small fixes

---
 .../example-basics/transport-example.md       |  43 ++++---
 examples/transport/main.cpp                   | 121 ++++++++++--------
 2 files changed, 91 insertions(+), 73 deletions(-)

diff --git a/docs/docs/examples/example-basics/transport-example.md b/docs/docs/examples/example-basics/transport-example.md
index 05d758ff..ff09f360 100644
--- a/docs/docs/examples/example-basics/transport-example.md
+++ b/docs/docs/examples/example-basics/transport-example.md
@@ -20,14 +20,16 @@ Custom vertex and edge. In order to use Dijkstra, we should provide the get_weig
 
 ```c++
 struct station {
-    int id{};
-	std::string name{};
-    double gaz_capacity{};
+  std::string name{};
 };
 
-struct road {
-	int length{};
-    int get_weight() { return length; }
+struct railroad : public graaf::weighted_edge<double> {
+  double kilometers{};
+  [[nodiscard]] double get_weight() const noexcept override {
+    return kilometers;
+  }
+  railroad(double distance) : kilometers(distance) {}
+  ~railroad() {}
 };
 ```
 
@@ -107,16 +109,21 @@ Second code block: traversing an unweighted graph for the shortest path and prin
 The last one is traversing the graph from a given vertex and printing the result to *.dot file.
 
 ```c++
- const auto [graph, start, target]{create_graph_with_start_and_target()};
-
-    const auto weighted_shortest_path{graaf::algorithm::dijkstra_shortest_path(graph, start, target)};
-    print_shortest_path(graph, weighted_shortest_path, "example_weighted_graph.dot");
-
-    const auto unweighted_shortest_path{graaf::algorithm::bfs_shortest_path(graph, start, target)};
-    print_shortest_path(graph, unweighted_shortest_path, "example_unwieghted_graph.dot");
-
-    seen_vertices_t seen_vertices{};
-    graaf::algorithm::breadth_first_traverse(
-        graph, start, record_vertex_callback{seen_vertices});
-    print_visited_vertices(graph, seen_vertices, "example_traverse_BFS_graph.dot");
+  const auto [graph, start, target]{create_graph_with_start_and_target()};
+
+  const auto weighted_shortest_path{
+      graaf::algorithm::dijkstra_shortest_path(graph, start, target)};
+  print_shortest_path(graph, weighted_shortest_path,
+                      "example_weighted_graph.dot");
+
+  const auto unweighted_shortest_path{
+      graaf::algorithm::bfs_shortest_path(graph, start, target)};
+  print_shortest_path(graph, unweighted_shortest_path,
+                      "example_unwieghted_graph.dot");
+
+  seen_vertices_t seen_vertices{};
+  graaf::algorithm::breadth_first_traverse(
+      graph, start, record_vertex_callback{seen_vertices});
+  print_visited_vertices(graph, seen_vertices,
+                         "example_traverse_BFS_graph.dot");
 ```
diff --git a/examples/transport/main.cpp b/examples/transport/main.cpp
index 7bb01bc9..db5c1ce7 100644
--- a/examples/transport/main.cpp
+++ b/examples/transport/main.cpp
@@ -11,7 +11,9 @@ struct station {
 
 struct railroad : public graaf::weighted_edge<double> {
   double kilometers{};
-  [[nodiscard]] double get_weight() const noexcept override { return kilometers; }
+  [[nodiscard]] double get_weight() const noexcept override {
+    return kilometers;
+  }
   railroad(double distance) : kilometers(distance) {}
   ~railroad() {}
 };
@@ -28,45 +30,55 @@ graph_with_start_and_target create_graph_with_start_and_target() {
   // Germany railway stations
   const auto station_13{my_stations.add_vertex(station{"Hamburg"})};
   const auto station_12{my_stations.add_vertex(station{"Bremen"})};
-  const auto station_3{my_stations.add_vertex(station{"Berlin Central Station"})};
-  const auto station_4{my_stations.add_vertex(station{"Hannover Hauptbahnhof"})};
+  const auto station_3{
+      my_stations.add_vertex(station{"Berlin Central Station"})};
+  const auto station_4{
+      my_stations.add_vertex(station{"Hannover Hauptbahnhof"})};
   const auto station_11{my_stations.add_vertex(station{"Dortmund"})};
   const auto station_5{my_stations.add_vertex(station{"Kassel Hbf"})};
-  const auto station_2{my_stations.add_vertex(station{"Leipzig Central Station"})}; 
-  const auto station_1{my_stations.add_vertex(station{"Dresden Central Station"})};
-  const auto station_10{my_stations.add_vertex(station{"Cologne Hauptbahnhof"})};
-  const auto station_9{my_stations.add_vertex(station{"Frankfurt Hauptbahnhof"})};
-  const auto station_6{my_stations.add_vertex(station{"Nurnberg Central Station"})};
-  const auto station_8{my_stations.add_vertex(station{"Stuttgart Central Station"})};
+  const auto station_2{
+      my_stations.add_vertex(station{"Leipzig Central Station"})};
+  const auto station_1{
+      my_stations.add_vertex(station{"Dresden Central Station"})};
+  const auto station_10{
+      my_stations.add_vertex(station{"Cologne Hauptbahnhof"})};
+  const auto station_9{
+      my_stations.add_vertex(station{"Frankfurt Hauptbahnhof"})};
+  const auto station_6{
+      my_stations.add_vertex(station{"Nurnberg Central Station"})};
+  const auto station_8{
+      my_stations.add_vertex(station{"Stuttgart Central Station"})};
   const auto station_7{my_stations.add_vertex(station{"Munchen Hbf"})};
-  
-  // Canada stations
-  const auto station_14{my_stations.add_vertex(station{"Edmonton central station"})};
-  const auto station_15{my_stations.add_vertex(station{"Toronto Union Station"})};
-
-  my_stations.add_edge(station_1, station_2, railroad{357.3});
-  my_stations.add_edge(station_1, station_3, railroad{730.67});
-  my_stations.add_edge(station_3, station_4, railroad{533.3});
-  my_stations.add_edge(station_2, station_5, railroad{693.3});
-  my_stations.add_edge(station_2, station_4, railroad{1152});
-  my_stations.add_edge(station_4, station_5, railroad{288});
-  my_stations.add_edge(station_2, station_6, railroad{741.3});
-  my_stations.add_edge(station_5, station_6, railroad{1464});
-  my_stations.add_edge(station_7, station_6, railroad{432});
-  my_stations.add_edge(station_7, station_8, railroad{930});
-  my_stations.add_edge(station_8, station_6, railroad{1236});
-  my_stations.add_edge(station_9, station_6, railroad{840});
-  my_stations.add_edge(station_9, station_10, railroad{498});
-  my_stations.add_edge(station_10, station_11, railroad{462});
-  my_stations.add_edge(station_13, station_4, railroad{480});
-  my_stations.add_edge(station_11, station_5, railroad{822});
-  my_stations.add_edge(station_11, station_4, railroad{582});
-  my_stations.add_edge(station_11, station_12, railroad{720});
-  my_stations.add_edge(station_12, station_13, railroad{330});
-  my_stations.add_edge(station_12, station_4, railroad{486});
-  my_stations.add_edge(station_13, station_3, railroad{732});
-
-  my_stations.add_edge(station_14, station_15, railroad{9920});
+
+  // Canada railway stations
+  const auto station_14{
+      my_stations.add_vertex(station{"Edmonton central station"})};
+  const auto station_15{
+      my_stations.add_vertex(station{"Toronto Union Station"})};
+
+  my_stations.add_edge(station_1, station_2, 357.3);
+  my_stations.add_edge(station_1, station_3, 730.67);
+  my_stations.add_edge(station_3, station_4, 533.3);
+  my_stations.add_edge(station_2, station_5, 693.3);
+  my_stations.add_edge(station_2, station_4, 1152);
+  my_stations.add_edge(station_4, station_5, 288);
+  my_stations.add_edge(station_2, station_6, 741.3);
+  my_stations.add_edge(station_5, station_6, 1464);
+  my_stations.add_edge(station_7, station_6, 432);
+  my_stations.add_edge(station_7, station_8, 930);
+  my_stations.add_edge(station_8, station_6, 1236);
+  my_stations.add_edge(station_9, station_6, 840);
+  my_stations.add_edge(station_9, station_10, 498);
+  my_stations.add_edge(station_10, station_11, 462);
+  my_stations.add_edge(station_13, station_4, 480);
+  my_stations.add_edge(station_11, station_5, 822);
+  my_stations.add_edge(station_11, station_4, 582);
+  my_stations.add_edge(station_11, station_12, 720);
+  my_stations.add_edge(station_12, station_13, 330);
+  my_stations.add_edge(station_12, station_4, 486);
+  my_stations.add_edge(station_13, station_3, 732);
+
+  my_stations.add_edge(station_14, station_15, 9920);
 
   return {my_stations, station_13, station_6};
 }
@@ -86,14 +98,14 @@ void print_shortest_path(
     prev = current;
   }
 
-  const auto vertex_writer{
-      [](graaf::vertex_id_t vertex_id, station vertex) -> std::string {
-        const auto style{"filled"};
-        return fmt::format(
-            "label=\"{}\", style={}, color=black, fontcolor=black, shape=rectangle,"
-            "fillcolor=mediumspringgreen",
-            vertex.name, style);
-      }};
+  const auto vertex_writer{[](graaf::vertex_id_t vertex_id,
+                              station vertex) -> std::string {
+    const auto style{"filled"};
+    return fmt::format(
+        "label=\"{}\", style={}, color=black, fontcolor=black, shape=rectangle,"
+        "fillcolor=mediumspringgreen",
+        vertex.name, style);
+  }};
 
   const auto edge_writer{[&edges_on_shortest_path](
                              const graaf::edge_id_t& edge_id,
@@ -126,8 +138,7 @@ struct record_vertex_callback {
 
 void print_visited_vertices(
     const graaf::undirected_graph<station, railroad>& graph,
-                            seen_vertices_t& seen,
-                            const std::string& filepath) {
+    seen_vertices_t& seen, const std::string& filepath) {
   std::unordered_set<graaf::edge_id_t, graaf::edge_id_hash> seen_edges{};
 
   for (const auto current : graph.get_edges()) {
@@ -136,15 +147,15 @@ void print_visited_vertices(
     if (seen.contains(from) && seen.contains(to)) seen_edges.insert({from, to});
   }
 
-  const auto vertex_writer{
-      [](graaf::vertex_id_t vertex_id, station vertex) -> std::string {
-        const auto style{"filled"};
+  const auto vertex_writer{[](graaf::vertex_id_t vertex_id,
+                              station vertex) -> std::string {
+    const auto style{"filled"};
 
-        return fmt::format(
-            "label=\"{}\", style={}, color=black, fontcolor=black, shape=rectangle,"
-            "fillcolor=mediumspringgreen",
-            vertex.name, style);
-      }};
+    return fmt::format(
+        "label=\"{}\", style={}, color=black, fontcolor=black, shape=rectangle,"
+        "fillcolor=mediumspringgreen",
+        vertex.name, style);
+  }};
 
   const auto edge_writer{[&seen_edges](const graaf::edge_id_t& edge_id,
                                        const auto& edge) -> std::string {

From ce5df25c62a054b5025a0b038c9af8c3089ae47e Mon Sep 17 00:00:00 2001
From: Bob Luppes <bobluppes@gmail.com>
Date: Sun, 13 Aug 2023 13:43:36 +0200
Subject: [PATCH 13/40] fix issues after merge

---
 .../example-basics/transport-example.md       | 24 +++++++--------
 examples/transport/main.cpp                   | 30 ++++++++-----------
 2 files changed, 24 insertions(+), 30 deletions(-)

diff --git a/docs/docs/examples/example-basics/transport-example.md b/docs/docs/examples/example-basics/transport-example.md
index ff09f360..0c060d02 100644
--- a/docs/docs/examples/example-basics/transport-example.md
+++ b/docs/docs/examples/example-basics/transport-example.md
@@ -79,20 +79,20 @@ void print_visited_vertices(const graaf::undirected_graph<station, road>& graph,
 }
 ```
 
-Creating a vertex callback structure that will be passed as an argument in the graph traverse function
+Creating an edge callback structure that will be passed as an argument in the graph traverse function
 The function is needed in order to be called inside the traverse function; see graph.tpp for context.
 
 ```c++
-using seen_vertices_t = std::unordered_multiset<graaf::vertex_id_t>;
-struct record_vertex_callback {
-    seen_vertices_t& seen_vertices;
+using seen_edges_t = std::unordered_set<graaf::edge_id_t, graaf::edge_id_hash>;
+struct record_edges_callback {
+  seen_edges_t& seen_edges;
 
-    record_vertex_callback(seen_vertices_t& seen_vertices)
-        : seen_vertices{seen_vertices} {}
+  record_edges_callback(seen_edges_t& seen_edges)
+      : seen_edges{seen_edges} {}
 
-    void operator()(const graaf::vertex_id_t vertex) const {
-        seen_vertices.insert(vertex);
-    }
+  void operator()(const graaf::edge_id_t& edge) const {
+    seen_edges.insert(edge);
+  }
 };
 ```
 
@@ -121,9 +121,9 @@ The last one is traversing the graph from a given vertex and printing the result
   print_shortest_path(graph, unweighted_shortest_path,
                       "example_unwieghted_graph.dot");
 
-  seen_vertices_t seen_vertices{};
+  seen_edges_t seen_edges{};
   graaf::algorithm::breadth_first_traverse(
-      graph, start, record_vertex_callback{seen_vertices});
-  print_visited_vertices(graph, seen_vertices,
+      graph, start, record_edges_callback{seen_edges});
+  print_visited_vertices(graph, seen_edges,
                          "example_traverse_BFS_graph.dot");
 ```
diff --git a/examples/transport/main.cpp b/examples/transport/main.cpp
index db5c1ce7..6578192f 100644
--- a/examples/transport/main.cpp
+++ b/examples/transport/main.cpp
@@ -4,6 +4,7 @@
 #include <graaflib/graph.h>
 #include <graaflib/io/dot.h>
 #include <graaflib/types.h>
+#include <unordered_set>
 
 struct station {
   std::string name{};
@@ -124,28 +125,21 @@ void print_shortest_path(
   graaf::io::to_dot(graph, output, vertex_writer, edge_writer);
 }
 
-using seen_vertices_t = std::unordered_multiset<graaf::vertex_id_t>;
-struct record_vertex_callback {
-  seen_vertices_t& seen_vertices;
+using seen_edges_t = std::unordered_set<graaf::edge_id_t, graaf::edge_id_hash>;
+struct record_edges_callback {
+  seen_edges_t& seen_edges;
 
-  record_vertex_callback(seen_vertices_t& seen_vertices)
-      : seen_vertices{seen_vertices} {}
+  record_edges_callback(seen_edges_t& seen_edges)
+      : seen_edges{seen_edges} {}
 
-  void operator()(const graaf::vertex_id_t vertex) const {
-    seen_vertices.insert(vertex);
+  void operator()(const graaf::edge_id_t& edge) const {
+    seen_edges.insert(edge);
   }
 };
 
 void print_visited_vertices(
     const graaf::undirected_graph<station, railroad>& graph,
-    seen_vertices_t& seen, const std::string& filepath) {
-  std::unordered_set<graaf::edge_id_t, graaf::edge_id_hash> seen_edges{};
-
-  for (const auto current : graph.get_edges()) {
-    const auto from = current.first.first;
-    const auto to = current.first.second;
-    if (seen.contains(from) && seen.contains(to)) seen_edges.insert({from, to});
-  }
+    seen_edges_t& seen_edges, const std::string& filepath) {
 
   const auto vertex_writer{[](graaf::vertex_id_t vertex_id,
                               station vertex) -> std::string {
@@ -186,9 +180,9 @@ int main() {
   print_shortest_path(graph, unweighted_shortest_path,
                       "example_unwieghted_graph.dot");
 
-  seen_vertices_t seen_vertices{};
+  seen_edges_t seen_edges{};
   graaf::algorithm::breadth_first_traverse(
-      graph, start, record_vertex_callback{seen_vertices});
-  print_visited_vertices(graph, seen_vertices,
+      graph, start, record_edges_callback{seen_edges});
+  print_visited_vertices(graph, seen_edges,
                          "example_traverse_BFS_graph.dot");
 }

From 1c82f04376563fb39698c60d12ab3918f809b190 Mon Sep 17 00:00:00 2001
From: Bob Luppes <bobluppes@gmail.com>
Date: Sun, 13 Aug 2023 13:44:33 +0200
Subject: [PATCH 14/40] fix syntax highlighting code blocks

---
 docs/docs/examples/example-basics/transport-example.md | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

diff --git a/docs/docs/examples/example-basics/transport-example.md b/docs/docs/examples/example-basics/transport-example.md
index 0c060d02..cd429e7f 100644
--- a/docs/docs/examples/example-basics/transport-example.md
+++ b/docs/docs/examples/example-basics/transport-example.md
@@ -18,7 +18,7 @@ Using the following graph:
 
 Custom vertex and edge. In order to use Dijkstra, we should provide the get_weight() function for the edge.
 
-```c++
+```cpp
 struct station {
   std::string name{};
 };
@@ -36,7 +36,7 @@ struct railroad : public graaf::weighted_edge<double> {
 # Initializing graph, start and end vertecies
 First, we create data structure and initializing graph with vertices and edges
 
-```c++
+```cpp
 struct graph_with_start_and_target {
     graaf::undirected_graph<station, road> graph{};
     graaf::vertex_id_t start{};
@@ -66,7 +66,7 @@ Result of weighted shortest path, chosen edges are coloured red
 </p>
 </pre>
 
-```c++
+```cpp
 void print_shortest_path(const graaf::undirected_graph<station, road>& graph,
                 const std::optional<graaf::algorithm::graph_path<int>>& path, const std::string & filepath) {
 ...
@@ -82,7 +82,7 @@ void print_visited_vertices(const graaf::undirected_graph<station, road>& graph,
 Creating an edge callback structure that will be passed as an argument in the graph traverse function
 The function is needed in order to be called inside the traverse function; see graph.tpp for context.
 
-```c++
+```cpp
 using seen_edges_t = std::unordered_set<graaf::edge_id_t, graaf::edge_id_hash>;
 struct record_edges_callback {
   seen_edges_t& seen_edges;
@@ -108,7 +108,7 @@ First code block: traversing a weighted graph for the shortest path (Dijkstra) a
 Second code block: traversing an unweighted graph for the shortest path and printing the result to *.dot file.
 The last one is traversing the graph from a given vertex and printing the result to *.dot file.
 
-```c++
+```cpp
   const auto [graph, start, target]{create_graph_with_start_and_target()};
 
   const auto weighted_shortest_path{

From 1c644a0edba76d813dd293eef0154f9756187ecf Mon Sep 17 00:00:00 2001
From: Bob Luppes <bobluppes@gmail.com>
Date: Sun, 13 Aug 2023 13:53:44 +0200
Subject: [PATCH 15/40] clang format

---
 examples/transport/main.cpp | 12 +++++-------
 1 file changed, 5 insertions(+), 7 deletions(-)

diff --git a/examples/transport/main.cpp b/examples/transport/main.cpp
index 6578192f..aa2c9b41 100644
--- a/examples/transport/main.cpp
+++ b/examples/transport/main.cpp
@@ -4,6 +4,7 @@
 #include <graaflib/graph.h>
 #include <graaflib/io/dot.h>
 #include <graaflib/types.h>
+
 #include <unordered_set>
 
 struct station {
@@ -129,8 +130,7 @@ using seen_edges_t = std::unordered_set<graaf::edge_id_t, graaf::edge_id_hash>;
 struct record_edges_callback {
   seen_edges_t& seen_edges;
 
-  record_edges_callback(seen_edges_t& seen_edges)
-      : seen_edges{seen_edges} {}
+  record_edges_callback(seen_edges_t& seen_edges) : seen_edges{seen_edges} {}
 
   void operator()(const graaf::edge_id_t& edge) const {
     seen_edges.insert(edge);
@@ -140,7 +140,6 @@ struct record_edges_callback {
 void print_visited_vertices(
     const graaf::undirected_graph<station, railroad>& graph,
     seen_edges_t& seen_edges, const std::string& filepath) {
-
   const auto vertex_writer{[](graaf::vertex_id_t vertex_id,
                               station vertex) -> std::string {
     const auto style{"filled"};
@@ -181,8 +180,7 @@ int main() {
                       "example_unwieghted_graph.dot");
 
   seen_edges_t seen_edges{};
-  graaf::algorithm::breadth_first_traverse(
-      graph, start, record_edges_callback{seen_edges});
-  print_visited_vertices(graph, seen_edges,
-                         "example_traverse_BFS_graph.dot");
+  graaf::algorithm::breadth_first_traverse(graph, start,
+                                           record_edges_callback{seen_edges});
+  print_visited_vertices(graph, seen_edges, "example_traverse_BFS_graph.dot");
 }

From c05cd278819d351b822bcfc975fa3eacae962357 Mon Sep 17 00:00:00 2001
From: Hromz <hromizz@gmail.com>
Date: Fri, 18 Aug 2023 19:58:20 +0300
Subject: [PATCH 16/40] - Added MST algorithm - Added test cases and docs

---
 README.md                                     |   1 +
 .../shortest-path/minimum_spanning_tree.md    |  60 +++++
 .../algorithm/minimum_spanning_tree.h         |  20 ++
 .../algorithm/minimum_spanning_tree.tpp       | 101 +++++++++
 .../algorithm/minimum_spanning_tree_test.cpp  | 208 ++++++++++++++++++
 5 files changed, 390 insertions(+)
 create mode 100644 docs/docs/algorithms/shortest-path/minimum_spanning_tree.md
 create mode 100644 include/graaflib/algorithm/minimum_spanning_tree.h
 create mode 100644 include/graaflib/algorithm/minimum_spanning_tree.tpp
 create mode 100644 test/graaflib/algorithm/minimum_spanning_tree_test.cpp

diff --git a/README.md b/README.md
index 08a2998a..20fe22b4 100644
--- a/README.md
+++ b/README.md
@@ -81,6 +81,7 @@ Algorithms implemented in the Graaf library include the following. For more info
     - BFS-Based Shortest Path
     - Dijkstra
     - Bellman-Ford
+    - Minimum spanning tree (MST)
 3. [**Cycle Detection Algorithms**](https://bobluppes.github.io/graaf/docs/category/cycle-detection-algorithms):
     - DFS-Based Cycle Detection
 
diff --git a/docs/docs/algorithms/shortest-path/minimum_spanning_tree.md b/docs/docs/algorithms/shortest-path/minimum_spanning_tree.md
new file mode 100644
index 00000000..dffc8848
--- /dev/null
+++ b/docs/docs/algorithms/shortest-path/minimum_spanning_tree.md
@@ -0,0 +1,60 @@
+---
+sidebar_position: 4
+---
+
+# Minimum spanning tree (MST) or minimum spanning forest
+Kruskal's algorithm finds the minimum spanning forest of an undirected edge-weighted graph. If the graph is connected, it finds a minimum spanning tree.
+The algorithm is implemented with disjoint set union and finding minimum weighted edges.
+Worst-case performance is `O(|E|log|V|)`, where `|E|` is the number of edges and `|V|` is the number of vertices in the
+graph. Memory usage is `O(V+E)` for maintaining vertices (DSU) and edges.
+
+[wikipedia](https://en.wikipedia.org/wiki/Kruskal%27s_algorithm)
+
+## Syntax
+
+Calculates the shortest path with the minimum edge sum.
+
+```cpp
+template <typename V, typename E>
+[[nodiscard]] std::vector<edge_id_t> kruskal_minimum_spanning_tree(
+    const graph<V, E, graph_type::UNDIRECTED>& graph);
+```
+
+- **graph** The graph to extract MST or MSF.
+- **return** Returns a vector of edges that form MST if the graph is connected, otherwise it returns the minimum spanning forest.
+
+### Special case
+In case of multiply edges with same weight leading to a vertex, prioritizing vertices with lesser vertex number.
+
+```cpp
+std::sort(edges_to_process.begin(), edges_to_process.end(),
+              [](detail::edge_to_process<E>& e1,
+                 detail::edge_to_process<E>& e2) {
+                       if (e1 != e2)
+                           return e1.get_weight() < e2.get_weight();
+          return e1.vertex_a < e2.vertex_a || e1.vertex_b < e2.vertex_b;
+        });
+```
+
+For custom type edge, we should provide < and != operators
+
+```cpp
+struct custom_edge : public graaf::weighted_edge<int> {
+ public:
+  int weight_{};
+
+  [[nodiscard]] int get_weight() const noexcept override { return weight_; }
+ 
+  custom_edge(int weight): weight_{weight} {};
+  custom_edge(){};
+  ~custom_edge(){};
+
+  // Providing '<' and '!=' operators for sorting edges
+  bool operator<(const custom_edge& e) const noexcept {
+    return this->weight_ < e.weight_;
+  }
+  bool operator!=(const custom_edge& e) const noexcept {
+    return this->weight_ != e.weight_;
+  }
+};
+```
diff --git a/include/graaflib/algorithm/minimum_spanning_tree.h b/include/graaflib/algorithm/minimum_spanning_tree.h
new file mode 100644
index 00000000..e3acfd6a
--- /dev/null
+++ b/include/graaflib/algorithm/minimum_spanning_tree.h
@@ -0,0 +1,20 @@
+#pragma once
+
+#include <graaflib/graph.h>
+
+namespace graaf::algorithm {
+/**
+ * Computes the minimum spanning tree (MST) or minimum spanning forest of a
+ * graph using Kruskal's algorithm.
+ *
+ * @tparam V The vertex type of the graph.
+ * @tparam E The edge type of the graph.
+ * @param graph The input graph.
+ * @return A vector of edges forming the MST or minimum spanning forest.
+ */
+template <typename V, typename E>
+[[nodiscard]] std::vector<edge_id_t> kruskal_minimum_spanning_tree(
+    const graph<V, E, graph_type::UNDIRECTED>& graph);
+
+};  // namespace graaf::algorithm
+#include "minimum_spanning_tree.tpp"
\ No newline at end of file
diff --git a/include/graaflib/algorithm/minimum_spanning_tree.tpp b/include/graaflib/algorithm/minimum_spanning_tree.tpp
new file mode 100644
index 00000000..f0998918
--- /dev/null
+++ b/include/graaflib/algorithm/minimum_spanning_tree.tpp
@@ -0,0 +1,101 @@
+#pragma once
+
+#include <algorithm>
+#include <unordered_map>
+#include <graaflib/types.h>
+
+namespace graaf::algorithm {
+
+// Disjoint Set Union to maintain sets of vertices
+namespace detail {
+void do_make_set(vertex_id_t v,
+    std::unordered_map<vertex_id_t, vertex_id_t>& parent, 
+    std::unordered_map<vertex_id_t, vertex_id_t>& rank) {
+    parent[v] = v;
+    rank[v] = 0;
+}
+
+vertex_id_t do_find_set(vertex_id_t vertex,
+    std::unordered_map<vertex_id_t, vertex_id_t>& parent) {
+    if (vertex == parent[vertex]) {
+      return vertex;
+    }
+    return parent[vertex] = do_find_set(parent[vertex], parent);
+}
+
+void do_merge_sets(vertex_id_t vertex_a, vertex_id_t vertex_b,
+    std::unordered_map<vertex_id_t, vertex_id_t>& parent,
+    std::unordered_map<vertex_id_t, vertex_id_t>& rank) {
+    vertex_a = do_find_set(vertex_a, parent);
+    vertex_b = do_find_set(vertex_b, parent);
+
+    if (vertex_a != vertex_b) {
+        if (rank[vertex_a] < rank[vertex_b]) {
+            std::swap(vertex_a, vertex_b);
+        }
+        parent[vertex_b] = vertex_a;
+
+        if (rank[vertex_a] == rank[vertex_b]) {
+            ++rank[vertex_a];
+        }
+    } 
+}
+
+template <typename T>
+struct edge_to_process : public weighted_edge<T>  {
+   public:
+    vertex_id_t vertex_a, vertex_b;
+    T weight_;
+
+    [[nodiscard]] T get_weight() const noexcept override { return weight_; }
+ 
+    edge_to_process(vertex_id_t vertex_u, vertex_id_t vertex_w,
+                    T weight)
+        : vertex_a{vertex_u}, vertex_b{vertex_w}, weight_{weight} {};
+    edge_to_process(){};
+    ~edge_to_process(){};
+
+    bool operator!=(const edge_to_process& e) const noexcept {
+        return this->weight_ != e.weight_;
+    }
+};
+}; // namespace detail
+
+template <typename V, typename E>
+std::vector<edge_id_t> kruskal_minimum_spanning_tree(
+    const graph<V, E, graph_type::UNDIRECTED>& graph) {
+
+    // unordered_map in case of deletion of vertices
+    std::unordered_map<vertex_id_t, vertex_id_t> rank, parent;
+    std::vector<detail::edge_to_process<E>> edges_to_process{};
+    std::vector<edge_id_t> mst_edges{};
+
+    for (const auto& vertex : graph.get_vertices()) {
+        detail::do_make_set(vertex.first, parent, rank);
+    }
+    for (const auto& edge : graph.get_edges()) {
+        edges_to_process.push_back({edge.first.first, edge.first.second, edge.second});
+    }
+
+    std::sort(edges_to_process.begin(), edges_to_process.end(),
+              [](detail::edge_to_process<E>& e1,
+                 detail::edge_to_process<E>& e2) {
+                       if (e1 != e2)
+                           return e1.get_weight() < e2.get_weight();
+          return e1.vertex_a < e2.vertex_a || e1.vertex_b < e2.vertex_b;
+        });
+
+     for (const auto& edge : edges_to_process) {
+        if (detail::do_find_set(edge.vertex_a, parent) !=
+            detail::do_find_set(edge.vertex_b, parent)) {
+              mst_edges.push_back({edge.vertex_a, edge.vertex_b});
+              detail::do_merge_sets(edge.vertex_a, edge.vertex_b, parent, rank);
+        }
+        // Found MST E == V - 1
+        if (mst_edges.size() == graph.vertex_count() - 1) 
+            return mst_edges;
+     }
+     // Returns minimum spanning forest
+     return mst_edges;
+}
+};  // namespace graaf::algorithm
diff --git a/test/graaflib/algorithm/minimum_spanning_tree_test.cpp b/test/graaflib/algorithm/minimum_spanning_tree_test.cpp
new file mode 100644
index 00000000..04b49f12
--- /dev/null
+++ b/test/graaflib/algorithm/minimum_spanning_tree_test.cpp
@@ -0,0 +1,208 @@
+#include <fmt/core.h>
+#include <graaflib/algorithm/minimum_spanning_tree.h>
+#include <graaflib/graph.h>
+#include <graaflib/types.h>
+#include <gtest/gtest.h>
+
+#include <type_traits>
+#include <utility>
+
+namespace graaf::algorithm {
+
+template <typename T>
+class my_weighted_edge : public weighted_edge<T> {
+ public:
+  explicit my_weighted_edge(T weight) : weight_{weight} {}
+
+  [[nodiscard]] T get_weight() const noexcept override { return weight_; }
+
+ private:
+  T weight_{};
+};
+
+template <typename T>
+struct MSTTest : public testing::Test {
+  using edge_t = typename T::second_type;
+};
+
+using weighted_graph_types = testing::Types<
+    /**
+     * Primitive edge type undirected graph
+     */
+    std::pair<undirected_graph<int, int>, int>,
+    std::pair<undirected_graph<int, unsigned long>, unsigned long>,
+    std::pair<undirected_graph<int, float>, float>,
+    std::pair<undirected_graph<int, long double>, long double>,
+
+    /**
+     * Non primitive weighted edge type undirected graph
+     */
+    std::pair<undirected_graph<int, my_weighted_edge<int>>,
+              my_weighted_edge<int>>,
+    std::pair<undirected_graph<int, my_weighted_edge<unsigned long>>,
+              my_weighted_edge<unsigned long>>,
+    std::pair<undirected_graph<int, my_weighted_edge<float>>,
+              my_weighted_edge<float>>,
+    std::pair<undirected_graph<int, my_weighted_edge<long double>>,
+              my_weighted_edge<long double>>>;
+
+TYPED_TEST_SUITE(MSTTest, weighted_graph_types);
+
+TYPED_TEST(MSTTest, SparseGraph) {
+  undirected_graph<int, int> graph{};
+  const auto vertex_1 = graph.add_vertex(1);
+  const auto vertex_2 = graph.add_vertex(2);
+  const auto vertex_3 = graph.add_vertex(3);
+  const auto vertex_4 = graph.add_vertex(4);
+
+  graph.add_edge(vertex_3, vertex_1, 4);
+  graph.add_edge(vertex_2, vertex_4, 6);
+  graph.add_edge(vertex_3, vertex_4, 5);
+  graph.add_edge(vertex_1, vertex_2, 15);
+
+  auto mst = graaf::algorithm::kruskal_minimum_spanning_tree(graph);
+  std::vector<edge_id_t> expected_mst{
+      {vertex_1, vertex_3}, {vertex_3, vertex_4}, {vertex_2, vertex_4}}; 
+
+  ASSERT_EQ(expected_mst, mst);
+}
+
+TYPED_TEST(MSTTest, TwoComponents) {
+  undirected_graph<int, float> graph{};
+
+  const auto vertex_1 = graph.add_vertex(1);
+  const auto vertex_2 = graph.add_vertex(2);
+  const auto vertex_3 = graph.add_vertex(3);
+  const auto vertex_4 = graph.add_vertex(4);
+
+  const auto vertex_5 = graph.add_vertex(5);
+  const auto vertex_6 = graph.add_vertex(6);
+  const auto vertex_7 = graph.add_vertex(7);
+  const auto vertex_8 = graph.add_vertex(8);
+  const auto vertex_9 = graph.add_vertex(9);
+
+  graph.add_edge(vertex_3, vertex_1, 0.3f);
+  graph.add_edge(vertex_2, vertex_4, 0.14f);
+  graph.add_edge(vertex_3, vertex_4, -5.3f);
+  graph.add_edge(vertex_1, vertex_2, 223.0f);
+
+  graph.add_edge(vertex_5, vertex_6, 2.0f);
+  graph.add_edge(vertex_7, vertex_8, 4.0f);
+  graph.add_edge(vertex_9, vertex_8, -23.0f);
+  graph.add_edge(vertex_6, vertex_9, 3.0f);
+  graph.add_edge(vertex_8, vertex_6, 0.15f);
+
+  auto mst = graaf::algorithm::kruskal_minimum_spanning_tree(graph);
+  std::vector<edge_id_t> expected_mst {{vertex_8, vertex_9},
+                                      {vertex_3, vertex_4},
+                                      {vertex_2, vertex_4},
+                                      {vertex_6, vertex_8},
+                                      {vertex_1, vertex_3},
+                                      {vertex_5, vertex_6},
+                                      {vertex_7, vertex_8}};
+
+  ASSERT_EQ(expected_mst, mst);
+}
+
+TYPED_TEST(MSTTest, EqualEdgeWeight) {
+  undirected_graph<int, int> graph{};
+  const auto vertex_1 = graph.add_vertex(1);
+  const auto vertex_2 = graph.add_vertex(2);
+  const auto vertex_3 = graph.add_vertex(3);
+  const auto vertex_4 = graph.add_vertex(4);
+
+  graph.add_edge(vertex_3, vertex_1, 5);
+  graph.add_edge(vertex_2, vertex_4, 5);
+  graph.add_edge(vertex_3, vertex_4, 5);
+  graph.add_edge(vertex_1, vertex_2, 5);
+  graph.add_edge(vertex_4, vertex_1, 5);
+
+  auto mst = graaf::algorithm::kruskal_minimum_spanning_tree(graph);
+  std::vector<edge_id_t> expected_mst{
+      {vertex_1, vertex_2}, {vertex_1, vertex_3}, {vertex_1, vertex_4}};
+
+  ASSERT_EQ(expected_mst, mst);
+}
+
+TYPED_TEST(MSTTest, CompleteGraph) {
+  undirected_graph<int, int> graph{};
+  const auto vertex_1 = graph.add_vertex(1);
+  const auto vertex_2 = graph.add_vertex(2);
+  const auto vertex_3 = graph.add_vertex(3);
+  const auto vertex_4 = graph.add_vertex(4);
+
+  graph.add_edge(vertex_1, vertex_2, 35);
+  graph.add_edge(vertex_1, vertex_3, 4);
+  graph.add_edge(vertex_1, vertex_4, 45);
+  graph.add_edge(vertex_2, vertex_4, 6);
+  graph.add_edge(vertex_2, vertex_3, 55);
+  graph.add_edge(vertex_3, vertex_4, 5);   
+
+  auto mst = graaf::algorithm::kruskal_minimum_spanning_tree(graph);
+  std::vector<edge_id_t> expected_mst{
+      {vertex_1, vertex_3}, {vertex_3, vertex_4}, {vertex_2, vertex_4}};
+
+  ASSERT_EQ(expected_mst, mst);
+}
+
+TYPED_TEST(MSTTest, NullGraph) {
+  undirected_graph<int, float> graph{};
+
+  const auto vertex_1 = graph.add_vertex(1);
+  const auto vertex_2 = graph.add_vertex(2);
+  const auto vertex_3 = graph.add_vertex(3);
+  const auto vertex_4 = graph.add_vertex(4);
+
+  auto mst = graaf::algorithm::kruskal_minimum_spanning_tree(graph);
+  std::vector<edge_id_t> example_mst{
+      {vertex_3, vertex_4}, {vertex_2, vertex_4}, {vertex_1, vertex_3}};
+
+  ASSERT_NE(example_mst, mst);
+}
+
+struct custom_vertex {
+  int vertex_{};
+  std::string name{};
+};
+
+struct custom_edge : public graaf::weighted_edge<int> {
+ public:
+  int weight_{};
+
+  [[nodiscard]] int get_weight() const noexcept override { return weight_; }
+ 
+  custom_edge(int weight): weight_{weight} {};
+  custom_edge(){};
+  ~custom_edge(){};
+
+  // Providing '<' and '!=' operators for sorting edges
+  bool operator<(const custom_edge& e) const noexcept {
+    return this->weight_ < e.weight_;
+  }
+  bool operator!=(const custom_edge& e) const noexcept {
+    return this->weight_ != e.weight_;
+  }
+};
+
+TYPED_TEST(MSTTest, CustomEdgeVertexOneComponentGraph) {
+    undirected_graph<custom_vertex, custom_edge> graph{};
+
+    const auto vertex_1 = graph.add_vertex(custom_vertex{1, "Custom vertex 1"});
+    const auto vertex_2 = graph.add_vertex(custom_vertex{2, "Custom vertex 2"});
+    const auto vertex_3 = graph.add_vertex(custom_vertex{3, "Custom vertex 3"});
+    const auto vertex_4 = graph.add_vertex(custom_vertex{4, "Custom vertex 4"});
+
+    graph.add_edge(vertex_3, vertex_1, 4);
+    graph.add_edge(vertex_2, vertex_4, 6);
+    graph.add_edge(vertex_3, vertex_4, 5);
+    graph.add_edge(vertex_1, vertex_2, 16);
+
+    auto mst = graaf::algorithm::kruskal_minimum_spanning_tree(graph);
+    std::vector<edge_id_t> expected_mst{
+        {vertex_1, vertex_3},
+        {vertex_3, vertex_4},
+        {vertex_2, vertex_4}}; 
+
+    ASSERT_EQ(expected_mst, mst);
+}
+}  // namespace graaf::algorithm

From b5db653e17ac541c5a3dccc0073564c01bf60fc3 Mon Sep 17 00:00:00 2001
From: Hromz <hromizz@gmail.com>
Date: Fri, 18 Aug 2023 20:43:02 +0300
Subject: [PATCH 17/40] clang style correction

---
 .../algorithm/minimum_spanning_tree_test.cpp  | 47 +++++++++----------
 1 file changed, 21 insertions(+), 26 deletions(-)

diff --git a/test/graaflib/algorithm/minimum_spanning_tree_test.cpp b/test/graaflib/algorithm/minimum_spanning_tree_test.cpp
index 04b49f12..8c0ee650 100644
--- a/test/graaflib/algorithm/minimum_spanning_tree_test.cpp
+++ b/test/graaflib/algorithm/minimum_spanning_tree_test.cpp
@@ -62,7 +62,7 @@ TYPED_TEST(MSTTest, SparseGraph) {
 
   auto mst = graaf::algorithm::kruskal_minimum_spanning_tree(graph);
   std::vector<edge_id_t> expected_mst{
-      {vertex_1, vertex_3}, {vertex_3, vertex_4}, {vertex_2, vertex_4}}; 
+      {vertex_1, vertex_3}, {vertex_3, vertex_4}, {vertex_2, vertex_4}};
 
   ASSERT_EQ(expected_mst, mst);
 }
@@ -93,13 +93,10 @@ TYPED_TEST(MSTTest, TwoComponents) {
   graph.add_edge(vertex_8, vertex_6, 0.15f);
 
   auto mst = graaf::algorithm::kruskal_minimum_spanning_tree(graph);
-  std::vector<edge_id_t> expected_mst {{vertex_8, vertex_9},
-                                      {vertex_3, vertex_4},
-                                      {vertex_2, vertex_4},
-                                      {vertex_6, vertex_8},
-                                      {vertex_1, vertex_3},
-                                      {vertex_5, vertex_6},
-                                      {vertex_7, vertex_8}};
+  std::vector<edge_id_t> expected_mst{
+      {vertex_8, vertex_9}, {vertex_3, vertex_4}, {vertex_2, vertex_4},
+      {vertex_6, vertex_8}, {vertex_1, vertex_3}, {vertex_5, vertex_6},
+      {vertex_7, vertex_8}};
 
   ASSERT_EQ(expected_mst, mst);
 }
@@ -136,7 +133,7 @@ TYPED_TEST(MSTTest, CompleteGraph) {
   graph.add_edge(vertex_1, vertex_4, 45);
   graph.add_edge(vertex_2, vertex_4, 6);
   graph.add_edge(vertex_2, vertex_3, 55);
-  graph.add_edge(vertex_3, vertex_4, 5);   
+  graph.add_edge(vertex_3, vertex_4, 5);
 
   auto mst = graaf::algorithm::kruskal_minimum_spanning_tree(graph);
   std::vector<edge_id_t> expected_mst{
@@ -170,8 +167,8 @@ struct custom_edge : public graaf::weighted_edge<int> {
   int weight_{};
 
   [[nodiscard]] int get_weight() const noexcept override { return weight_; }
- 
-  custom_edge(int weight): weight_{weight} {};
+
+  custom_edge(int weight) : weight_{weight} {};
   custom_edge(){};
   ~custom_edge(){};
 
@@ -185,24 +182,22 @@ struct custom_edge : public graaf::weighted_edge<int> {
 };
 
 TYPED_TEST(MSTTest, CustomEdgeVertexOneComponentGraph) {
-    undirected_graph<custom_vertex, custom_edge> graph{};
+  undirected_graph<custom_vertex, custom_edge> graph{};
 
-    const auto vertex_1 = graph.add_vertex(custom_vertex{1, "Custom vertex 1"});
-    const auto vertex_2 = graph.add_vertex(custom_vertex{2, "Custom vertex 2"});
-    const auto vertex_3 = graph.add_vertex(custom_vertex{3, "Custom vertex 3"});
-    const auto vertex_4 = graph.add_vertex(custom_vertex{4, "Custom vertex 4"});
+  const auto vertex_1 = graph.add_vertex(custom_vertex{1, "Custom vertex 1"});
+  const auto vertex_2 = graph.add_vertex(custom_vertex{2, "Custom vertex 2"});
+  const auto vertex_3 = graph.add_vertex(custom_vertex{3, "Custom vertex 3"});
+  const auto vertex_4 = graph.add_vertex(custom_vertex{4, "Custom vertex 4"});
 
-    graph.add_edge(vertex_3, vertex_1, 4);
-    graph.add_edge(vertex_2, vertex_4, 6);
-    graph.add_edge(vertex_3, vertex_4, 5);
-    graph.add_edge(vertex_1, vertex_2, 16);
+  graph.add_edge(vertex_3, vertex_1, 4);
+  graph.add_edge(vertex_2, vertex_4, 6);
+  graph.add_edge(vertex_3, vertex_4, 5);
+  graph.add_edge(vertex_1, vertex_2, 16);
 
-    auto mst = graaf::algorithm::kruskal_minimum_spanning_tree(graph);
-    std::vector<edge_id_t> expected_mst{
-        {vertex_1, vertex_3},
-        {vertex_3, vertex_4},
-        {vertex_2, vertex_4}}; 
+  auto mst = graaf::algorithm::kruskal_minimum_spanning_tree(graph);
+  std::vector<edge_id_t> expected_mst{
+      {vertex_1, vertex_3}, {vertex_3, vertex_4}, {vertex_2, vertex_4}};
 
-    ASSERT_EQ(expected_mst, mst);
+  ASSERT_EQ(expected_mst, mst);
 }
 }  // namespace graaf::algorithm

From 057ee77c46d2b25bff636b60df66732f34e66c61 Mon Sep 17 00:00:00 2001
From: Bob Luppes <bobluppes@gmail.com>
Date: Thu, 31 Aug 2023 20:57:06 +0200
Subject: [PATCH 18/40] Apply suggestions from code review

---
 README.md                                                   | 3 ++-
 docs/docs/algorithms/shortest-path/minimum_spanning_tree.md | 2 +-
 2 files changed, 3 insertions(+), 2 deletions(-)

diff --git a/README.md b/README.md
index 20fe22b4..9aa57baa 100644
--- a/README.md
+++ b/README.md
@@ -81,9 +81,10 @@ Algorithms implemented in the Graaf library include the following. For more info
     - BFS-Based Shortest Path
     - Dijkstra
     - Bellman-Ford
-    - Minimum spanning tree (MST)
 3. [**Cycle Detection Algorithms**](https://bobluppes.github.io/graaf/docs/category/cycle-detection-algorithms):
     - DFS-Based Cycle Detection
+4. **Minimum Spanning Tree (MST) Algorithms**
+    - Kruskal's Algorithm
 
 # Contributing
 The Graaf library welcomes contributions 🎊 
diff --git a/docs/docs/algorithms/shortest-path/minimum_spanning_tree.md b/docs/docs/algorithms/shortest-path/minimum_spanning_tree.md
index dffc8848..e3d5bfb8 100644
--- a/docs/docs/algorithms/shortest-path/minimum_spanning_tree.md
+++ b/docs/docs/algorithms/shortest-path/minimum_spanning_tree.md
@@ -2,7 +2,7 @@
 sidebar_position: 4
 ---
 
-# Minimum spanning tree (MST) or minimum spanning forest
+# Kruskal's Algorithm
 Kruskal's algorithm finds the minimum spanning forest of an undirected edge-weighted graph. If the graph is connected, it finds a minimum spanning tree.
 The algorithm is implemented with disjoint set union and finding minimum weighted edges.
 Worst-case performance is `O(|E|log|V|)`, where `|E|` is the number of edges and `|V|` is the number of vertices in the

From 5dce08b86fa07701b13cfe59be340656516f76b2 Mon Sep 17 00:00:00 2001
From: Hromz <hromizz@gmail.com>
Date: Tue, 5 Sep 2023 12:16:06 +0300
Subject: [PATCH 19/40] Added topological sort algorithm DFS-based

---
 README.md                                     |   2 +
 .../topological-sort/topological-sort.md      |  21 +++
 .../graaflib/algorithm/topological_sorting.h  |  20 ++
 .../algorithm/topological_sorting.tpp         |  60 ++++++
 .../algorithm/topological_sorting_test.cpp    | 178 ++++++++++++++++++
 5 files changed, 281 insertions(+)
 create mode 100644 docs/docs/algorithms/topological-sort/topological-sort.md
 create mode 100644 include/graaflib/algorithm/topological_sorting.h
 create mode 100644 include/graaflib/algorithm/topological_sorting.tpp
 create mode 100644 test/graaflib/algorithm/topological_sorting_test.cpp

diff --git a/README.md b/README.md
index 88b70236..18899a88 100644
--- a/README.md
+++ b/README.md
@@ -88,6 +88,8 @@ Algorithms implemented in the Graaf library include the following. For more info
     - Kruskal's Algorithm
 5. [**Strongly Connected Components Algorithms**](https://bobluppes.github.io/graaf/docs/category/strongly-connected-components):
     - Tarjan's Strongly Connected Components 
+6. [**Topological Sorting Algorithms**](https://bobluppes.github.io/graaf/docs/category/topological-sorting):
+    - Topological sorting DFS-based
 
 # Contributing
 The Graaf library welcomes contributions 🎊 
diff --git a/docs/docs/algorithms/topological-sort/topological-sort.md b/docs/docs/algorithms/topological-sort/topological-sort.md
new file mode 100644
index 00000000..0951ad42
--- /dev/null
+++ b/docs/docs/algorithms/topological-sort/topological-sort.md
@@ -0,0 +1,21 @@
+---
+sidebar_position: 1
+---
+
+# Topological sort algorithm
+Topological sort algorithm processing DAG(directed acyclic graph) using DFS traversal.
+Each vertex is visited only after all its dependencies are visited.
+The runtime of the algorithm is `O(|V|+|E|)` and the memory consumption is `O(|V|)`.
+
+[wikipedia](https://en.wikipedia.org/wiki/Topological_sorting)
+
+## Syntax
+
+```cpp
+template <typename V, typename E>
+[[nodiscard]] std::vector<edge_id_t> kruskal_minimum_spanning_tree(
+    const graph<V, E, graph_type::UNDIRECTED>& graph);
+```
+
+- **graph** The graph to traverse.
+- **return** Vector of vertices sorted in topological order. If the graph contains cycles, it returns an empty vector.
\ No newline at end of file
diff --git a/include/graaflib/algorithm/topological_sorting.h b/include/graaflib/algorithm/topological_sorting.h
new file mode 100644
index 00000000..28e2ea3b
--- /dev/null
+++ b/include/graaflib/algorithm/topological_sorting.h
@@ -0,0 +1,20 @@
+#pragma once
+
+#include <graaflib/graph.h>
+
+namespace graaf::algorithm {
+/**
+* @brief Calculates order of vertices in topological order 
+* using DFS traversal
+* 
+* @tparam V The vertex type of the graph.
+* @tparam E The edge type of the graph.
+* @param graph The input graph.
+* @return Vector of vertices sorted in topological order
+*/
+template <typename V, typename E>
+[[nodiscard]] std::vector<vertex_id_t> topological_sort(
+    const graph<V, E, graph_type::DIRECTED>& graph);
+
+} // namespace graaf::algorithm
+#include "topological_sorting.tpp"
diff --git a/include/graaflib/algorithm/topological_sorting.tpp b/include/graaflib/algorithm/topological_sorting.tpp
new file mode 100644
index 00000000..817185bd
--- /dev/null
+++ b/include/graaflib/algorithm/topological_sorting.tpp
@@ -0,0 +1,60 @@
+#pragma once
+
+#include <graaflib/algorithm/cycle_detection.h>
+#include <graaflib/algorithm/topological_sorting.h>
+
+#include <vector>
+#include <unordered_map>
+
+namespace graaf::algorithm {
+
+namespace detail {
+
+enum class vertex_status { UNVISITED, VISITED};
+
+// DFS topological sort
+template <typename V, typename E>
+void do_dfs_topological_sort(
+    const graph<V, E, graph_type::DIRECTED>& graph,
+    vertex_id_t start_vertex,
+    std::unordered_map<vertex_id_t, vertex_status>& processed_vertices,
+    std::vector<vertex_id_t>& sorted_vertices) {
+    
+    processed_vertices[start_vertex] = vertex_status::VISITED;
+    for (const auto& next_vertex : graph.get_neighbors(start_vertex)) {
+        if (processed_vertices[next_vertex] == vertex_status::UNVISITED) {
+            do_dfs_topological_sort(graph, next_vertex, processed_vertices,
+                sorted_vertices);
+        }
+    }
+
+        sorted_vertices.push_back(start_vertex);
+    }
+
+}; // namespace detail
+
+template <typename V, typename E>
+std::vector<vertex_id_t> topological_sort(
+    const graph<V, E, graph_type::DIRECTED>& graph) {
+    
+    // Graph should be acyclic
+    if (dfs_cycle_detection(graph)) {
+        return {};    
+    }
+
+    using enum detail::vertex_status;
+    std::vector<vertex_id_t> sorted_vertices{};
+    sorted_vertices.reserve(graph.vertex_count());
+    std::unordered_map<vertex_id_t, detail::vertex_status> processed_vertices{};
+
+    for (const auto& vertex : graph.get_vertices()) {
+        if (processed_vertices[vertex.first] == UNVISITED) {
+            detail::do_dfs_topological_sort(graph, vertex.first, processed_vertices, sorted_vertices);
+        }
+    }
+
+    std::reverse(sorted_vertices.begin(), sorted_vertices.end());
+    return sorted_vertices;
+}
+
+};  // namespace graaf::algorithm
diff --git a/test/graaflib/algorithm/topological_sorting_test.cpp b/test/graaflib/algorithm/topological_sorting_test.cpp
new file mode 100644
index 00000000..03e2ce71
--- /dev/null
+++ b/test/graaflib/algorithm/topological_sorting_test.cpp
@@ -0,0 +1,178 @@
+#include <fmt/core.h>
+#include <graaflib/algorithm/topological_sorting.h>
+#include <graaflib/graph.h>
+#include <graaflib/types.h>
+#include <gtest/gtest.h>
+
+namespace graaf::algorithm {
+namespace {
+template <typename T>
+struct TypedTopologicalSort : public testing::Test {
+  using graph_t = T;
+};
+
+using graph_types = testing::Types<directed_graph<int, int>>;
+TYPED_TEST_SUITE(TypedTopologicalSort, graph_types);
+
+};  // namespace
+
+TYPED_TEST(TypedTopologicalSort, ShortGraph) {
+  // GIVEN
+  using graph_t = typename TestFixture::graph_t;
+  graph_t graph{};
+
+  const auto vertex_1{graph.add_vertex(10)};
+  const auto vertex_2{graph.add_vertex(20)};
+  const auto vertex_3{graph.add_vertex(30)};
+  const auto vertex_4{graph.add_vertex(40)};
+
+  graph.add_edge(vertex_1, vertex_2, 25);
+  graph.add_edge(vertex_2, vertex_3, 35);
+  graph.add_edge(vertex_3, vertex_4, 45);
+
+  // WHEN;
+  auto sorted_vertices = topological_sort(graph);
+  std::vector<vertex_id_t> expected_vertices{0, 1, 2, 3};
+
+  // THEN
+  ASSERT_EQ(expected_vertices, sorted_vertices);
+}
+
+TYPED_TEST(TypedTopologicalSort, CycleGraph) {
+  // GIVEN
+  using graph_t = typename TestFixture::graph_t;
+  graph_t graph{};
+
+  const auto vertex_1{graph.add_vertex(10)};
+  const auto vertex_2{graph.add_vertex(20)};
+  const auto vertex_3{graph.add_vertex(30)};
+  const auto vertex_4{graph.add_vertex(40)};
+
+  graph.add_edge(vertex_1, vertex_2, 25);
+  graph.add_edge(vertex_2, vertex_3, 35);
+  graph.add_edge(vertex_3, vertex_4, 45);
+  graph.add_edge(vertex_4, vertex_1, 55);
+
+  // WHEN;
+  auto sorted_vertices = topological_sort(graph);
+  std::vector<vertex_id_t> expected_vertices{};
+
+  // THEN
+  ASSERT_EQ(expected_vertices, sorted_vertices);
+}
+
+TYPED_TEST(TypedTopologicalSort, GraphWithParallelEdge) {
+  // GIVEN
+  using graph_t = typename TestFixture::graph_t;
+  graph_t graph{};
+
+  const auto vertex_1{graph.add_vertex(10)};
+  const auto vertex_2{graph.add_vertex(20)};
+  const auto vertex_3{graph.add_vertex(30)};
+  const auto vertex_4{graph.add_vertex(40)};
+
+  graph.add_edge(vertex_1, vertex_2, 25);
+  graph.add_edge(vertex_3, vertex_4, 35);
+  graph.add_edge(vertex_4, vertex_1, 45);
+  graph.add_edge(vertex_1, vertex_4, 55);
+
+  // WHEN;
+  auto sorted_vertices = topological_sort(graph);
+  std::vector<vertex_id_t> expected_vertices{};
+
+  // THEN
+  ASSERT_EQ(expected_vertices, sorted_vertices);
+}
+
+TYPED_TEST(TypedTopologicalSort, SelfLoop) {
+  // GIVEN
+  using graph_t = typename TestFixture::graph_t;
+  graph_t graph{};
+
+  const auto vertex_1{graph.add_vertex(10)};
+  const auto vertex_2{graph.add_vertex(20)};
+  const auto vertex_3{graph.add_vertex(30)};
+  const auto vertex_4{graph.add_vertex(40)};
+
+  graph.add_edge(vertex_1, vertex_1, -1);
+  graph.add_edge(vertex_2, vertex_2, -1);
+  graph.add_edge(vertex_1, vertex_2, 15);
+  graph.add_edge(vertex_3, vertex_4, 25);
+
+  // WHEN;
+  auto sorted_vertices = topological_sort(graph);
+  std::vector<vertex_id_t> expected_vertices{};
+
+  // THEN
+  ASSERT_EQ(expected_vertices, sorted_vertices);
+}
+
+TYPED_TEST(TypedTopologicalSort, SimpleGraph) {
+	// GIVEN
+	using graph_t = typename TestFixture::graph_t;
+	graph_t graph{};
+
+	const auto vertex_1{graph.add_vertex(10)};
+    const auto vertex_2{graph.add_vertex(20)};
+    const auto vertex_3{graph.add_vertex(30)};
+    const auto vertex_4{graph.add_vertex(40)};
+    const auto vertex_5{graph.add_vertex(50)};
+    const auto vertex_6{graph.add_vertex(60)};
+    const auto vertex_7{graph.add_vertex(70)};
+
+    graph.add_edge(vertex_1, vertex_5, 1);
+    graph.add_edge(vertex_5, vertex_3, 2);
+    graph.add_edge(vertex_3, vertex_7, 3);
+    graph.add_edge(vertex_1, vertex_4, 4);
+    graph.add_edge(vertex_1, vertex_2, 5);
+    graph.add_edge(vertex_4, vertex_2, 6);
+    graph.add_edge(vertex_2, vertex_6, 7);
+    graph.add_edge(vertex_6, vertex_3, 8);
+
+    // WHEN;
+    auto sorted_vertices = topological_sort(graph);
+    std::vector<vertex_id_t> expected_vertices{0, 3, 1, 5, 4, 2, 6};
+    
+    // THEN
+    ASSERT_EQ(expected_vertices, sorted_vertices);
+}
+
+TYPED_TEST(TypedTopologicalSort, SixSortResults) {
+    // GIVEN
+    using graph_t = typename TestFixture::graph_t;
+    graph_t graph{};
+
+    const auto vertex_1{graph.add_vertex(10)};
+    const auto vertex_2{graph.add_vertex(20)};
+    const auto vertex_3{graph.add_vertex(30)};
+    const auto vertex_4{graph.add_vertex(40)};
+    const auto vertex_5{graph.add_vertex(50)};
+    const auto vertex_6{graph.add_vertex(60)};
+    const auto vertex_7{graph.add_vertex(70)};
+
+    graph.add_edge(vertex_1, vertex_2, 1);
+    graph.add_edge(vertex_2, vertex_3, 2);
+    graph.add_edge(vertex_1, vertex_4, 3);
+    graph.add_edge(vertex_4, vertex_5, 4);
+    graph.add_edge(vertex_1, vertex_6, 5);
+    graph.add_edge(vertex_6, vertex_7, 6);
+
+    // WHEN;
+    auto sorted_vertices = topological_sort(graph);
+    std::vector<vertex_id_t> expected_vertices_1{0, 1, 2, 3, 4, 5, 6};
+    std::vector<vertex_id_t> expected_vertices_2{0, 1, 2, 5, 6, 3, 4};
+    std::vector<vertex_id_t> expected_vertices_3{0, 5, 6, 1, 2, 3, 4};
+    std::vector<vertex_id_t> expected_vertices_4{0, 5, 6, 3, 4, 1, 2};
+    std::vector<vertex_id_t> expected_vertices_5{0, 3, 4, 5, 6, 1, 2};
+    std::vector<vertex_id_t> expected_vertices_6{0, 3, 4, 1, 2, 5, 6};
+
+    // THEN
+    ASSERT_TRUE((expected_vertices_1 == sorted_vertices) ||
+                (expected_vertices_2 == sorted_vertices) ||
+                (expected_vertices_3 == sorted_vertices) ||
+                (expected_vertices_4 == sorted_vertices) ||
+                (expected_vertices_4 == sorted_vertices) ||
+                (expected_vertices_6 == sorted_vertices) );
+}
+
+};  // namespace graaf::algorithm
\ No newline at end of file

From f8cd4fb0f95708fced31ad1ac1354722788511d1 Mon Sep 17 00:00:00 2001
From: Hromz <hromizz@gmail.com>
Date: Tue, 5 Sep 2023 13:51:34 +0300
Subject: [PATCH 20/40] small fixes

---
 .../algorithm/topological_sorting_test.cpp    | 134 ++++++++++--------
 1 file changed, 71 insertions(+), 63 deletions(-)

diff --git a/test/graaflib/algorithm/topological_sorting_test.cpp b/test/graaflib/algorithm/topological_sorting_test.cpp
index 03e2ce71..7a3dcc87 100644
--- a/test/graaflib/algorithm/topological_sorting_test.cpp
+++ b/test/graaflib/algorithm/topological_sorting_test.cpp
@@ -76,7 +76,7 @@ TYPED_TEST(TypedTopologicalSort, GraphWithParallelEdge) {
   graph.add_edge(vertex_4, vertex_1, 45);
   graph.add_edge(vertex_1, vertex_4, 55);
 
-  // WHEN;
+  // WHEN
   auto sorted_vertices = topological_sort(graph);
   std::vector<vertex_id_t> expected_vertices{};
 
@@ -108,71 +108,79 @@ TYPED_TEST(TypedTopologicalSort, SelfLoop) {
 }
 
 TYPED_TEST(TypedTopologicalSort, SimpleGraph) {
-	// GIVEN
-	using graph_t = typename TestFixture::graph_t;
-	graph_t graph{};
-
-	const auto vertex_1{graph.add_vertex(10)};
-    const auto vertex_2{graph.add_vertex(20)};
-    const auto vertex_3{graph.add_vertex(30)};
-    const auto vertex_4{graph.add_vertex(40)};
-    const auto vertex_5{graph.add_vertex(50)};
-    const auto vertex_6{graph.add_vertex(60)};
-    const auto vertex_7{graph.add_vertex(70)};
-
-    graph.add_edge(vertex_1, vertex_5, 1);
-    graph.add_edge(vertex_5, vertex_3, 2);
-    graph.add_edge(vertex_3, vertex_7, 3);
-    graph.add_edge(vertex_1, vertex_4, 4);
-    graph.add_edge(vertex_1, vertex_2, 5);
-    graph.add_edge(vertex_4, vertex_2, 6);
-    graph.add_edge(vertex_2, vertex_6, 7);
-    graph.add_edge(vertex_6, vertex_3, 8);
-
-    // WHEN;
-    auto sorted_vertices = topological_sort(graph);
-    std::vector<vertex_id_t> expected_vertices{0, 3, 1, 5, 4, 2, 6};
-    
-    // THEN
-    ASSERT_EQ(expected_vertices, sorted_vertices);
+  // GIVEN
+  using graph_t = typename TestFixture::graph_t;
+  graph_t graph{};
+
+  const auto vertex_1{graph.add_vertex(10)};
+  const auto vertex_2{graph.add_vertex(20)};
+  const auto vertex_3{graph.add_vertex(30)};
+  const auto vertex_4{graph.add_vertex(40)};
+  const auto vertex_5{graph.add_vertex(50)};
+  const auto vertex_6{graph.add_vertex(60)};
+  const auto vertex_7{graph.add_vertex(70)};
+
+  graph.add_edge(vertex_1, vertex_5, 1);
+  graph.add_edge(vertex_5, vertex_3, 2);
+  graph.add_edge(vertex_3, vertex_7, 3);
+  graph.add_edge(vertex_1, vertex_4, 4);
+  graph.add_edge(vertex_1, vertex_2, 5);
+  graph.add_edge(vertex_4, vertex_2, 6);
+  graph.add_edge(vertex_2, vertex_6, 7);
+  graph.add_edge(vertex_6, vertex_3, 8);
+
+  // WHEN;
+  auto sorted_vertices = topological_sort(graph);
+  std::vector<vertex_id_t> expected_vertices_1{0, 3, 1, 5, 4, 2, 6};
+  std::vector<vertex_id_t> expected_vertices_2{0, 1, 3, 5, 4, 2, 6};
+  std::vector<vertex_id_t> expected_vertices_3{0, 1, 3, 4, 5, 2, 6};
+  std::vector<vertex_id_t> expected_vertices_4{0, 4, 3, 1, 5, 2, 6};
+  std::vector<vertex_id_t> expected_vertices_5{0, 4, 1, 3, 5, 2, 6};
+
+  // THEN
+  ASSERT_TRUE((expected_vertices_1 == sorted_vertices) ||
+              (expected_vertices_2 == sorted_vertices) ||
+              (expected_vertices_3 == sorted_vertices) ||
+              (expected_vertices_4 == sorted_vertices) ||
+              (expected_vertices_5 == sorted_vertices));
 }
 
 TYPED_TEST(TypedTopologicalSort, SixSortResults) {
-    // GIVEN
-    using graph_t = typename TestFixture::graph_t;
-    graph_t graph{};
-
-    const auto vertex_1{graph.add_vertex(10)};
-    const auto vertex_2{graph.add_vertex(20)};
-    const auto vertex_3{graph.add_vertex(30)};
-    const auto vertex_4{graph.add_vertex(40)};
-    const auto vertex_5{graph.add_vertex(50)};
-    const auto vertex_6{graph.add_vertex(60)};
-    const auto vertex_7{graph.add_vertex(70)};
-
-    graph.add_edge(vertex_1, vertex_2, 1);
-    graph.add_edge(vertex_2, vertex_3, 2);
-    graph.add_edge(vertex_1, vertex_4, 3);
-    graph.add_edge(vertex_4, vertex_5, 4);
-    graph.add_edge(vertex_1, vertex_6, 5);
-    graph.add_edge(vertex_6, vertex_7, 6);
-
-    // WHEN;
-    auto sorted_vertices = topological_sort(graph);
-    std::vector<vertex_id_t> expected_vertices_1{0, 1, 2, 3, 4, 5, 6};
-    std::vector<vertex_id_t> expected_vertices_2{0, 1, 2, 5, 6, 3, 4};
-    std::vector<vertex_id_t> expected_vertices_3{0, 5, 6, 1, 2, 3, 4};
-    std::vector<vertex_id_t> expected_vertices_4{0, 5, 6, 3, 4, 1, 2};
-    std::vector<vertex_id_t> expected_vertices_5{0, 3, 4, 5, 6, 1, 2};
-    std::vector<vertex_id_t> expected_vertices_6{0, 3, 4, 1, 2, 5, 6};
-
-    // THEN
-    ASSERT_TRUE((expected_vertices_1 == sorted_vertices) ||
-                (expected_vertices_2 == sorted_vertices) ||
-                (expected_vertices_3 == sorted_vertices) ||
-                (expected_vertices_4 == sorted_vertices) ||
-                (expected_vertices_4 == sorted_vertices) ||
-                (expected_vertices_6 == sorted_vertices) );
+  // GIVEN
+  using graph_t = typename TestFixture::graph_t;
+  graph_t graph{};
+
+  const auto vertex_1{graph.add_vertex(10)};
+  const auto vertex_2{graph.add_vertex(20)};
+  const auto vertex_3{graph.add_vertex(30)};
+  const auto vertex_4{graph.add_vertex(40)};
+  const auto vertex_5{graph.add_vertex(50)};
+  const auto vertex_6{graph.add_vertex(60)};
+  const auto vertex_7{graph.add_vertex(70)};
+
+  graph.add_edge(vertex_1, vertex_2, 1);
+  graph.add_edge(vertex_2, vertex_3, 2);
+  graph.add_edge(vertex_1, vertex_4, 3);
+  graph.add_edge(vertex_4, vertex_5, 4);
+  graph.add_edge(vertex_1, vertex_6, 5);
+  graph.add_edge(vertex_6, vertex_7, 6);
+
+  // WHEN;
+  auto sorted_vertices = topological_sort(graph);
+  std::vector<vertex_id_t> expected_vertices_1{0, 1, 2, 3, 4, 5, 6};
+  std::vector<vertex_id_t> expected_vertices_2{0, 1, 2, 5, 6, 3, 4};
+  std::vector<vertex_id_t> expected_vertices_3{0, 5, 6, 1, 2, 3, 4};
+  std::vector<vertex_id_t> expected_vertices_4{0, 5, 6, 3, 4, 1, 2};
+  std::vector<vertex_id_t> expected_vertices_5{0, 3, 4, 5, 6, 1, 2};
+  std::vector<vertex_id_t> expected_vertices_6{0, 3, 4, 1, 2, 5, 6};
+
+  // THEN
+  ASSERT_TRUE((expected_vertices_1 == sorted_vertices) ||
+              (expected_vertices_2 == sorted_vertices) ||
+              (expected_vertices_3 == sorted_vertices) ||
+              (expected_vertices_4 == sorted_vertices) ||
+              (expected_vertices_4 == sorted_vertices) ||
+              (expected_vertices_6 == sorted_vertices));
 }
 
 };  // namespace graaf::algorithm
\ No newline at end of file

From 14f0b8d9876c4ac9d2284f2f3cc7832add4c666b Mon Sep 17 00:00:00 2001
From: Hromz <hromizz@gmail.com>
Date: Tue, 5 Sep 2023 14:00:35 +0300
Subject: [PATCH 21/40] clang format fix

---
 .../graaflib/algorithm/topological_sorting.h   | 18 +++++++++---------
 1 file changed, 9 insertions(+), 9 deletions(-)

diff --git a/include/graaflib/algorithm/topological_sorting.h b/include/graaflib/algorithm/topological_sorting.h
index 28e2ea3b..9faba554 100644
--- a/include/graaflib/algorithm/topological_sorting.h
+++ b/include/graaflib/algorithm/topological_sorting.h
@@ -4,17 +4,17 @@
 
 namespace graaf::algorithm {
 /**
-* @brief Calculates order of vertices in topological order 
-* using DFS traversal
-* 
-* @tparam V The vertex type of the graph.
-* @tparam E The edge type of the graph.
-* @param graph The input graph.
-* @return Vector of vertices sorted in topological order
-*/
+ * @brief Calculates order of vertices in topological order
+ * using DFS traversal
+ *
+ * @tparam V The vertex type of the graph.
+ * @tparam E The edge type of the graph.
+ * @param graph The input graph.
+ * @return Vector of vertices sorted in topological order
+ */
 template <typename V, typename E>
 [[nodiscard]] std::vector<vertex_id_t> topological_sort(
     const graph<V, E, graph_type::DIRECTED>& graph);
 
-} // namespace graaf::algorithm
+}  // namespace graaf::algorithm
 #include "topological_sorting.tpp"

From 7efd134a41d9f06db1be90e0d609edaa7964b656 Mon Sep 17 00:00:00 2001
From: Hromz <hromizz@gmail.com>
Date: Tue, 5 Sep 2023 14:26:19 +0300
Subject: [PATCH 22/40] added test

---
 test/graaflib/algorithm/topological_sorting_test.cpp | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/test/graaflib/algorithm/topological_sorting_test.cpp b/test/graaflib/algorithm/topological_sorting_test.cpp
index 7a3dcc87..7a1f886c 100644
--- a/test/graaflib/algorithm/topological_sorting_test.cpp
+++ b/test/graaflib/algorithm/topological_sorting_test.cpp
@@ -136,13 +136,15 @@ TYPED_TEST(TypedTopologicalSort, SimpleGraph) {
   std::vector<vertex_id_t> expected_vertices_3{0, 1, 3, 4, 5, 2, 6};
   std::vector<vertex_id_t> expected_vertices_4{0, 4, 3, 1, 5, 2, 6};
   std::vector<vertex_id_t> expected_vertices_5{0, 4, 1, 3, 5, 2, 6};
+  std::vector<vertex_id_t> expected_vertices_6{0, 1, 4, 3, 5, 2, 6};
 
   // THEN
   ASSERT_TRUE((expected_vertices_1 == sorted_vertices) ||
               (expected_vertices_2 == sorted_vertices) ||
               (expected_vertices_3 == sorted_vertices) ||
               (expected_vertices_4 == sorted_vertices) ||
-              (expected_vertices_5 == sorted_vertices));
+              (expected_vertices_5 == sorted_vertices) ||
+              (expected_vertices_6 == sorted_vertices ));
 }
 
 TYPED_TEST(TypedTopologicalSort, SixSortResults) {

From 0bcad82a6738a7a6f1e48586608d75fb5373dbdb Mon Sep 17 00:00:00 2001
From: Hromz <hromizz@gmail.com>
Date: Tue, 5 Sep 2023 14:33:26 +0300
Subject: [PATCH 23/40] more tests

---
 test/graaflib/algorithm/topological_sorting_test.cpp | 6 +++++-
 1 file changed, 5 insertions(+), 1 deletion(-)

diff --git a/test/graaflib/algorithm/topological_sorting_test.cpp b/test/graaflib/algorithm/topological_sorting_test.cpp
index 7a1f886c..a5f224de 100644
--- a/test/graaflib/algorithm/topological_sorting_test.cpp
+++ b/test/graaflib/algorithm/topological_sorting_test.cpp
@@ -137,6 +137,8 @@ TYPED_TEST(TypedTopologicalSort, SimpleGraph) {
   std::vector<vertex_id_t> expected_vertices_4{0, 4, 3, 1, 5, 2, 6};
   std::vector<vertex_id_t> expected_vertices_5{0, 4, 1, 3, 5, 2, 6};
   std::vector<vertex_id_t> expected_vertices_6{0, 1, 4, 3, 5, 2, 6};
+  std::vector<vertex_id_t> expected_vertices_7{0, 3, 1, 4, 5, 2, 6};
+  std::vector<vertex_id_t> expected_vertices_8{0, 3, 4, 1, 5, 2, 6};
 
   // THEN
   ASSERT_TRUE((expected_vertices_1 == sorted_vertices) ||
@@ -144,7 +146,9 @@ TYPED_TEST(TypedTopologicalSort, SimpleGraph) {
               (expected_vertices_3 == sorted_vertices) ||
               (expected_vertices_4 == sorted_vertices) ||
               (expected_vertices_5 == sorted_vertices) ||
-              (expected_vertices_6 == sorted_vertices ));
+              (expected_vertices_6 == sorted_vertices) ||
+              (expected_vertices_7 == sorted_vertices) ||
+              (expected_vertices_8 == sorted_vertices));
 }
 
 TYPED_TEST(TypedTopologicalSort, SixSortResults) {

From f96849a5e3b624bc6a3a8f4fa5a042b9c3fc9a52 Mon Sep 17 00:00:00 2001
From: Hromz <hromizz@gmail.com>
Date: Sun, 10 Sep 2023 11:30:02 +0300
Subject: [PATCH 24/40] Minor fixes Added one test

---
 .../topological-sort/topological-sort.md      |  6 +-
 .../graaflib/algorithm/topological_sorting.h  |  3 +-
 .../algorithm/topological_sorting.tpp         | 26 +++----
 .../algorithm/topological_sorting_test.cpp    | 78 ++++++++++++++-----
 4 files changed, 77 insertions(+), 36 deletions(-)

diff --git a/docs/docs/algorithms/topological-sort/topological-sort.md b/docs/docs/algorithms/topological-sort/topological-sort.md
index 0951ad42..0d81af79 100644
--- a/docs/docs/algorithms/topological-sort/topological-sort.md
+++ b/docs/docs/algorithms/topological-sort/topological-sort.md
@@ -13,9 +13,9 @@ The runtime of the algorithm is `O(|V|+|E|)` and the memory consumption is `O(|V
 
 ```cpp
 template <typename V, typename E>
-[[nodiscard]] std::vector<edge_id_t> kruskal_minimum_spanning_tree(
-    const graph<V, E, graph_type::UNDIRECTED>& graph);
+[[nodiscard]] std::optional<std::vector<vertex_id_t>> topological_sort(
+    const graph<V, E, graph_type::DIRECTED>& graph);
 ```
 
-- **graph** The graph to traverse.
+- **graph** The directed graph to traverse.
 - **return** Vector of vertices sorted in topological order. If the graph contains cycles, it returns an empty vector.
\ No newline at end of file
diff --git a/include/graaflib/algorithm/topological_sorting.h b/include/graaflib/algorithm/topological_sorting.h
index 9faba554..a3b263a4 100644
--- a/include/graaflib/algorithm/topological_sorting.h
+++ b/include/graaflib/algorithm/topological_sorting.h
@@ -1,5 +1,6 @@
 #pragma once
 
+#include <optional>
 #include <graaflib/graph.h>
 
 namespace graaf::algorithm {
@@ -13,7 +14,7 @@ namespace graaf::algorithm {
  * @return Vector of vertices sorted in topological order
  */
 template <typename V, typename E>
-[[nodiscard]] std::vector<vertex_id_t> topological_sort(
+[[nodiscard]] std::optional<std::vector<vertex_id_t>> topological_sort(
     const graph<V, E, graph_type::DIRECTED>& graph);
 
 }  // namespace graaf::algorithm
diff --git a/include/graaflib/algorithm/topological_sorting.tpp b/include/graaflib/algorithm/topological_sorting.tpp
index 817185bd..bcd7d30a 100644
--- a/include/graaflib/algorithm/topological_sorting.tpp
+++ b/include/graaflib/algorithm/topological_sorting.tpp
@@ -4,52 +4,50 @@
 #include <graaflib/algorithm/topological_sorting.h>
 
 #include <vector>
-#include <unordered_map>
+#include <optional>
+#include <unordered_set>
 
 namespace graaf::algorithm {
 
 namespace detail {
 
-enum class vertex_status { UNVISITED, VISITED};
-
 // DFS topological sort
 template <typename V, typename E>
 void do_dfs_topological_sort(
     const graph<V, E, graph_type::DIRECTED>& graph,
     vertex_id_t start_vertex,
-    std::unordered_map<vertex_id_t, vertex_status>& processed_vertices,
+    std::unordered_set<vertex_id_t>& processed_vertices,
     std::vector<vertex_id_t>& sorted_vertices) {
     
-    processed_vertices[start_vertex] = vertex_status::VISITED;
+    processed_vertices.insert(start_vertex);
     for (const auto& next_vertex : graph.get_neighbors(start_vertex)) {
-        if (processed_vertices[next_vertex] == vertex_status::UNVISITED) {
+        if (!processed_vertices.contains(next_vertex)) {
             do_dfs_topological_sort(graph, next_vertex, processed_vertices,
                 sorted_vertices);
         }
     }
 
-        sorted_vertices.push_back(start_vertex);
+    sorted_vertices.push_back(start_vertex);       
     }
 
 }; // namespace detail
 
 template <typename V, typename E>
-std::vector<vertex_id_t> topological_sort(
+std::optional<std::vector<vertex_id_t>> topological_sort(
     const graph<V, E, graph_type::DIRECTED>& graph) {
     
     // Graph should be acyclic
     if (dfs_cycle_detection(graph)) {
-        return {};    
+        return std::nullopt;    
     }
 
-    using enum detail::vertex_status;
     std::vector<vertex_id_t> sorted_vertices{};
     sorted_vertices.reserve(graph.vertex_count());
-    std::unordered_map<vertex_id_t, detail::vertex_status> processed_vertices{};
+    std::unordered_set<vertex_id_t> processed_vertices{};
 
-    for (const auto& vertex : graph.get_vertices()) {
-        if (processed_vertices[vertex.first] == UNVISITED) {
-            detail::do_dfs_topological_sort(graph, vertex.first, processed_vertices, sorted_vertices);
+    for (const auto& [vertex_id, _] : graph.get_vertices()) {
+        if (!processed_vertices.contains(vertex_id)) {
+            detail::do_dfs_topological_sort(graph, vertex_id, processed_vertices, sorted_vertices);
         }
     }
 
diff --git a/test/graaflib/algorithm/topological_sorting_test.cpp b/test/graaflib/algorithm/topological_sorting_test.cpp
index a5f224de..642b15d4 100644
--- a/test/graaflib/algorithm/topological_sorting_test.cpp
+++ b/test/graaflib/algorithm/topological_sorting_test.cpp
@@ -32,12 +32,40 @@ TYPED_TEST(TypedTopologicalSort, ShortGraph) {
 
   // WHEN;
   auto sorted_vertices = topological_sort(graph);
-  std::vector<vertex_id_t> expected_vertices{0, 1, 2, 3};
+  std::vector<vertex_id_t> expected_vertices{vertex_1, vertex_2, vertex_3,
+                                             vertex_4};
 
   // THEN
   ASSERT_EQ(expected_vertices, sorted_vertices);
 }
 
+TYPED_TEST(TypedTopologicalSort, RhombusShapeGraph) {
+  // GIVEN
+  using graph_t = typename TestFixture::graph_t;
+  graph_t graph{};
+
+  const auto vertex_1{graph.add_vertex(10)};
+  const auto vertex_2{graph.add_vertex(20)};
+  const auto vertex_3{graph.add_vertex(30)};
+  const auto vertex_4{graph.add_vertex(40)};
+
+  graph.add_edge(vertex_1, vertex_2, 25);
+  graph.add_edge(vertex_1, vertex_3, 35);
+  graph.add_edge(vertex_3, vertex_4, 45);
+  graph.add_edge(vertex_2, vertex_4, 55);
+
+  // WHEN;
+  auto sorted_vertices = topological_sort(graph);
+  std::vector<vertex_id_t> expected_vertices_1{vertex_1, vertex_2, vertex_3,
+                                               vertex_4};
+  std::vector<vertex_id_t> expected_vertices_2{vertex_1, vertex_3, vertex_2,
+                                               vertex_4};
+
+  // THEN
+  ASSERT_TRUE(expected_vertices_1 == sorted_vertices ||
+              expected_vertices_2 == sorted_vertices);
+}
+
 TYPED_TEST(TypedTopologicalSort, CycleGraph) {
   // GIVEN
   using graph_t = typename TestFixture::graph_t;
@@ -55,7 +83,7 @@ TYPED_TEST(TypedTopologicalSort, CycleGraph) {
 
   // WHEN;
   auto sorted_vertices = topological_sort(graph);
-  std::vector<vertex_id_t> expected_vertices{};
+  const auto expected_vertices = std::nullopt;
 
   // THEN
   ASSERT_EQ(expected_vertices, sorted_vertices);
@@ -78,7 +106,7 @@ TYPED_TEST(TypedTopologicalSort, GraphWithParallelEdge) {
 
   // WHEN
   auto sorted_vertices = topological_sort(graph);
-  std::vector<vertex_id_t> expected_vertices{};
+  const auto expected_vertices = std::nullopt;
 
   // THEN
   ASSERT_EQ(expected_vertices, sorted_vertices);
@@ -101,7 +129,7 @@ TYPED_TEST(TypedTopologicalSort, SelfLoop) {
 
   // WHEN;
   auto sorted_vertices = topological_sort(graph);
-  std::vector<vertex_id_t> expected_vertices{};
+  const auto expected_vertices = std::nullopt;
 
   // THEN
   ASSERT_EQ(expected_vertices, sorted_vertices);
@@ -131,14 +159,22 @@ TYPED_TEST(TypedTopologicalSort, SimpleGraph) {
 
   // WHEN;
   auto sorted_vertices = topological_sort(graph);
-  std::vector<vertex_id_t> expected_vertices_1{0, 3, 1, 5, 4, 2, 6};
-  std::vector<vertex_id_t> expected_vertices_2{0, 1, 3, 5, 4, 2, 6};
-  std::vector<vertex_id_t> expected_vertices_3{0, 1, 3, 4, 5, 2, 6};
-  std::vector<vertex_id_t> expected_vertices_4{0, 4, 3, 1, 5, 2, 6};
-  std::vector<vertex_id_t> expected_vertices_5{0, 4, 1, 3, 5, 2, 6};
-  std::vector<vertex_id_t> expected_vertices_6{0, 1, 4, 3, 5, 2, 6};
-  std::vector<vertex_id_t> expected_vertices_7{0, 3, 1, 4, 5, 2, 6};
-  std::vector<vertex_id_t> expected_vertices_8{0, 3, 4, 1, 5, 2, 6};
+  std::vector<vertex_id_t> expected_vertices_1{
+      vertex_1, vertex_4, vertex_2, vertex_6, vertex_5, vertex_3, vertex_7};
+  std::vector<vertex_id_t> expected_vertices_2{
+      vertex_1, vertex_2, vertex_4, vertex_6, vertex_5, vertex_3, vertex_7};
+  std::vector<vertex_id_t> expected_vertices_3{
+      vertex_1, vertex_2, vertex_4, vertex_5, vertex_6, vertex_3, vertex_7};
+  std::vector<vertex_id_t> expected_vertices_4{
+      vertex_1, vertex_5, vertex_4, vertex_2, vertex_6, vertex_3, vertex_7};
+  std::vector<vertex_id_t> expected_vertices_5{
+      vertex_1, vertex_5, vertex_2, vertex_4, vertex_6, vertex_3, vertex_7};
+  std::vector<vertex_id_t> expected_vertices_6{
+      vertex_1, vertex_2, vertex_5, vertex_4, vertex_6, vertex_3, vertex_7};
+  std::vector<vertex_id_t> expected_vertices_7{
+      vertex_1, vertex_4, vertex_2, vertex_5, vertex_6, vertex_3, vertex_7};
+  std::vector<vertex_id_t> expected_vertices_8{
+      vertex_1, vertex_4, vertex_5, vertex_2, vertex_6, vertex_3, vertex_7};
 
   // THEN
   ASSERT_TRUE((expected_vertices_1 == sorted_vertices) ||
@@ -173,12 +209,18 @@ TYPED_TEST(TypedTopologicalSort, SixSortResults) {
 
   // WHEN;
   auto sorted_vertices = topological_sort(graph);
-  std::vector<vertex_id_t> expected_vertices_1{0, 1, 2, 3, 4, 5, 6};
-  std::vector<vertex_id_t> expected_vertices_2{0, 1, 2, 5, 6, 3, 4};
-  std::vector<vertex_id_t> expected_vertices_3{0, 5, 6, 1, 2, 3, 4};
-  std::vector<vertex_id_t> expected_vertices_4{0, 5, 6, 3, 4, 1, 2};
-  std::vector<vertex_id_t> expected_vertices_5{0, 3, 4, 5, 6, 1, 2};
-  std::vector<vertex_id_t> expected_vertices_6{0, 3, 4, 1, 2, 5, 6};
+  std::vector<vertex_id_t> expected_vertices_1{
+      vertex_1, vertex_2, vertex_3, vertex_4, vertex_5, vertex_6, vertex_7};
+  std::vector<vertex_id_t> expected_vertices_2{
+      vertex_1, vertex_2, vertex_3, vertex_6, vertex_7, vertex_4, vertex_5};
+  std::vector<vertex_id_t> expected_vertices_3{
+      vertex_1, vertex_6, vertex_7, vertex_2, vertex_3, vertex_4, vertex_5};
+  std::vector<vertex_id_t> expected_vertices_4{
+      vertex_1, vertex_6, vertex_7, vertex_4, vertex_5, vertex_2, vertex_3};
+  std::vector<vertex_id_t> expected_vertices_5{
+      vertex_1, vertex_4, vertex_5, vertex_6, vertex_7, vertex_2, vertex_3};
+  std::vector<vertex_id_t> expected_vertices_6{
+      vertex_1, vertex_4, vertex_5, vertex_2, vertex_3, vertex_6, vertex_7};
 
   // THEN
   ASSERT_TRUE((expected_vertices_1 == sorted_vertices) ||

From 57d3c4735de92cac1486e333814c1414160777e1 Mon Sep 17 00:00:00 2001
From: Hromz <hromizz@gmail.com>
Date: Sun, 10 Sep 2023 11:38:10 +0300
Subject: [PATCH 25/40] Clang format

---
 include/graaflib/algorithm/topological_sorting.h | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/include/graaflib/algorithm/topological_sorting.h b/include/graaflib/algorithm/topological_sorting.h
index a3b263a4..5cae4ae9 100644
--- a/include/graaflib/algorithm/topological_sorting.h
+++ b/include/graaflib/algorithm/topological_sorting.h
@@ -1,8 +1,9 @@
 #pragma once
 
-#include <optional>
 #include <graaflib/graph.h>
 
+#include <optional>
+
 namespace graaf::algorithm {
 /**
  * @brief Calculates order of vertices in topological order

From c5ddba1679a5a6ee20cf4a7c5fd32d12bfc35a68 Mon Sep 17 00:00:00 2001
From: Aleksandr <hromizz@gmail.com>
Date: Sun, 10 Sep 2023 23:31:19 +0300
Subject: [PATCH 26/40] Update topological-sort.md

Corrected doc file
---
 docs/docs/algorithms/topological-sort/topological-sort.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/docs/docs/algorithms/topological-sort/topological-sort.md b/docs/docs/algorithms/topological-sort/topological-sort.md
index 0d81af79..a8d544cd 100644
--- a/docs/docs/algorithms/topological-sort/topological-sort.md
+++ b/docs/docs/algorithms/topological-sort/topological-sort.md
@@ -18,4 +18,4 @@ template <typename V, typename E>
 ```
 
 - **graph** The directed graph to traverse.
-- **return** Vector of vertices sorted in topological order. If the graph contains cycles, it returns an empty vector.
\ No newline at end of file
+- **return** Vector of vertices sorted in topological order. If the graph contains cycles, it returns std::nullopt.

From 19ea438c081c3eef6515c90c9cbb911666c2835e Mon Sep 17 00:00:00 2001
From: Hromz <hromizz@gmail.com>
Date: Thu, 14 Sep 2023 14:41:30 +0300
Subject: [PATCH 27/40] DOCS for DFS based cycle detection

---
 .../algorithms/cycle-detection/dfs-based.md   | 52 ++++++++++++++++++-
 1 file changed, 51 insertions(+), 1 deletion(-)

diff --git a/docs/docs/algorithms/cycle-detection/dfs-based.md b/docs/docs/algorithms/cycle-detection/dfs-based.md
index 7c8cc550..8d0740f8 100644
--- a/docs/docs/algorithms/cycle-detection/dfs-based.md
+++ b/docs/docs/algorithms/cycle-detection/dfs-based.md
@@ -2,4 +2,54 @@
 sidebar_position: 1
 ---
 
-# DFS Based Cycle Detection
\ No newline at end of file
+# DFS Based Cycle Detection
+A DFS based cycle detection algorithm is used to identify cycles in graphs, both directed and undirected.
+The algorithm doesn't work on edges with weight and therefore cannot be used for negative weight cycles.
+
+# Directed graph
+The key idea is that when a vertex is processed, mark it as: UNVISITED, VISITED and NO_CYCLE.
+By default all vertices marked as UNVISITED. During the traversal, we label vertices as VISITED. At the exit of the recursion, we label the vertex as NO CYCLE.
+If we met a vertex labeled VISITED, we found a cycle in the graph.
+
+# Undirected graph
+The key idea is to store the parent of each vertex during the traversal. So when we check neighboring vertices, we skip back edge.
+During the traversal we mark the vertex as visited and continue the traversal. In case a vertex was visited before and vertices have different parents, we found a cycle.
+ 
+The runtime of the algorithm is `O(|V| + |E|)` and memory consumption is `O(|V|)`. Where V is the number of vertices in the graph and E the number of edges.
+The algorithm uses DFS traversal and therefore suffers the same limitations (see depth-first-search.md).
+
+# Use cases
+- Resource dependencies:
+  - Redundant connections.
+  - Deadlocks in concurrent systems.
+- Logical dependencies:
+  - Data base relation.
+  - Dependency management.
+  - Circuit design.
+- Infinity loops.
+
+[wikipedia]('https://en.wikipedia.org/wiki/Cycle_(graph_theory)#Cycle_detection')
+
+## Syntax
+Cycle detection for directed graph.
+
+```cpp
+template <typename V, typename E>
+[[nodiscard]] bool dfs_cycle_detection(
+    const graph<V, E, graph_type::DIRECTED> &graph);
+
+```
+
+Cycle detection for unidrected graph.
+```cpp
+template <typename V, typename E>
+[[nodiscard]] bool dfs_cycle_detection(
+    const graph<V, E, graph_type::UNDIRECTED> &graph);
+```
+
+- **graph** The graph to traverse.
+- **return** Returns true in case of cycle otherwise returns false.
+
+## Similar algorithms
+There are many algorithms for cycle detection or algorithms with specific cycle conditions.
+See [wikipedia]('https://en.wikipedia.org/wiki/Cycle_(graph_theory)#Graph_classes_defined_by_cycle')

From 68c2c2be73f636ad3bc67e331d41d51f9cb24ead Mon Sep 17 00:00:00 2001
From: Hromz <hromizz@gmail.com>
Date: Thu, 14 Sep 2023 14:46:20 +0300
Subject: [PATCH 28/40] small fixes

---
 docs/docs/algorithms/cycle-detection/dfs-based.md | 5 +++--
 1 file changed, 3 insertions(+), 2 deletions(-)

diff --git a/docs/docs/algorithms/cycle-detection/dfs-based.md b/docs/docs/algorithms/cycle-detection/dfs-based.md
index 8d0740f8..a5e99b12 100644
--- a/docs/docs/algorithms/cycle-detection/dfs-based.md
+++ b/docs/docs/algorithms/cycle-detection/dfs-based.md
@@ -22,13 +22,14 @@ The algorithm uses DFS traversal and therefore suffers the same limitations (see
 - Resource dependencies:
   - Redundant connections.
   - Deadlocks in concurrent systems.
+  - Deadlocks in concurrent systems.
 - Logical dependencies:
   - Data base relation.
   - Dependency management.
   - Circuit design.
 - Infinity loops.
 
-[wikipedia]('https://en.wikipedia.org/wiki/Cycle_(graph_theory)#Cycle_detection')
+[wikipedia](https://en.wikipedia.org/wiki/Cycle_(graph_theory)#Cycle_detection)
 
 ## Syntax
 Cycle detection for directed graph.
@@ -52,4 +53,4 @@ template <typename V, typename E>
 
 ## Similar algorithms
 There are many algorithms for cycle detection or algorithms with specific cycle conditions.
-See [wikipedia]('https://en.wikipedia.org/wiki/Cycle_(graph_theory)#Graph_classes_defined_by_cycle')
+See [wikipedia](https://en.wikipedia.org/wiki/Cycle_(graph_theory)#Graph_classes_defined_by_cycle)

From 55d39728c2fb68953fa0377008360fbcca040b16 Mon Sep 17 00:00:00 2001
From: Aleksandr <hromizz@gmail.com>
Date: Mon, 18 Sep 2023 07:52:13 +0300
Subject: [PATCH 29/40] Update dfs-based.md

---
 docs/docs/algorithms/cycle-detection/dfs-based.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/docs/docs/algorithms/cycle-detection/dfs-based.md b/docs/docs/algorithms/cycle-detection/dfs-based.md
index a5e99b12..43cdf4d0 100644
--- a/docs/docs/algorithms/cycle-detection/dfs-based.md
+++ b/docs/docs/algorithms/cycle-detection/dfs-based.md
@@ -4,7 +4,7 @@ sidebar_position: 1
 
 # DFS Based Cycle Detection
 A DFS based cycle detection algorithm is used to identify cycles in graphs, both directed and undirected.
-The algorithm doesn't work on edges with weight and therefore cannot be used for negative weight cycles.
+The algorithm can be used to detect cycles in the structure of a graph, as it does not consider edge weights.
 
 # Directed graph
 The key idea is that when a vertex is processed, mark it as: UNVISITED, VISITED and NO_CYCLE.

From da97d6265a4042213746f0dc9e50eb7c9cbf2539 Mon Sep 17 00:00:00 2001
From: Hromz <hromizz@gmail.com>
Date: Sun, 24 Sep 2023 13:29:36 +0300
Subject: [PATCH 30/40] Added Floyd-WArshall algorithm - algorithm - test -
 documentation

---
 .../shortest-path/floyd-warshall.md           |  28 ++
 .../algorithm/shortest_path/floyd_warshall.h  |  30 ++
 .../shortest_path/floyd_warshall.tpp          |  80 +++++
 .../algorithm/floyd_warshall_test.cpp         | 290 ++++++++++++++++++
 4 files changed, 428 insertions(+)
 create mode 100644 docs/docs/algorithms/shortest-path/floyd-warshall.md
 create mode 100644 include/graaflib/algorithm/shortest_path/floyd_warshall.h
 create mode 100644 include/graaflib/algorithm/shortest_path/floyd_warshall.tpp
 create mode 100644 test/graaflib/algorithm/floyd_warshall_test.cpp

diff --git a/docs/docs/algorithms/shortest-path/floyd-warshall.md b/docs/docs/algorithms/shortest-path/floyd-warshall.md
new file mode 100644
index 00000000..ac6fc1a2
--- /dev/null
+++ b/docs/docs/algorithms/shortest-path/floyd-warshall.md
@@ -0,0 +1,28 @@
+---
+sidebar_position: 5
+---
+
+# Floyd-Warshall algorithm
+Floyd-Warshall algorithm computes the shortest path between any two vertices in a graph, both directed and undirected.
+The key idea of the algorithm is to relax the weighted shortest path between any two vertices, using any vertex as an intermediate one.
+Advantage of the algorithm is that it processes vertices instead of edges. This advantage can be used when the number of edges is large enough, aka a dense graph.
+Runtime of the algorithm is O(|V<sup>3</sup>|) and memory consumption is O(|V<sup>2</sup>|).
+
+[wikipedia](https://en.wikipedia.org/wiki/Floyd%E2%80%93Warshall_algorithm)
+
+## Syntax
+
+Calculates the shortest path between any two vertices.
+
+```cpp
+template <typename V, typename E, graph_type T,
+          typename WEIGHT_T = decltype(get_weight(std::declval<E>()))>
+std::vector<std::vector<WEIGHT_T>> floyd_warshall_shortest_paths(
+    const graph<V, E, T>& graph);
+```
+
+- **graph** The graph to extract the shortest path from.
+- **return** Returns a 2D vector of the shortest path. If a path doesn't exist between two vertices, mark it as TYPE_MAX.
+
+### Special case
+In the case of a negative cycle in both directed and undirected graphs, the algorithm marks vertices as TYPE_MIN.
\ No newline at end of file
diff --git a/include/graaflib/algorithm/shortest_path/floyd_warshall.h b/include/graaflib/algorithm/shortest_path/floyd_warshall.h
new file mode 100644
index 00000000..ca022ecf
--- /dev/null
+++ b/include/graaflib/algorithm/shortest_path/floyd_warshall.h
@@ -0,0 +1,30 @@
+#pragma once
+
+#include <graaflib/graph.h>
+#include <graaflib/types.h>
+
+namespace graaf::algorithm {
+/**
+ * @brief Floyd-Warshall Algorithm
+ *
+ * This function computes the shortest paths between all pairs of vertices in a
+ * given weighted graph. It works for graphs with negative weight edges as well,
+ * but not for graphs with negative weight cycles. The function returns an
+ * adjacency matrix representing the shortest distances.
+ *
+ * @tparam V The type of a graph vertex
+ * @tparam E The type of a graph edge
+ * @tparam T the graph type (DIRECTED or UNDIRECTED)
+ * @tparam WEIGHT_T The weight type of an edge in the graph
+ * @param graph The graph object
+ * @return A 2D vector where element at [i][j] is the shortest distance from
+ * vertex i to vertex j.
+ */
+template <typename V, typename E, graph_type T,
+          typename WEIGHT_T = decltype(get_weight(std::declval<E>()))>
+std::vector<std::vector<WEIGHT_T>> floyd_warshall_shortest_paths(
+    const graph<V, E, T>& graph);
+
+}; // namespace graaf::algorithm
+
+#include "floyd_warshall.tpp"
\ No newline at end of file
diff --git a/include/graaflib/algorithm/shortest_path/floyd_warshall.tpp b/include/graaflib/algorithm/shortest_path/floyd_warshall.tpp
new file mode 100644
index 00000000..44fd2769
--- /dev/null
+++ b/include/graaflib/algorithm/shortest_path/floyd_warshall.tpp
@@ -0,0 +1,80 @@
+#pragma once
+
+#include <graaflib/algorithm/shortest_path/floyd_warshall.h>
+
+#include <limits>
+#include <vector>
+
+namespace graaf::algorithm {
+
+namespace detail {
+
+// Mark vertices in negative cycle as NO_PATH
+template<typename WEIGHT_T>
+void do_fw_detect_negative_cycle(
+    std::vector<std::vector<WEIGHT_T>>& distance, WEIGHT_T ZERO, WEIGHT_T INF,
+    WEIGHT_T NO_PATH, size_t n){
+
+  for(std::size_t start_vertex = 0; start_vertex < n; ++start_vertex){
+    for(std::size_t end_vertex = 0; end_vertex < n; ++end_vertex){
+      for(std::size_t through_vertex = 0; through_vertex < n; ++through_vertex){
+        if(distance[start_vertex][through_vertex] < INF &&
+            distance[through_vertex][through_vertex] < ZERO &&
+            distance[through_vertex][end_vertex] < INF){
+          distance[start_vertex][end_vertex] = NO_PATH;
+        }
+      }
+    }
+  }
+}
+
+}; // namespace detail
+
+template <typename V, typename E, graph_type T, typename WEIGHT_T>
+std::vector<std::vector<WEIGHT_T>> floyd_warshall_shortest_paths(
+    const graph<V, E, T>& graph){
+
+  WEIGHT_T ZERO{};
+  std::size_t n = graph.vertex_count();
+  auto INF = std::numeric_limits<WEIGHT_T>::max();
+  auto NO_PATH = std::numeric_limits<WEIGHT_T>::min();
+
+   std::vector<std::vector<WEIGHT_T>> shortest_paths(
+       n, std::vector<WEIGHT_T>(n, INF));
+
+   for(std::size_t vertex = 0; vertex < n; ++vertex){
+      shortest_paths[vertex][vertex] = ZERO;
+   }
+
+   // Initial weights between vertices
+   for(std::size_t from_vertex = 0; from_vertex < n; ++from_vertex){
+      for(const auto & to_vertex : graph.get_neighbors(from_vertex)){
+            shortest_paths[from_vertex][to_vertex] =
+          std::min(shortest_paths[from_vertex][to_vertex],
+          get_weight(graph.get_edge(from_vertex, to_vertex)));
+      }
+   }
+
+   for(std::size_t through_vertex = 0; through_vertex < n; ++through_vertex){
+      for(std::size_t start_vertex = 0; start_vertex < n; ++start_vertex){
+            if(shortest_paths[start_vertex][through_vertex] < INF) {
+
+        for (std::size_t end_vertex = 0; end_vertex < n; ++end_vertex) {
+
+          if (shortest_paths[through_vertex][end_vertex] < INF) {
+            shortest_paths[start_vertex][end_vertex] =
+                std::min(shortest_paths[start_vertex][end_vertex],
+                         shortest_paths[start_vertex][through_vertex] +
+                             shortest_paths[through_vertex][end_vertex]);
+           }
+         }
+       }
+     }
+   }
+
+   // Mark vertices in negative cycles with INF
+   detail::do_fw_detect_negative_cycle(shortest_paths,ZERO, INF, NO_PATH, n);
+   return shortest_paths;
+}
+
+}; // namespace graaf::algorithm
\ No newline at end of file
diff --git a/test/graaflib/algorithm/floyd_warshall_test.cpp b/test/graaflib/algorithm/floyd_warshall_test.cpp
new file mode 100644
index 00000000..2e36929a
--- /dev/null
+++ b/test/graaflib/algorithm/floyd_warshall_test.cpp
@@ -0,0 +1,290 @@
+#include <graaflib/algorithm/shortest_path/floyd_warshall.h>
+#include <graaflib/graph.h>
+#include <graaflib/types.h>
+#include <gtest/gtest.h>
+
+namespace graaf::algorithm {
+
+namespace {
+
+template <typename T>
+class my_weighted_edge : public weighted_edge<T> {
+ public:
+  explicit my_weighted_edge(T weight) : weight_{weight} {}
+
+  [[nodiscard]] T get_weight() const noexcept override { return weight_; }
+
+ private:
+  T weight_{};
+};
+
+template <typename T>
+struct FloydWarshallTest : public testing::Test {
+  using graph_t = typename T::first_type;
+  using edge_t = typename T::second_type;
+};
+} // namespace
+
+using weighted_graph_types = testing::Types<
+
+    /**
+     * Primitive edge type directed graph
+     */
+    std::pair<directed_graph<int, int>, int>,
+    std::pair<directed_graph<int, unsigned long>, unsigned long>,
+    std::pair<directed_graph<int, float>, float>,
+    std::pair<directed_graph<int, long double>, long double>,
+
+    /**
+     * Non primitive weighted edge type directed graph
+     */
+
+    std::pair<directed_graph<int, my_weighted_edge<int>>,
+              my_weighted_edge<int>>,
+    std::pair<directed_graph<int, my_weighted_edge<unsigned long>>,
+              my_weighted_edge<unsigned long>>,
+    std::pair<directed_graph<int, my_weighted_edge<float>>,
+              my_weighted_edge<float>>,
+    std::pair<directed_graph<int, my_weighted_edge<long double>>,
+              my_weighted_edge<long double>>,
+
+    /**
+     * Primitive edge type undirected graph
+     */
+    std::pair<undirected_graph<int, int>, int>,
+    std::pair<undirected_graph<int, unsigned long>, unsigned long>,
+    std::pair<undirected_graph<int, float>, float>,
+    std::pair<undirected_graph<int, long double>, long double>,
+
+    /**
+     * Non primitive weighted edge type undirected graph
+     */
+    std::pair<undirected_graph<int, my_weighted_edge<int>>,
+              my_weighted_edge<int>>,
+    std::pair<undirected_graph<int, my_weighted_edge<unsigned long>>,
+              my_weighted_edge<unsigned long>>,
+    std::pair<undirected_graph<int, my_weighted_edge<float>>,
+              my_weighted_edge<float>>,
+    std::pair<undirected_graph<int, my_weighted_edge<long double>>,
+              my_weighted_edge<long double>>>;
+
+TYPED_TEST_SUITE(FloydWarshallTest, weighted_graph_types);
+
+TYPED_TEST(FloydWarshallTest, UndirectedGraph) {
+  // GIVEN
+  undirected_graph<int, int> graph{};
+
+  // graph vertices
+  const auto vertex_1{graph.add_vertex(10)};
+  const auto vertex_2{graph.add_vertex(20)};
+  const auto vertex_3{graph.add_vertex(30)};
+
+  // adding edges to our graph
+  graph.add_edge(vertex_1, vertex_2, 100);
+  graph.add_edge(vertex_2, vertex_3, 300);
+  graph.add_edge(vertex_3, vertex_1, 300);
+
+  auto shortest_paths = floyd_warshall_shortest_paths(graph);
+  std::vector<std::vector<int>> expected_paths = {{0, 100, 300}, {100, 0, 300},
+                                                  {300, 300, 0}};
+
+  ASSERT_EQ(shortest_paths, expected_paths);
+  }
+
+  TYPED_TEST(FloydWarshallTest, DirectedGraph){
+  // GIVEN
+  directed_graph<int, int> graph{};
+
+  // graph vertices
+  const auto vertex_1{graph.add_vertex(10)};
+  const auto vertex_2{graph.add_vertex(20)};
+  const auto vertex_3{graph.add_vertex(30)};
+
+  // adding edges to our graph
+  graph.add_edge(vertex_1, vertex_2, 100);
+  graph.add_edge(vertex_2, vertex_3, 300);
+  graph.add_edge(vertex_3, vertex_1, 300);
+
+  auto shortest_paths = floyd_warshall_shortest_paths(graph);
+  std::vector<std::vector<int>> expected_paths = {{0, 100, 400}, {600, 0, 300},
+                                                  {300, 400, 0}};
+
+  ASSERT_EQ(shortest_paths, expected_paths);
+  }
+
+  TYPED_TEST(FloydWarshallTest, DirectedGraphNegativeCycle){
+  // GIVEN
+  directed_graph<int,int> graph{};
+
+  // graph vertices
+  const auto vertex_1{graph.add_vertex(10)};
+  const auto vertex_2{graph.add_vertex(20)};
+  const auto vertex_3{graph.add_vertex(30)};
+  const auto vertex_4{graph.add_vertex(40)};
+
+  // adding edges to our graph
+  graph.add_edge(vertex_1, vertex_2, -100);
+  graph.add_edge(vertex_2, vertex_3, 300);
+  graph.add_edge(vertex_3, vertex_1, -300);
+  graph.add_edge(vertex_4, vertex_2, 300);
+
+  auto NEG_CYCLE = INT_MIN;
+  auto NO_PATH = INT_MAX;
+
+  auto shortest_paths = floyd_warshall_shortest_paths(graph);
+  std::vector<std::vector<int>> expected_paths =
+      {{NEG_CYCLE, NEG_CYCLE, NEG_CYCLE, NO_PATH},
+       {NEG_CYCLE, NEG_CYCLE, NEG_CYCLE, NO_PATH},
+       {NEG_CYCLE, NEG_CYCLE, NEG_CYCLE, NO_PATH},
+       {NEG_CYCLE, NEG_CYCLE, NEG_CYCLE, 0}};
+
+  ASSERT_EQ(shortest_paths, expected_paths);
+  }
+
+  TYPED_TEST(FloydWarshallTest, UndirectedGraphNegativeCycle){
+  // GIVEN
+  undirected_graph<int,int> graph{};
+
+  // graph vertices
+  const auto vertex_1{graph.add_vertex(10)};
+  const auto vertex_2{graph.add_vertex(20)};
+  const auto vertex_3{graph.add_vertex(30)};
+  const auto vertex_4{graph.add_vertex(40)};
+
+  // adding edges to our graph
+  graph.add_edge(vertex_1, vertex_2, -100);
+  graph.add_edge(vertex_2, vertex_3, 300);
+  graph.add_edge(vertex_3, vertex_1, -300);
+  graph.add_edge(vertex_4, vertex_2, 300);
+
+  auto NEG_CYCLE = INT_MIN;
+  auto NO_PATH = INT_MAX;
+
+  auto shortest_paths = floyd_warshall_shortest_paths(graph);
+  std::vector<std::vector<int>> expected_paths =
+      {{NEG_CYCLE, NEG_CYCLE, NEG_CYCLE, NEG_CYCLE},
+       {NEG_CYCLE, NEG_CYCLE, NEG_CYCLE, NEG_CYCLE},
+       {NEG_CYCLE, NEG_CYCLE, NEG_CYCLE, NEG_CYCLE},
+       {NEG_CYCLE, NEG_CYCLE, NEG_CYCLE, NEG_CYCLE}};
+
+  ASSERT_EQ(shortest_paths, expected_paths);
+  }
+
+  TYPED_TEST(FloydWarshallTest, DirectedGraphNoCycleNegativeWeight){
+  directed_graph<int,int> graph{};
+
+  // graph vertices
+  const auto vertex_1{graph.add_vertex(10)};
+  const auto vertex_2{graph.add_vertex(20)};
+  const auto vertex_3{graph.add_vertex(30)};
+  const auto vertex_4{graph.add_vertex(40)};
+  const auto vertex_5{graph.add_vertex(50)};
+  const auto vertex_6{graph.add_vertex(60)};
+
+  // adding edges to our graph
+  graph.add_edge(vertex_1, vertex_2, 100);
+  graph.add_edge(vertex_2, vertex_3, 50);
+  graph.add_edge(vertex_2, vertex_4, -20);
+  graph.add_edge(vertex_3, vertex_6, -3);
+  graph.add_edge(vertex_4, vertex_6, 100);
+  graph.add_edge(vertex_5, vertex_2, -75);
+
+  auto NEG_CYCLE = INT_MIN;
+  auto NO_PATH = INT_MAX;
+
+  auto shortest_paths = floyd_warshall_shortest_paths(graph);
+  std::vector<std::vector<int>> expected_paths =
+      {{0, 100, 150, 80, NO_PATH, 147},
+      {NO_PATH, 0, 50, -20, NO_PATH, 47},
+      {NO_PATH, NO_PATH, 0, NO_PATH, NO_PATH, -3},
+      {NO_PATH, NO_PATH, NO_PATH , 0, NO_PATH, 100},
+      {NO_PATH, -75, -25, -95, 0, -28},
+      {NO_PATH, NO_PATH, NO_PATH, NO_PATH, NO_PATH, 0}};
+
+  ASSERT_EQ(shortest_paths, expected_paths);
+  }
+
+  TYPED_TEST(FloydWarshallTest, DenseDirectedGraph){
+  directed_graph<int,int> graph{};
+
+  // graph vertices
+  const auto vertex_1{graph.add_vertex(10)};
+  const auto vertex_2{graph.add_vertex(20)};
+  const auto vertex_3{graph.add_vertex(30)};
+  const auto vertex_4{graph.add_vertex(40)};
+
+  // adding edges to our graph
+  graph.add_edge(vertex_1, vertex_2, 10);
+  graph.add_edge(vertex_2, vertex_3, 50);
+  graph.add_edge(vertex_2, vertex_1, 20);
+  graph.add_edge(vertex_3, vertex_2, 3);
+  graph.add_edge(vertex_4, vertex_1, 10);
+  graph.add_edge(vertex_4, vertex_3, 75);
+  graph.add_edge(vertex_4, vertex_2, 12);
+  graph.add_edge(vertex_1, vertex_4, 12);
+
+  auto shortest_paths = floyd_warshall_shortest_paths(graph);
+  std::vector<std::vector<int>> expected_paths{{0, 10, 60, 12},
+                                               {20, 0, 50, 32},
+                                               {23, 3, 0, 35},
+                                               {10, 12, 62, 0 }};
+
+  ASSERT_EQ(shortest_paths, expected_paths);
+  }
+
+  TYPED_TEST(FloydWarshallTest, DenseUndirectedGraph){
+  undirected_graph<int,int> graph{};
+
+  // graph vertices
+  const auto vertex_1{graph.add_vertex(10)};
+  const auto vertex_2{graph.add_vertex(20)};
+  const auto vertex_3{graph.add_vertex(30)};
+  const auto vertex_4{graph.add_vertex(40)};
+
+  // adding edges to our graph
+  graph.add_edge(vertex_1, vertex_2, 10);
+  graph.add_edge(vertex_3, vertex_2, 3);
+  graph.add_edge(vertex_4, vertex_1, 10);
+  graph.add_edge(vertex_4, vertex_3, 75);
+  graph.add_edge(vertex_4, vertex_2, 12);
+  graph.add_edge(vertex_1, vertex_4, 12);
+
+  auto shortest_paths = floyd_warshall_shortest_paths(graph);
+  std::vector<std::vector<int>> expected_paths{{0, 10, 13, 10},
+                                               {10, 0, 3, 12},
+                                               {13, 3, 0, 15},
+                                               {10, 12, 15, 0 }};
+
+  ASSERT_EQ(shortest_paths, expected_paths);
+  }
+
+  TYPED_TEST(FloydWarshallTest, DirectedGraphWithSubgraphNegativeCycle){
+  directed_graph<int,int> graph{};
+
+  // graph vertices
+  const auto vertex_1{graph.add_vertex(10)};
+  const auto vertex_2{graph.add_vertex(20)};
+  const auto vertex_3{graph.add_vertex(30)};
+  const auto vertex_4{graph.add_vertex(40)};
+
+  // adding edges to our graph
+  graph.add_edge(vertex_1, vertex_2, 10);
+  graph.add_edge(vertex_2, vertex_1, -20);
+
+  graph.add_edge(vertex_4, vertex_3, 75);
+  graph.add_edge(vertex_3, vertex_4, 12);
+
+  auto NEG_CYCLE = INT_MIN;
+  auto NO_PATH = INT_MAX;
+
+  auto shortest_paths = floyd_warshall_shortest_paths(graph);
+  std::vector<std::vector<int>> expected_paths =
+      {{NEG_CYCLE, NEG_CYCLE, NO_PATH, NO_PATH},
+       {NEG_CYCLE, NEG_CYCLE, NO_PATH, NO_PATH},
+       {NO_PATH, NO_PATH, 0, 12},
+       {NO_PATH, NO_PATH, 75, 0 }};
+
+  ASSERT_EQ(shortest_paths, expected_paths);
+  }
+
+} // namespace graaf::algorithm
\ No newline at end of file

From 7a1ca3c0bb893e71808fc4adda55e0cacf254425 Mon Sep 17 00:00:00 2001
From: Hromz <hromizz@gmail.com>
Date: Sun, 24 Sep 2023 14:11:10 +0300
Subject: [PATCH 31/40] clang tidy

---
 .../algorithm/shortest_path/floyd_warshall.h  |   2 +-
 .../shortest_path/floyd_warshall.tpp          |  75 +++++++------
 .../algorithm/floyd_warshall_test.cpp         | 102 +++++++++---------
 3 files changed, 86 insertions(+), 93 deletions(-)

diff --git a/include/graaflib/algorithm/shortest_path/floyd_warshall.h b/include/graaflib/algorithm/shortest_path/floyd_warshall.h
index ca022ecf..8797cec1 100644
--- a/include/graaflib/algorithm/shortest_path/floyd_warshall.h
+++ b/include/graaflib/algorithm/shortest_path/floyd_warshall.h
@@ -25,6 +25,6 @@ template <typename V, typename E, graph_type T,
 std::vector<std::vector<WEIGHT_T>> floyd_warshall_shortest_paths(
     const graph<V, E, T>& graph);
 
-}; // namespace graaf::algorithm
+};  // namespace graaf::algorithm
 
 #include "floyd_warshall.tpp"
\ No newline at end of file
diff --git a/include/graaflib/algorithm/shortest_path/floyd_warshall.tpp b/include/graaflib/algorithm/shortest_path/floyd_warshall.tpp
index 44fd2769..ffed28fc 100644
--- a/include/graaflib/algorithm/shortest_path/floyd_warshall.tpp
+++ b/include/graaflib/algorithm/shortest_path/floyd_warshall.tpp
@@ -10,17 +10,17 @@ namespace graaf::algorithm {
 namespace detail {
 
 // Mark vertices in negative cycle as NO_PATH
-template<typename WEIGHT_T>
-void do_fw_detect_negative_cycle(
-    std::vector<std::vector<WEIGHT_T>>& distance, WEIGHT_T ZERO, WEIGHT_T INF,
-    WEIGHT_T NO_PATH, size_t n){
-
-  for(std::size_t start_vertex = 0; start_vertex < n; ++start_vertex){
-    for(std::size_t end_vertex = 0; end_vertex < n; ++end_vertex){
-      for(std::size_t through_vertex = 0; through_vertex < n; ++through_vertex){
-        if(distance[start_vertex][through_vertex] < INF &&
+template <typename WEIGHT_T>
+void do_fw_detect_negative_cycle(std::vector<std::vector<WEIGHT_T>>& distance,
+                                 WEIGHT_T ZERO, WEIGHT_T INF, WEIGHT_T NO_PATH,
+                                 size_t n) {
+  for (std::size_t start_vertex = 0; start_vertex < n; ++start_vertex) {
+    for (std::size_t end_vertex = 0; end_vertex < n; ++end_vertex) {
+      for (std::size_t through_vertex = 0; through_vertex < n;
+           ++through_vertex) {
+        if (distance[start_vertex][through_vertex] < INF &&
             distance[through_vertex][through_vertex] < ZERO &&
-            distance[through_vertex][end_vertex] < INF){
+            distance[through_vertex][end_vertex] < INF) {
           distance[start_vertex][end_vertex] = NO_PATH;
         }
       }
@@ -28,53 +28,50 @@ void do_fw_detect_negative_cycle(
   }
 }
 
-}; // namespace detail
+};  // namespace detail
 
 template <typename V, typename E, graph_type T, typename WEIGHT_T>
 std::vector<std::vector<WEIGHT_T>> floyd_warshall_shortest_paths(
-    const graph<V, E, T>& graph){
-
+    const graph<V, E, T>& graph) {
   WEIGHT_T ZERO{};
   std::size_t n = graph.vertex_count();
   auto INF = std::numeric_limits<WEIGHT_T>::max();
   auto NO_PATH = std::numeric_limits<WEIGHT_T>::min();
 
-   std::vector<std::vector<WEIGHT_T>> shortest_paths(
-       n, std::vector<WEIGHT_T>(n, INF));
+  std::vector<std::vector<WEIGHT_T>> shortest_paths(
+      n, std::vector<WEIGHT_T>(n, INF));
 
-   for(std::size_t vertex = 0; vertex < n; ++vertex){
-      shortest_paths[vertex][vertex] = ZERO;
-   }
+  for (std::size_t vertex = 0; vertex < n; ++vertex) {
+    shortest_paths[vertex][vertex] = ZERO;
+  }
 
-   // Initial weights between vertices
-   for(std::size_t from_vertex = 0; from_vertex < n; ++from_vertex){
-      for(const auto & to_vertex : graph.get_neighbors(from_vertex)){
-            shortest_paths[from_vertex][to_vertex] =
+  // Initial weights between vertices
+  for (std::size_t from_vertex = 0; from_vertex < n; ++from_vertex) {
+    for (const auto& to_vertex : graph.get_neighbors(from_vertex)) {
+      shortest_paths[from_vertex][to_vertex] =
           std::min(shortest_paths[from_vertex][to_vertex],
-          get_weight(graph.get_edge(from_vertex, to_vertex)));
-      }
-   }
-
-   for(std::size_t through_vertex = 0; through_vertex < n; ++through_vertex){
-      for(std::size_t start_vertex = 0; start_vertex < n; ++start_vertex){
-            if(shortest_paths[start_vertex][through_vertex] < INF) {
+                   get_weight(graph.get_edge(from_vertex, to_vertex)));
+    }
+  }
 
+  for (std::size_t through_vertex = 0; through_vertex < n; ++through_vertex) {
+    for (std::size_t start_vertex = 0; start_vertex < n; ++start_vertex) {
+      if (shortest_paths[start_vertex][through_vertex] < INF) {
         for (std::size_t end_vertex = 0; end_vertex < n; ++end_vertex) {
-
           if (shortest_paths[through_vertex][end_vertex] < INF) {
             shortest_paths[start_vertex][end_vertex] =
                 std::min(shortest_paths[start_vertex][end_vertex],
                          shortest_paths[start_vertex][through_vertex] +
                              shortest_paths[through_vertex][end_vertex]);
-           }
-         }
-       }
-     }
-   }
+          }
+        }
+      }
+    }
+  }
 
-   // Mark vertices in negative cycles with INF
-   detail::do_fw_detect_negative_cycle(shortest_paths,ZERO, INF, NO_PATH, n);
-   return shortest_paths;
+  // Mark vertices in negative cycles with INF
+  detail::do_fw_detect_negative_cycle(shortest_paths, ZERO, INF, NO_PATH, n);
+  return shortest_paths;
 }
 
-}; // namespace graaf::algorithm
\ No newline at end of file
+};  // namespace graaf::algorithm
\ No newline at end of file
diff --git a/test/graaflib/algorithm/floyd_warshall_test.cpp b/test/graaflib/algorithm/floyd_warshall_test.cpp
index 2e36929a..29d6e731 100644
--- a/test/graaflib/algorithm/floyd_warshall_test.cpp
+++ b/test/graaflib/algorithm/floyd_warshall_test.cpp
@@ -23,7 +23,7 @@ struct FloydWarshallTest : public testing::Test {
   using graph_t = typename T::first_type;
   using edge_t = typename T::second_type;
 };
-} // namespace
+}  // namespace
 
 using weighted_graph_types = testing::Types<
 
@@ -85,13 +85,13 @@ TYPED_TEST(FloydWarshallTest, UndirectedGraph) {
   graph.add_edge(vertex_3, vertex_1, 300);
 
   auto shortest_paths = floyd_warshall_shortest_paths(graph);
-  std::vector<std::vector<int>> expected_paths = {{0, 100, 300}, {100, 0, 300},
-                                                  {300, 300, 0}};
+  std::vector<std::vector<int>> expected_paths = {
+      {0, 100, 300}, {100, 0, 300}, {300, 300, 0}};
 
   ASSERT_EQ(shortest_paths, expected_paths);
-  }
+}
 
-  TYPED_TEST(FloydWarshallTest, DirectedGraph){
+TYPED_TEST(FloydWarshallTest, DirectedGraph) {
   // GIVEN
   directed_graph<int, int> graph{};
 
@@ -106,15 +106,15 @@ TYPED_TEST(FloydWarshallTest, UndirectedGraph) {
   graph.add_edge(vertex_3, vertex_1, 300);
 
   auto shortest_paths = floyd_warshall_shortest_paths(graph);
-  std::vector<std::vector<int>> expected_paths = {{0, 100, 400}, {600, 0, 300},
-                                                  {300, 400, 0}};
+  std::vector<std::vector<int>> expected_paths = {
+      {0, 100, 400}, {600, 0, 300}, {300, 400, 0}};
 
   ASSERT_EQ(shortest_paths, expected_paths);
-  }
+}
 
-  TYPED_TEST(FloydWarshallTest, DirectedGraphNegativeCycle){
+TYPED_TEST(FloydWarshallTest, DirectedGraphNegativeCycle) {
   // GIVEN
-  directed_graph<int,int> graph{};
+  directed_graph<int, int> graph{};
 
   // graph vertices
   const auto vertex_1{graph.add_vertex(10)};
@@ -132,18 +132,18 @@ TYPED_TEST(FloydWarshallTest, UndirectedGraph) {
   auto NO_PATH = INT_MAX;
 
   auto shortest_paths = floyd_warshall_shortest_paths(graph);
-  std::vector<std::vector<int>> expected_paths =
-      {{NEG_CYCLE, NEG_CYCLE, NEG_CYCLE, NO_PATH},
-       {NEG_CYCLE, NEG_CYCLE, NEG_CYCLE, NO_PATH},
-       {NEG_CYCLE, NEG_CYCLE, NEG_CYCLE, NO_PATH},
-       {NEG_CYCLE, NEG_CYCLE, NEG_CYCLE, 0}};
+  std::vector<std::vector<int>> expected_paths = {
+      {NEG_CYCLE, NEG_CYCLE, NEG_CYCLE, NO_PATH},
+      {NEG_CYCLE, NEG_CYCLE, NEG_CYCLE, NO_PATH},
+      {NEG_CYCLE, NEG_CYCLE, NEG_CYCLE, NO_PATH},
+      {NEG_CYCLE, NEG_CYCLE, NEG_CYCLE, 0}};
 
   ASSERT_EQ(shortest_paths, expected_paths);
-  }
+}
 
-  TYPED_TEST(FloydWarshallTest, UndirectedGraphNegativeCycle){
+TYPED_TEST(FloydWarshallTest, UndirectedGraphNegativeCycle) {
   // GIVEN
-  undirected_graph<int,int> graph{};
+  undirected_graph<int, int> graph{};
 
   // graph vertices
   const auto vertex_1{graph.add_vertex(10)};
@@ -161,17 +161,17 @@ TYPED_TEST(FloydWarshallTest, UndirectedGraph) {
   auto NO_PATH = INT_MAX;
 
   auto shortest_paths = floyd_warshall_shortest_paths(graph);
-  std::vector<std::vector<int>> expected_paths =
-      {{NEG_CYCLE, NEG_CYCLE, NEG_CYCLE, NEG_CYCLE},
-       {NEG_CYCLE, NEG_CYCLE, NEG_CYCLE, NEG_CYCLE},
-       {NEG_CYCLE, NEG_CYCLE, NEG_CYCLE, NEG_CYCLE},
-       {NEG_CYCLE, NEG_CYCLE, NEG_CYCLE, NEG_CYCLE}};
+  std::vector<std::vector<int>> expected_paths = {
+      {NEG_CYCLE, NEG_CYCLE, NEG_CYCLE, NEG_CYCLE},
+      {NEG_CYCLE, NEG_CYCLE, NEG_CYCLE, NEG_CYCLE},
+      {NEG_CYCLE, NEG_CYCLE, NEG_CYCLE, NEG_CYCLE},
+      {NEG_CYCLE, NEG_CYCLE, NEG_CYCLE, NEG_CYCLE}};
 
   ASSERT_EQ(shortest_paths, expected_paths);
-  }
+}
 
-  TYPED_TEST(FloydWarshallTest, DirectedGraphNoCycleNegativeWeight){
-  directed_graph<int,int> graph{};
+TYPED_TEST(FloydWarshallTest, DirectedGraphNoCycleNegativeWeight) {
+  directed_graph<int, int> graph{};
 
   // graph vertices
   const auto vertex_1{graph.add_vertex(10)};
@@ -193,19 +193,19 @@ TYPED_TEST(FloydWarshallTest, UndirectedGraph) {
   auto NO_PATH = INT_MAX;
 
   auto shortest_paths = floyd_warshall_shortest_paths(graph);
-  std::vector<std::vector<int>> expected_paths =
-      {{0, 100, 150, 80, NO_PATH, 147},
+  std::vector<std::vector<int>> expected_paths = {
+      {0, 100, 150, 80, NO_PATH, 147},
       {NO_PATH, 0, 50, -20, NO_PATH, 47},
       {NO_PATH, NO_PATH, 0, NO_PATH, NO_PATH, -3},
-      {NO_PATH, NO_PATH, NO_PATH , 0, NO_PATH, 100},
+      {NO_PATH, NO_PATH, NO_PATH, 0, NO_PATH, 100},
       {NO_PATH, -75, -25, -95, 0, -28},
       {NO_PATH, NO_PATH, NO_PATH, NO_PATH, NO_PATH, 0}};
 
   ASSERT_EQ(shortest_paths, expected_paths);
-  }
+}
 
-  TYPED_TEST(FloydWarshallTest, DenseDirectedGraph){
-  directed_graph<int,int> graph{};
+TYPED_TEST(FloydWarshallTest, DenseDirectedGraph) {
+  directed_graph<int, int> graph{};
 
   // graph vertices
   const auto vertex_1{graph.add_vertex(10)};
@@ -224,16 +224,14 @@ TYPED_TEST(FloydWarshallTest, UndirectedGraph) {
   graph.add_edge(vertex_1, vertex_4, 12);
 
   auto shortest_paths = floyd_warshall_shortest_paths(graph);
-  std::vector<std::vector<int>> expected_paths{{0, 10, 60, 12},
-                                               {20, 0, 50, 32},
-                                               {23, 3, 0, 35},
-                                               {10, 12, 62, 0 }};
+  std::vector<std::vector<int>> expected_paths{
+      {0, 10, 60, 12}, {20, 0, 50, 32}, {23, 3, 0, 35}, {10, 12, 62, 0}};
 
   ASSERT_EQ(shortest_paths, expected_paths);
-  }
+}
 
-  TYPED_TEST(FloydWarshallTest, DenseUndirectedGraph){
-  undirected_graph<int,int> graph{};
+TYPED_TEST(FloydWarshallTest, DenseUndirectedGraph) {
+  undirected_graph<int, int> graph{};
 
   // graph vertices
   const auto vertex_1{graph.add_vertex(10)};
@@ -250,16 +248,14 @@ TYPED_TEST(FloydWarshallTest, UndirectedGraph) {
   graph.add_edge(vertex_1, vertex_4, 12);
 
   auto shortest_paths = floyd_warshall_shortest_paths(graph);
-  std::vector<std::vector<int>> expected_paths{{0, 10, 13, 10},
-                                               {10, 0, 3, 12},
-                                               {13, 3, 0, 15},
-                                               {10, 12, 15, 0 }};
+  std::vector<std::vector<int>> expected_paths{
+      {0, 10, 13, 10}, {10, 0, 3, 12}, {13, 3, 0, 15}, {10, 12, 15, 0}};
 
   ASSERT_EQ(shortest_paths, expected_paths);
-  }
+}
 
-  TYPED_TEST(FloydWarshallTest, DirectedGraphWithSubgraphNegativeCycle){
-  directed_graph<int,int> graph{};
+TYPED_TEST(FloydWarshallTest, DirectedGraphWithSubgraphNegativeCycle) {
+  directed_graph<int, int> graph{};
 
   // graph vertices
   const auto vertex_1{graph.add_vertex(10)};
@@ -278,13 +274,13 @@ TYPED_TEST(FloydWarshallTest, UndirectedGraph) {
   auto NO_PATH = INT_MAX;
 
   auto shortest_paths = floyd_warshall_shortest_paths(graph);
-  std::vector<std::vector<int>> expected_paths =
-      {{NEG_CYCLE, NEG_CYCLE, NO_PATH, NO_PATH},
-       {NEG_CYCLE, NEG_CYCLE, NO_PATH, NO_PATH},
-       {NO_PATH, NO_PATH, 0, 12},
-       {NO_PATH, NO_PATH, 75, 0 }};
+  std::vector<std::vector<int>> expected_paths = {
+      {NEG_CYCLE, NEG_CYCLE, NO_PATH, NO_PATH},
+      {NEG_CYCLE, NEG_CYCLE, NO_PATH, NO_PATH},
+      {NO_PATH, NO_PATH, 0, 12},
+      {NO_PATH, NO_PATH, 75, 0}};
 
   ASSERT_EQ(shortest_paths, expected_paths);
-  }
+}
 
-} // namespace graaf::algorithm
\ No newline at end of file
+}  // namespace graaf::algorithm
\ No newline at end of file

From 4a43bce1df9305317fe796582958016464a4fac6 Mon Sep 17 00:00:00 2001
From: Hromz <hromizz@gmail.com>
Date: Wed, 27 Sep 2023 10:29:10 +0300
Subject: [PATCH 32/40] removed redundant negative cicle check and according
 tests, added two new tests

---
 .../shortest-path/floyd-warshall.md           |  14 +-
 .../shortest_path/floyd_warshall.tpp          |  26 ----
 .../algorithm/floyd_warshall_test.cpp         | 140 +++++++++---------
 3 files changed, 77 insertions(+), 103 deletions(-)

diff --git a/docs/docs/algorithms/shortest-path/floyd-warshall.md b/docs/docs/algorithms/shortest-path/floyd-warshall.md
index ac6fc1a2..645049cd 100644
--- a/docs/docs/algorithms/shortest-path/floyd-warshall.md
+++ b/docs/docs/algorithms/shortest-path/floyd-warshall.md
@@ -3,9 +3,13 @@ sidebar_position: 5
 ---
 
 # Floyd-Warshall algorithm
+
 Floyd-Warshall algorithm computes the shortest path between any two vertices in a graph, both directed and undirected.
-The key idea of the algorithm is to relax the weighted shortest path between any two vertices, using any vertex as an intermediate one.
-Advantage of the algorithm is that it processes vertices instead of edges. This advantage can be used when the number of edges is large enough, aka a dense graph.
+The algorithm does not work for graphs with negative weight cycles.
+The key idea of the algorithm is to relax the weighted shortest path between any two vertices, using any vertex as an
+intermediate one.
+Advantage of the algorithm is that it processes vertices instead of edges. This advantage can be used when the number of
+edges is large enough, aka a dense graph.
 Runtime of the algorithm is O(|V<sup>3</sup>|) and memory consumption is O(|V<sup>2</sup>|).
 
 [wikipedia](https://en.wikipedia.org/wiki/Floyd%E2%80%93Warshall_algorithm)
@@ -22,7 +26,5 @@ std::vector<std::vector<WEIGHT_T>> floyd_warshall_shortest_paths(
 ```
 
 - **graph** The graph to extract the shortest path from.
-- **return** Returns a 2D vector of the shortest path. If a path doesn't exist between two vertices, mark it as TYPE_MAX.
-
-### Special case
-In the case of a negative cycle in both directed and undirected graphs, the algorithm marks vertices as TYPE_MIN.
\ No newline at end of file
+- **return** Returns a 2D vector of the shortest path. If a path doesn't exist between two vertices, mark it as
+  TYPE_MAX.
\ No newline at end of file
diff --git a/include/graaflib/algorithm/shortest_path/floyd_warshall.tpp b/include/graaflib/algorithm/shortest_path/floyd_warshall.tpp
index ffed28fc..d7a4c2c1 100644
--- a/include/graaflib/algorithm/shortest_path/floyd_warshall.tpp
+++ b/include/graaflib/algorithm/shortest_path/floyd_warshall.tpp
@@ -7,36 +7,12 @@
 
 namespace graaf::algorithm {
 
-namespace detail {
-
-// Mark vertices in negative cycle as NO_PATH
-template <typename WEIGHT_T>
-void do_fw_detect_negative_cycle(std::vector<std::vector<WEIGHT_T>>& distance,
-                                 WEIGHT_T ZERO, WEIGHT_T INF, WEIGHT_T NO_PATH,
-                                 size_t n) {
-  for (std::size_t start_vertex = 0; start_vertex < n; ++start_vertex) {
-    for (std::size_t end_vertex = 0; end_vertex < n; ++end_vertex) {
-      for (std::size_t through_vertex = 0; through_vertex < n;
-           ++through_vertex) {
-        if (distance[start_vertex][through_vertex] < INF &&
-            distance[through_vertex][through_vertex] < ZERO &&
-            distance[through_vertex][end_vertex] < INF) {
-          distance[start_vertex][end_vertex] = NO_PATH;
-        }
-      }
-    }
-  }
-}
-
-};  // namespace detail
-
 template <typename V, typename E, graph_type T, typename WEIGHT_T>
 std::vector<std::vector<WEIGHT_T>> floyd_warshall_shortest_paths(
     const graph<V, E, T>& graph) {
   WEIGHT_T ZERO{};
   std::size_t n = graph.vertex_count();
   auto INF = std::numeric_limits<WEIGHT_T>::max();
-  auto NO_PATH = std::numeric_limits<WEIGHT_T>::min();
 
   std::vector<std::vector<WEIGHT_T>> shortest_paths(
       n, std::vector<WEIGHT_T>(n, INF));
@@ -69,8 +45,6 @@ std::vector<std::vector<WEIGHT_T>> floyd_warshall_shortest_paths(
     }
   }
 
-  // Mark vertices in negative cycles with INF
-  detail::do_fw_detect_negative_cycle(shortest_paths, ZERO, INF, NO_PATH, n);
   return shortest_paths;
 }
 
diff --git a/test/graaflib/algorithm/floyd_warshall_test.cpp b/test/graaflib/algorithm/floyd_warshall_test.cpp
index 29d6e731..11d9578b 100644
--- a/test/graaflib/algorithm/floyd_warshall_test.cpp
+++ b/test/graaflib/algorithm/floyd_warshall_test.cpp
@@ -112,64 +112,6 @@ TYPED_TEST(FloydWarshallTest, DirectedGraph) {
   ASSERT_EQ(shortest_paths, expected_paths);
 }
 
-TYPED_TEST(FloydWarshallTest, DirectedGraphNegativeCycle) {
-  // GIVEN
-  directed_graph<int, int> graph{};
-
-  // graph vertices
-  const auto vertex_1{graph.add_vertex(10)};
-  const auto vertex_2{graph.add_vertex(20)};
-  const auto vertex_3{graph.add_vertex(30)};
-  const auto vertex_4{graph.add_vertex(40)};
-
-  // adding edges to our graph
-  graph.add_edge(vertex_1, vertex_2, -100);
-  graph.add_edge(vertex_2, vertex_3, 300);
-  graph.add_edge(vertex_3, vertex_1, -300);
-  graph.add_edge(vertex_4, vertex_2, 300);
-
-  auto NEG_CYCLE = INT_MIN;
-  auto NO_PATH = INT_MAX;
-
-  auto shortest_paths = floyd_warshall_shortest_paths(graph);
-  std::vector<std::vector<int>> expected_paths = {
-      {NEG_CYCLE, NEG_CYCLE, NEG_CYCLE, NO_PATH},
-      {NEG_CYCLE, NEG_CYCLE, NEG_CYCLE, NO_PATH},
-      {NEG_CYCLE, NEG_CYCLE, NEG_CYCLE, NO_PATH},
-      {NEG_CYCLE, NEG_CYCLE, NEG_CYCLE, 0}};
-
-  ASSERT_EQ(shortest_paths, expected_paths);
-}
-
-TYPED_TEST(FloydWarshallTest, UndirectedGraphNegativeCycle) {
-  // GIVEN
-  undirected_graph<int, int> graph{};
-
-  // graph vertices
-  const auto vertex_1{graph.add_vertex(10)};
-  const auto vertex_2{graph.add_vertex(20)};
-  const auto vertex_3{graph.add_vertex(30)};
-  const auto vertex_4{graph.add_vertex(40)};
-
-  // adding edges to our graph
-  graph.add_edge(vertex_1, vertex_2, -100);
-  graph.add_edge(vertex_2, vertex_3, 300);
-  graph.add_edge(vertex_3, vertex_1, -300);
-  graph.add_edge(vertex_4, vertex_2, 300);
-
-  auto NEG_CYCLE = INT_MIN;
-  auto NO_PATH = INT_MAX;
-
-  auto shortest_paths = floyd_warshall_shortest_paths(graph);
-  std::vector<std::vector<int>> expected_paths = {
-      {NEG_CYCLE, NEG_CYCLE, NEG_CYCLE, NEG_CYCLE},
-      {NEG_CYCLE, NEG_CYCLE, NEG_CYCLE, NEG_CYCLE},
-      {NEG_CYCLE, NEG_CYCLE, NEG_CYCLE, NEG_CYCLE},
-      {NEG_CYCLE, NEG_CYCLE, NEG_CYCLE, NEG_CYCLE}};
-
-  ASSERT_EQ(shortest_paths, expected_paths);
-}
-
 TYPED_TEST(FloydWarshallTest, DirectedGraphNoCycleNegativeWeight) {
   directed_graph<int, int> graph{};
 
@@ -189,7 +131,6 @@ TYPED_TEST(FloydWarshallTest, DirectedGraphNoCycleNegativeWeight) {
   graph.add_edge(vertex_4, vertex_6, 100);
   graph.add_edge(vertex_5, vertex_2, -75);
 
-  auto NEG_CYCLE = INT_MIN;
   auto NO_PATH = INT_MAX;
 
   auto shortest_paths = floyd_warshall_shortest_paths(graph);
@@ -254,31 +195,88 @@ TYPED_TEST(FloydWarshallTest, DenseUndirectedGraph) {
   ASSERT_EQ(shortest_paths, expected_paths);
 }
 
-TYPED_TEST(FloydWarshallTest, DirectedGraphWithSubgraphNegativeCycle) {
-  directed_graph<int, int> graph{};
+TYPED_TEST(FloydWarshallTest, UndirectedGraphTwoComponents) {
+  undirected_graph<int, int> graph{};
 
   // graph vertices
   const auto vertex_1{graph.add_vertex(10)};
   const auto vertex_2{graph.add_vertex(20)};
   const auto vertex_3{graph.add_vertex(30)};
   const auto vertex_4{graph.add_vertex(40)};
+  const auto vertex_5{graph.add_vertex(40)};
+  const auto vertex_6{graph.add_vertex(40)};
+  const auto vertex_7{graph.add_vertex(40)};
+  const auto vertex_8{graph.add_vertex(40)};
 
   // adding edges to our graph
-  graph.add_edge(vertex_1, vertex_2, 10);
-  graph.add_edge(vertex_2, vertex_1, -20);
+  graph.add_edge(vertex_1, vertex_2, 12);
+  graph.add_edge(vertex_1, vertex_3, 11);
+  graph.add_edge(vertex_1, vertex_5, 6);
+  graph.add_edge(vertex_2, vertex_5, 14);
+  graph.add_edge(vertex_2, vertex_4, 15);
+  graph.add_edge(vertex_4, vertex_5, 9);
+  graph.add_edge(vertex_4, vertex_3, 7);
+  graph.add_edge(vertex_5, vertex_3, 7);
+
+  graph.add_edge(vertex_6, vertex_7, 4);
+  graph.add_edge(vertex_6, vertex_8, 2);
+  graph.add_edge(vertex_7, vertex_8, 3);
 
-  graph.add_edge(vertex_4, vertex_3, 75);
-  graph.add_edge(vertex_3, vertex_4, 12);
+  auto NO_PATH = INT_MAX;
+
+  auto shortest_paths = floyd_warshall_shortest_paths(graph);
+  std::vector<std::vector<int>> expected_paths{
+      {0, 12, 11, 15, 6, NO_PATH, NO_PATH, NO_PATH},
+      {12, 0, 21, 15, 14, NO_PATH, NO_PATH, NO_PATH},
+      {11, 21, 0, 7, 7, NO_PATH, NO_PATH, NO_PATH},
+      {15, 15, 7, 0, 9, NO_PATH, NO_PATH, NO_PATH},
+      {6, 14, 7, 9, 0, NO_PATH, NO_PATH, NO_PATH},
+      {NO_PATH, NO_PATH, NO_PATH, NO_PATH, NO_PATH, 0, 4, 2},
+      {NO_PATH, NO_PATH, NO_PATH, NO_PATH, NO_PATH, 4, 0, 3},
+      {NO_PATH, NO_PATH, NO_PATH, NO_PATH, NO_PATH, 2, 3, 0}};
+
+  ASSERT_EQ(shortest_paths, expected_paths);
+}
+
+TYPED_TEST(FloydWarshallTest, DirectedGraphTwoComponents) {
+  undirected_graph<int, int> graph{};
+
+  // graph vertices
+  const auto vertex_1{graph.add_vertex(10)};
+  const auto vertex_2{graph.add_vertex(20)};
+  const auto vertex_3{graph.add_vertex(30)};
+  const auto vertex_4{graph.add_vertex(40)};
+  const auto vertex_5{graph.add_vertex(40)};
+  const auto vertex_6{graph.add_vertex(40)};
+  const auto vertex_7{graph.add_vertex(40)};
+  const auto vertex_8{graph.add_vertex(40)};
+
+  // adding edges to our graph
+  graph.add_edge(vertex_1, vertex_2, 12);
+  graph.add_edge(vertex_1, vertex_3, 11);
+  graph.add_edge(vertex_5, vertex_1, 6);
+  graph.add_edge(vertex_2, vertex_5, 14);
+  graph.add_edge(vertex_2, vertex_4, 15);
+  graph.add_edge(vertex_5, vertex_4, 9);
+  graph.add_edge(vertex_4, vertex_3, 7);
+  graph.add_edge(vertex_3, vertex_5, 7);
+
+  graph.add_edge(vertex_6, vertex_7, 4);
+  graph.add_edge(vertex_6, vertex_8, 2);
+  graph.add_edge(vertex_8, vertex_7, 3);
 
-  auto NEG_CYCLE = INT_MIN;
   auto NO_PATH = INT_MAX;
 
   auto shortest_paths = floyd_warshall_shortest_paths(graph);
-  std::vector<std::vector<int>> expected_paths = {
-      {NEG_CYCLE, NEG_CYCLE, NO_PATH, NO_PATH},
-      {NEG_CYCLE, NEG_CYCLE, NO_PATH, NO_PATH},
-      {NO_PATH, NO_PATH, 0, 12},
-      {NO_PATH, NO_PATH, 75, 0}};
+  std::vector<std::vector<int>> expected_paths{
+      {0, 12, 11, 15, 6, NO_PATH, NO_PATH, NO_PATH},
+      {12, 0, 21, 15, 14, NO_PATH, NO_PATH, NO_PATH},
+      {11, 21, 0, 7, 7, NO_PATH, NO_PATH, NO_PATH},
+      {15, 15, 7, 0, 9, NO_PATH, NO_PATH, NO_PATH},
+      {6, 14, 7, 9, 0, NO_PATH, NO_PATH, NO_PATH},
+      {NO_PATH, NO_PATH, NO_PATH, NO_PATH, NO_PATH, 0, 4, 2},
+      {NO_PATH, NO_PATH, NO_PATH, NO_PATH, NO_PATH, 4, 0, 3},
+      {NO_PATH, NO_PATH, NO_PATH, NO_PATH, NO_PATH, 2, 3, 0}};
 
   ASSERT_EQ(shortest_paths, expected_paths);
 }

From f3274c9e89a50ee0f0ea9e17f4c5ef2b159e5cac Mon Sep 17 00:00:00 2001
From: Hromz <hromizz@gmail.com>
Date: Fri, 6 Oct 2023 16:44:35 +0300
Subject: [PATCH 33/40] Bron-Kerbosch algorithm

---
 docs/docs/algorithms/clique/bron_kerbosch.md  |  25 ++
 .../graaflib/algorithm/clique/bron_kerbosch.h |  27 ++
 .../algorithm/clique/bron_kerbosch.tpp        |  97 ++++++
 .../algorithm/clique/bron_kerbosch_test.cpp   | 299 ++++++++++++++++++
 4 files changed, 448 insertions(+)
 create mode 100644 docs/docs/algorithms/clique/bron_kerbosch.md
 create mode 100644 include/graaflib/algorithm/clique/bron_kerbosch.h
 create mode 100644 include/graaflib/algorithm/clique/bron_kerbosch.tpp
 create mode 100644 test/graaflib/algorithm/clique/bron_kerbosch_test.cpp

diff --git a/docs/docs/algorithms/clique/bron_kerbosch.md b/docs/docs/algorithms/clique/bron_kerbosch.md
new file mode 100644
index 00000000..e4c09c9f
--- /dev/null
+++ b/docs/docs/algorithms/clique/bron_kerbosch.md
@@ -0,0 +1,25 @@
+---
+sidebar_position: 1
+---
+
+# Bron-Kerbosch algorithm
+
+Bron-Kerbosch algorithm finding all maximal cliques in an undirected graph. A clique is a subset of vertices such that
+where every two distinct vertices are adjacent to each other.
+The maximal clique is the subset of vertices of an undirected graph where no additional vertex can be added
+due to the complete connectivity rule. The algorithm lists all maximum cliques of an undirected graph.
+
+The worst-case run time of the algorithm is 3<sup>V/3</sup>.
+[wikipedia](https://en.wikipedia.org/wiki/Bron%E2%80%93Kerbosch_algorithm#Worst-case_analysis)
+
+## Syntax
+
+```cpp
+template <typename V, typename E>
+std::vector<std::vector<vertex_id_t>> bron_kerbosch(
+    const graph<V, E, graph_type::UNDIRECTED>& graph);
+```
+
+- **graph** The graph to extract maximal cliques.
+- **return** Returns 2D vector of vertices each vector represent set of vertices that form clique.
+
diff --git a/include/graaflib/algorithm/clique/bron_kerbosch.h b/include/graaflib/algorithm/clique/bron_kerbosch.h
new file mode 100644
index 00000000..9547e040
--- /dev/null
+++ b/include/graaflib/algorithm/clique/bron_kerbosch.h
@@ -0,0 +1,27 @@
+#pragma once
+
+#include <graaflib/graph.h>
+
+namespace graaf::algorithm {
+/**
+ * @brief Finds all cliques in an undirected graph using the Bron-Kerbosch
+ * algorithm.
+ *
+ * The Bron-Kerbosch algorithm is used for finding all cliques in an undirected
+ * graph. A clique is a subset of vertices such that every two distinct vertices
+ * are adjacent. This function returns a list of all cliques, each represented
+ * as a vector of vertex identifiers.
+ *
+ * @tparam V The vertex type of the graph.
+ * @tparam E The edge type of the graph.
+ * @param graph The graph in which we want to find the cliques.
+ * @return A vector of cliques, each represented as a vector of vertex
+ * identifiers.
+ */
+template <typename V, typename E>
+std::vector<std::vector<vertex_id_t>> bron_kerbosch(
+    const graph<V, E, graph_type::UNDIRECTED>& graph);
+
+}  // namespace graaf::algorithm
+
+#include "bron_kerbosch.tpp"
diff --git a/include/graaflib/algorithm/clique/bron_kerbosch.tpp b/include/graaflib/algorithm/clique/bron_kerbosch.tpp
new file mode 100644
index 00000000..c20492dd
--- /dev/null
+++ b/include/graaflib/algorithm/clique/bron_kerbosch.tpp
@@ -0,0 +1,97 @@
+#pragma once
+
+#include <graaflib/algorithm/clique/bron_kerbosch.h>
+
+#include <iostream>
+#include <iterator>
+#include <optional>
+#include <ranges>
+#include <unordered_set>
+#include <vector>
+
+namespace graaf::algorithm {
+
+namespace detail {
+
+void do_get_intersection(std::unordered_set<vertex_id_t>& s1,
+                         std::unordered_set<vertex_id_t>& s2,
+                         std::unordered_set<vertex_id_t>& intersection) {
+  for (const auto& vertex : s1) {
+    if (s2.find(vertex) != s2.end()) {
+      intersection.insert(vertex);
+    }
+  }
+}
+
+template <typename V, typename E>
+void do_bron_kerbosch_maximal_clique(
+    std::vector<vertex_id_t>& clique, std::unordered_set<vertex_id_t>& vertices,
+    std::unordered_set<vertex_id_t>& excluded_vertices,
+    std::vector<std::vector<vertex_id_t>>& maximal_cliques,
+    const graph<V, E, graph_type::UNDIRECTED>& graph) {
+  if (vertices.empty() && excluded_vertices.empty()) {
+    maximal_cliques.push_back(clique);
+    return;
+  }
+
+  // union_set = candidate_vertices ⋃ excluded_vertices
+  auto union_set = vertices;
+  for (const auto& vertex : excluded_vertices) union_set.insert(vertex);
+
+  // Get pivot vertex with most amount of neighbors
+  // to reduce recursion calls
+  auto pivot_vertex = *union_set.begin();
+  for (const auto& vertex : union_set) {
+    if (graph.get_neighbors(pivot_vertex).size() <
+        graph.get_neighbors(vertex).size()) {
+      pivot_vertex = vertex;
+    }
+  }
+
+  // vertices_to_process = candidate_vertices \ N(pivot_vertex)
+  auto vertices_to_process = vertices;
+  for (const auto& vertex : graph.get_neighbors(pivot_vertex)) {
+    vertices_to_process.erase(vertex);
+  }
+
+  for (const auto& vertex : vertices_to_process) {
+    auto vertex_neighbors = graph.get_neighbors(vertex);
+
+    // Intersection candidate_vertices ⋂ N(vertex)
+    std::unordered_set<vertex_id_t> vertices_intersection{};
+    do_get_intersection(vertices, vertex_neighbors, vertices_intersection);
+
+    // Intersection excluded_vertices ⋂ N(vertex)
+    std::unordered_set<vertex_id_t> exclude_intersection{};
+    do_get_intersection(excluded_vertices, vertex_neighbors,
+                        exclude_intersection);
+
+    clique.push_back(vertex);
+    do_bron_kerbosch_maximal_clique(clique, vertices_intersection,
+                                    exclude_intersection, maximal_cliques,
+                                    graph);
+    clique.pop_back();
+
+    vertices.erase(vertex);
+    excluded_vertices.insert(vertex);
+  }
+}
+};  // namespace detail
+
+template <typename V, typename E>
+std::vector<std::vector<vertex_id_t>> bron_kerbosch(
+    const graph<V, E, graph_type::UNDIRECTED>& graph) {
+  std::vector<std::vector<vertex_id_t>> maximal_cliques{};
+
+  std::vector<vertex_id_t> clique;
+  std::unordered_set<vertex_id_t> vertices, excluded;
+  for (const auto& [vertex, _] : graph.get_vertices()) {
+    vertices.insert(vertex);
+  }
+  detail::do_bron_kerbosch_maximal_clique(clique, vertices, excluded,
+                                          maximal_cliques, graph);
+
+  return maximal_cliques;
+}
+
+};  // namespace graaf::algorithm
\ No newline at end of file
diff --git a/test/graaflib/algorithm/clique/bron_kerbosch_test.cpp b/test/graaflib/algorithm/clique/bron_kerbosch_test.cpp
new file mode 100644
index 00000000..9bb9ba4e
--- /dev/null
+++ b/test/graaflib/algorithm/clique/bron_kerbosch_test.cpp
@@ -0,0 +1,299 @@
+#include <fmt/core.h>
+#include <graaflib/algorithm/clique/bron_kerbosch.h>
+#include <graaflib/graph.h>
+#include <graaflib/types.h>
+#include <gtest/gtest.h>
+
+#include <random>
+
+namespace graaf::algorithm {
+namespace {
+template <typename T>
+struct BronKerbosch : public testing::Test {
+  using graph_t = T;
+};
+
+using graph_types = testing::Types<undirected_graph<int, int>>;
+TYPED_TEST_SUITE(BronKerbosch, graph_types);
+
+};  // namespace
+
+void sort_vectors(std::vector<std::vector<vertex_id_t>>& vec1,
+                  std::vector<std::vector<vertex_id_t>>& vec2) {
+  // Sort 1D vectors
+  for (std::vector<vertex_id_t>& inner_vec : vec1) {
+    std::sort(inner_vec.begin(), inner_vec.end());
+  }
+  for (std::vector<vertex_id_t>& inner_vec : vec2) {
+    std::sort(inner_vec.begin(), inner_vec.end());
+  }
+
+  // Sort 2D vectors
+  std::sort(vec1.begin(), vec1.end());
+  std::sort(vec2.begin(), vec2.end());
+}
+
+TYPED_TEST(BronKerbosch, ThreeCliques) {
+  using graph_t = typename TestFixture::graph_t;
+  graph_t graph{};
+
+  const auto vertex_1{graph.add_vertex(1)};
+  const auto vertex_2{graph.add_vertex(2)};
+  const auto vertex_3{graph.add_vertex(3)};
+  const auto vertex_4{graph.add_vertex(4)};
+  const auto vertex_5{graph.add_vertex(5)};
+
+  graph.add_edge(vertex_1, vertex_2, 1);
+  graph.add_edge(vertex_1, vertex_3, 1);
+  graph.add_edge(vertex_3, vertex_2, 1);
+  graph.add_edge(vertex_3, vertex_4, 1);
+
+  auto cliques = bron_kerbosch(graph);
+  std::vector<std::vector<vertex_id_t>> expected_cliques{
+      {vertex_1, vertex_2, vertex_3}, {vertex_3, vertex_4}, {vertex_5}};
+
+  sort_vectors(cliques, expected_cliques);
+
+  ASSERT_EQ(cliques, expected_cliques);
+}
+
+TYPED_TEST(BronKerbosch, OneClique) {
+  using graph_t = typename TestFixture::graph_t;
+  graph_t graph{};
+
+  const auto vertex_1{graph.add_vertex(1)};
+  const auto vertex_2{graph.add_vertex(2)};
+  const auto vertex_3{graph.add_vertex(3)};
+  const auto vertex_4{graph.add_vertex(4)};
+
+  graph.add_edge(vertex_1, vertex_2, 1);
+  graph.add_edge(vertex_1, vertex_3, 1);
+  graph.add_edge(vertex_1, vertex_4, 1);
+  graph.add_edge(vertex_2, vertex_4, 1);
+  graph.add_edge(vertex_2, vertex_3, 1);
+  graph.add_edge(vertex_3, vertex_4, 1);
+
+  auto cliques = bron_kerbosch(graph);
+  std::vector<std::vector<vertex_id_t>> expected_cliques{
+      {vertex_1, vertex_2, vertex_3, vertex_4}};
+
+  sort_vectors(cliques, expected_cliques);
+  ASSERT_EQ(cliques, expected_cliques);
+}
+
+TYPED_TEST(BronKerbosch, FourCliques) {
+  using graph_t = typename TestFixture::graph_t;
+  graph_t graph{};
+
+  const auto vertex_1{graph.add_vertex(1)};
+  const auto vertex_2{graph.add_vertex(2)};
+  const auto vertex_3{graph.add_vertex(3)};
+  const auto vertex_4{graph.add_vertex(4)};
+  const auto vertex_5{graph.add_vertex(5)};
+  const auto vertex_6{graph.add_vertex(6)};
+  const auto vertex_7{graph.add_vertex(7)};
+
+  graph.add_edge(vertex_1, vertex_2, 1);
+  graph.add_edge(vertex_1, vertex_3, 1);
+  graph.add_edge(vertex_2, vertex_3, 1);
+
+  graph.add_edge(vertex_4, vertex_5, 1);
+  graph.add_edge(vertex_5, vertex_6, 1);
+  graph.add_edge(vertex_6, vertex_7, 1);
+
+  auto cliques = bron_kerbosch(graph);
+  std::vector<std::vector<vertex_id_t>> expected_cliques{
+      {vertex_1, vertex_2, vertex_3},
+      {vertex_4, vertex_5},
+      {vertex_6, vertex_7},
+      {vertex_6, vertex_5}};
+
+  sort_vectors(cliques, expected_cliques);
+  ASSERT_EQ(cliques, expected_cliques);
+}
+
+TYPED_TEST(BronKerbosch, GraphPentogram) {
+  using graph_t = typename TestFixture::graph_t;
+  graph_t graph{};
+
+  const auto vertex_1{graph.add_vertex(1)};
+  const auto vertex_2{graph.add_vertex(2)};
+  const auto vertex_3{graph.add_vertex(3)};
+  const auto vertex_4{graph.add_vertex(4)};
+  const auto vertex_5{graph.add_vertex(5)};
+  const auto vertex_6{graph.add_vertex(6)};
+  const auto vertex_7{graph.add_vertex(7)};
+
+  graph.add_edge(vertex_1, vertex_2, 1);
+  graph.add_edge(vertex_1, vertex_7, 1);
+  graph.add_edge(vertex_1, vertex_4, 1);
+  graph.add_edge(vertex_4, vertex_7, 1);
+  graph.add_edge(vertex_2, vertex_7, 1);
+  graph.add_edge(vertex_2, vertex_3, 1);
+  graph.add_edge(vertex_3, vertex_7, 1);
+  graph.add_edge(vertex_3, vertex_6, 1);
+  graph.add_edge(vertex_6, vertex_7, 1);
+  graph.add_edge(vertex_5, vertex_6, 1);
+  graph.add_edge(vertex_5, vertex_7, 1);
+  graph.add_edge(vertex_4, vertex_5, 1);
+
+  auto cliques = bron_kerbosch(graph);
+  std::vector<std::vector<vertex_id_t>> expected_cliques{
+      {vertex_1, vertex_2, vertex_7}, {vertex_1, vertex_4, vertex_7},
+      {vertex_2, vertex_3, vertex_7}, {vertex_3, vertex_6, vertex_7},
+      {vertex_4, vertex_5, vertex_7}, {vertex_5, vertex_6, vertex_7}};
+  sort_vectors(cliques, expected_cliques);
+
+  ASSERT_EQ(cliques, expected_cliques);
+}
+
+TYPED_TEST(BronKerbosch, GraphTriangle) {
+  using graph_t = typename TestFixture::graph_t;
+  graph_t graph{};
+
+  const auto vertex_1{graph.add_vertex(1)};
+  const auto vertex_2{graph.add_vertex(2)};
+  const auto vertex_3{graph.add_vertex(3)};
+  const auto vertex_4{graph.add_vertex(4)};
+
+  graph.add_edge(vertex_1, vertex_2, 1);
+  graph.add_edge(vertex_1, vertex_3, 1);
+  graph.add_edge(vertex_1, vertex_4, 1);
+  graph.add_edge(vertex_2, vertex_3, 1);
+  graph.add_edge(vertex_2, vertex_4, 1);
+  graph.add_edge(vertex_3, vertex_4, 1);
+
+  auto cliques = bron_kerbosch(graph);
+  std::vector<std::vector<vertex_id_t>> expected_cliques{
+      {vertex_1, vertex_2, vertex_3, vertex_4}};
+  sort_vectors(cliques, expected_cliques);
+
+  ASSERT_EQ(cliques, expected_cliques);
+}
+
+TYPED_TEST(BronKerbosch, GraphCone) {
+  using graph_t = typename TestFixture::graph_t;
+  graph_t graph{};
+
+  const auto vertex_1{graph.add_vertex(1)};
+  const auto vertex_2{graph.add_vertex(2)};
+  const auto vertex_3{graph.add_vertex(3)};
+  const auto vertex_4{graph.add_vertex(4)};
+  const auto vertex_5{graph.add_vertex(4)};
+
+  // Bottom
+  graph.add_edge(vertex_1, vertex_2, 1);
+  graph.add_edge(vertex_1, vertex_3, 1);
+  graph.add_edge(vertex_1, vertex_4, 1);
+  graph.add_edge(vertex_2, vertex_3, 1);
+  graph.add_edge(vertex_2, vertex_4, 1);
+  graph.add_edge(vertex_3, vertex_4, 1);
+
+  // Top
+  graph.add_edge(vertex_5, vertex_1, 1);
+  graph.add_edge(vertex_5, vertex_2, 1);
+  graph.add_edge(vertex_5, vertex_3, 1);
+  graph.add_edge(vertex_5, vertex_4, 1);
+
+  auto cliques = bron_kerbosch(graph);
+  std::vector<std::vector<vertex_id_t>> expected_cliques{
+      {vertex_1, vertex_2, vertex_3, vertex_4, vertex_5}};
+  sort_vectors(cliques, expected_cliques);
+
+  ASSERT_EQ(cliques, expected_cliques);
+}
+
+TYPED_TEST(BronKerbosch, GraphEightSideStar) {
+  using graph_t = typename TestFixture::graph_t;
+  graph_t graph{};
+
+  const auto vertex_1{graph.add_vertex(1)};
+  const auto vertex_2{graph.add_vertex(2)};
+  const auto vertex_3{graph.add_vertex(3)};
+  const auto vertex_4{graph.add_vertex(4)};
+  const auto vertex_5{graph.add_vertex(5)};
+  const auto vertex_6{graph.add_vertex(6)};
+  const auto vertex_7{graph.add_vertex(7)};
+  const auto vertex_8{graph.add_vertex(8)};
+  const auto vertex_9{graph.add_vertex(9)};
+  const auto vertex_10{graph.add_vertex(10)};
+  const auto vertex_11{graph.add_vertex(11)};
+  const auto vertex_12{graph.add_vertex(12)};
+  const auto vertex_13{graph.add_vertex(13)};
+  const auto vertex_14{graph.add_vertex(14)};
+  const auto vertex_15{graph.add_vertex(15)};
+  const auto vertex_16{graph.add_vertex(16)};
+
+  graph.add_edge(vertex_1, vertex_2, 1);
+  graph.add_edge(vertex_1, vertex_15, 1);
+  graph.add_edge(vertex_2, vertex_15, 1);
+
+  graph.add_edge(vertex_2, vertex_4, 1);
+  graph.add_edge(vertex_2, vertex_3, 1);
+  graph.add_edge(vertex_3, vertex_4, 1);
+
+  graph.add_edge(vertex_4, vertex_6, 1);
+  graph.add_edge(vertex_4, vertex_5, 1);
+  graph.add_edge(vertex_5, vertex_6, 1);
+
+  graph.add_edge(vertex_6, vertex_7, 1);
+  graph.add_edge(vertex_6, vertex_8, 1);
+  graph.add_edge(vertex_7, vertex_8, 1);
+
+  graph.add_edge(vertex_8, vertex_9, 1);
+  graph.add_edge(vertex_8, vertex_10, 1);
+  graph.add_edge(vertex_9, vertex_10, 1);
+
+  graph.add_edge(vertex_10, vertex_11, 1);
+  graph.add_edge(vertex_10, vertex_12, 1);
+  graph.add_edge(vertex_11, vertex_12, 1);
+
+  graph.add_edge(vertex_12, vertex_13, 1);
+  graph.add_edge(vertex_12, vertex_14, 1);
+  graph.add_edge(vertex_13, vertex_14, 1);
+
+  graph.add_edge(vertex_14, vertex_15, 1);
+  graph.add_edge(vertex_14, vertex_16, 1);
+  graph.add_edge(vertex_15, vertex_16, 1);
+
+  auto cliques = bron_kerbosch(graph);
+  std::vector<std::vector<vertex_id_t>> expected_cliques{
+      {vertex_1, vertex_2, vertex_15},   {vertex_2, vertex_3, vertex_4},
+      {vertex_5, vertex_4, vertex_6},    {vertex_7, vertex_6, vertex_8},
+      {vertex_8, vertex_9, vertex_10},   {vertex_10, vertex_11, vertex_12},
+      {vertex_12, vertex_13, vertex_14}, {vertex_14, vertex_15, vertex_16},
+  };
+  sort_vectors(cliques, expected_cliques);
+
+  ASSERT_EQ(cliques, expected_cliques);
+}
+
+TYPED_TEST(BronKerbosch, RandomGraphCheckRunTime) {
+  using graph_t = typename TestFixture::graph_t;
+  graph_t graph{};
+
+  std::vector<vertex_id_t> vertices;
+
+  for (int i = 1; i <= 70; ++i) {
+    vertices.push_back(graph.add_vertex(i));
+  }
+
+  std::random_device dev;
+  std::mt19937 rng(dev());
+  std::uniform_int_distribution<std::mt19937::result_type> rand_vertex(0, 69);
+
+  for (int i = 0; i < 1360; ++i) {
+    graph.add_edge(vertices[rand_vertex(rng)], vertices[rand_vertex(rng)], 1);
+  }
+
+  auto start = std::chrono::high_resolution_clock::now();
+  auto cliques = bron_kerbosch(graph);
+  auto stop = std::chrono::high_resolution_clock::now();
+
+  int expected_time = 900;
+
+  ASSERT_TRUE(expected_time >=
+              duration_cast<std::chrono::milliseconds>(stop - start).count());
+}
+
+};  // namespace graaf::algorithm
\ No newline at end of file

From 9ac7524c314ad6485b8e9bdb4f5e6e2decc5c79c Mon Sep 17 00:00:00 2001
From: Hromz <hromizz@gmail.com>
Date: Fri, 6 Oct 2023 19:01:25 +0300
Subject: [PATCH 34/40] Added to readme

---
 README.md | 29 ++++++++++++++++-------------
 1 file changed, 16 insertions(+), 13 deletions(-)

diff --git a/README.md b/README.md
index 5a714804..66a0b98b 100644
--- a/README.md
+++ b/README.md
@@ -92,24 +92,27 @@ Algorithms implemented in the Graaf library include the following. For more info
 take a look at the [docs](https://bobluppes.github.io/graaf/docs/algorithms/intro).
 
 1. [**Cycle Detection Algorithms**](https://bobluppes.github.io/graaf/docs/category/cycle-detection-algorithms):
-   - DFS-Based Cycle Detection
+    - DFS-Based Cycle Detection
 2. [**Graph Coloring Algorithms**](https://bobluppes.github.io/graaf/docs/category/coloring):
-   - Greedy Graph Coloring
+    - Greedy Graph Coloring
 3. [**Minimum Spanning Tree (MST) Algorithms**](https://bobluppes.github.io/graaf/docs/category/minimum-spanning-tree)
-   - Kruskal's Algorithm
-   - Prim's Algorithm
+    - Kruskal's Algorithm
+    - Prim's Algorithm
 4. [**Shortest Path Algorithms**](https://bobluppes.github.io/graaf/docs/category/shortest-path-algorithms):
-   - A\* search
-   - BFS-Based Shortest Path
-   - Dijkstra
-   - Bellman-Ford
-5. [**Strongly Connected Components Algorithms**](https://bobluppes.github.io/graaf/docs/category/strongly-connected-components):
-   - Tarjan's Strongly Connected Components
+    - A\* search
+    - BFS-Based Shortest Path
+    - Dijkstra
+    - Bellman-Ford
+5. [**Strongly Connected Components Algorithms
+   **](https://bobluppes.github.io/graaf/docs/category/strongly-connected-components):
+    - Tarjan's Strongly Connected Components
 6. [**Topological Sorting Algorithms**](https://bobluppes.github.io/graaf/docs/category/topological-sorting):
-   - Topological sorting DFS-based
+    - Topological sorting DFS-based
 7. [**Traversal Algorithms**](https://bobluppes.github.io/graaf/docs/category/traversal-algorithms):
-   - Breadth-First Search (BFS)
-   - Depth-First Search (DFS)
+    - Breadth-First Search (BFS)
+    - Depth-First Search (DFS)
+8. [**Clique**](https://bobluppes.github.io/graaf/docs/category/clique)
+    - Bron-Kerbosch
 
 # Contributing
 

From 14ccc5a8657499f5abea4ffcbd7197c9bb480597 Mon Sep 17 00:00:00 2001
From: Hromz <hromizz@gmail.com>
Date: Mon, 9 Oct 2023 11:56:18 +0300
Subject: [PATCH 35/40] corrected according to comments

---
 README.md                                     |   2 +-
 docs/docs/algorithms/clique/bron_kerbosch.md  |   2 +-
 .../algorithm/clique/bron_kerbosch.tpp        |  78 +++++++-----
 .../algorithm/clique/bron_kerbosch_test.cpp   | 117 +++++++++++-------
 4 files changed, 121 insertions(+), 78 deletions(-)

diff --git a/README.md b/README.md
index 66a0b98b..17da09eb 100644
--- a/README.md
+++ b/README.md
@@ -111,7 +111,7 @@ take a look at the [docs](https://bobluppes.github.io/graaf/docs/algorithms/intr
 7. [**Traversal Algorithms**](https://bobluppes.github.io/graaf/docs/category/traversal-algorithms):
     - Breadth-First Search (BFS)
     - Depth-First Search (DFS)
-8. [**Clique**](https://bobluppes.github.io/graaf/docs/category/clique)
+8. [**Clique Detection**](https://bobluppes.github.io/graaf/docs/category/clique)
     - Bron-Kerbosch
 
 # Contributing
diff --git a/docs/docs/algorithms/clique/bron_kerbosch.md b/docs/docs/algorithms/clique/bron_kerbosch.md
index e4c09c9f..c4a98815 100644
--- a/docs/docs/algorithms/clique/bron_kerbosch.md
+++ b/docs/docs/algorithms/clique/bron_kerbosch.md
@@ -5,7 +5,7 @@ sidebar_position: 1
 # Bron-Kerbosch algorithm
 
 Bron-Kerbosch algorithm finding all maximal cliques in an undirected graph. A clique is a subset of vertices such that
-where every two distinct vertices are adjacent to each other.
+every two distinct vertices are adjacent to each other.
 The maximal clique is the subset of vertices of an undirected graph where no additional vertex can be added
 due to the complete connectivity rule. The algorithm lists all maximum cliques of an undirected graph.
 
diff --git a/include/graaflib/algorithm/clique/bron_kerbosch.tpp b/include/graaflib/algorithm/clique/bron_kerbosch.tpp
index c20492dd..3a55196a 100644
--- a/include/graaflib/algorithm/clique/bron_kerbosch.tpp
+++ b/include/graaflib/algorithm/clique/bron_kerbosch.tpp
@@ -2,6 +2,7 @@
 
 #include <graaflib/algorithm/clique/bron_kerbosch.h>
 
+#include <algorithm>
 #include <iostream>
 #include <iterator>
 #include <optional>
@@ -12,22 +13,43 @@
 namespace graaf::algorithm {
 
 namespace detail {
+using clique_collection_t = std::vector<std::vector<vertex_id_t>>;
+using vertex_set_t = std::unordered_set<vertex_id_t>;
 
-void do_get_intersection(std::unordered_set<vertex_id_t>& s1,
-                         std::unordered_set<vertex_id_t>& s2,
-                         std::unordered_set<vertex_id_t>& intersection) {
-  for (const auto& vertex : s1) {
-    if (s2.find(vertex) != s2.end()) {
+vertex_set_t do_get_intersection(const vertex_set_t& lhs,
+                                 const vertex_set_t& rhs) {
+  vertex_set_t intersection{};
+
+  for (const auto& vertex : lhs) {
+    if (rhs.contains(vertex)) {
       intersection.insert(vertex);
     }
   }
+
+  return intersection;
+}
+
+vertex_set_t set_union(const vertex_set_t& lhs, const vertex_set_t& rhs) {
+  vertex_set_t union_set = lhs;
+  for (const auto& vertex : rhs) union_set.insert(vertex);
+
+  return union_set;
+}
+
+vertex_set_t set_difference(const vertex_set_t& lhs, const vertex_set_t rhs) {
+  vertex_set_t difference_set = lhs;
+
+  for (const auto& vertex : rhs) {
+    difference_set.erase(vertex);
+  }
+
+  return difference_set;
 }
 
 template <typename V, typename E>
 void do_bron_kerbosch_maximal_clique(
-    std::vector<vertex_id_t>& clique, std::unordered_set<vertex_id_t>& vertices,
-    std::unordered_set<vertex_id_t>& excluded_vertices,
-    std::vector<std::vector<vertex_id_t>>& maximal_cliques,
+    std::vector<vertex_id_t>& clique, vertex_set_t& vertices,
+    vertex_set_t& excluded_vertices, clique_collection_t& maximal_cliques,
     const graph<V, E, graph_type::UNDIRECTED>& graph) {
   if (vertices.empty() && excluded_vertices.empty()) {
     maximal_cliques.push_back(clique);
@@ -35,36 +57,27 @@ void do_bron_kerbosch_maximal_clique(
   }
 
   // union_set = candidate_vertices ⋃ excluded_vertices
-  auto union_set = vertices;
-  for (const auto& vertex : excluded_vertices) union_set.insert(vertex);
-
-  // Get pivot vertex with most amount of neighbors
-  // to reduce recursion calls
-  auto pivot_vertex = *union_set.begin();
-  for (const auto& vertex : union_set) {
-    if (graph.get_neighbors(pivot_vertex).size() <
-        graph.get_neighbors(vertex).size()) {
-      pivot_vertex = vertex;
-    }
-  }
+  auto union_set = set_union(vertices, excluded_vertices);
+
+  const auto pivot_vertex = *std::ranges::max_element(
+      union_set, {},
+      [&graph](vertex_id_t id) { return graph.get_neighbors(id).size(); });
 
   // vertices_to_process = candidate_vertices \ N(pivot_vertex)
-  auto vertices_to_process = vertices;
-  for (const auto& vertex : graph.get_neighbors(pivot_vertex)) {
-    vertices_to_process.erase(vertex);
-  }
+  auto vertices_to_process =
+      set_difference(vertices, graph.get_neighbors(pivot_vertex));
 
   for (const auto& vertex : vertices_to_process) {
     auto vertex_neighbors = graph.get_neighbors(vertex);
 
     // Intersection candidate_vertices ⋂ N(vertex)
     std::unordered_set<vertex_id_t> vertices_intersection{};
-    do_get_intersection(vertices, vertex_neighbors, vertices_intersection);
+    vertices_intersection = do_get_intersection(vertices, vertex_neighbors);
 
     // Intersection excluded_vertices ⋂ N(vertex)
     std::unordered_set<vertex_id_t> exclude_intersection{};
-    do_get_intersection(excluded_vertices, vertex_neighbors,
-                        exclude_intersection);
+    exclude_intersection =
+        do_get_intersection(excluded_vertices, vertex_neighbors);
 
     clique.push_back(vertex);
     do_bron_kerbosch_maximal_clique(clique, vertices_intersection,
@@ -81,12 +94,13 @@ void do_bron_kerbosch_maximal_clique(
 template <typename V, typename E>
 std::vector<std::vector<vertex_id_t>> bron_kerbosch(
     const graph<V, E, graph_type::UNDIRECTED>& graph) {
-  std::vector<std::vector<vertex_id_t>> maximal_cliques{};
+  detail::clique_collection_t maximal_cliques{};
+  std::vector<vertex_id_t> clique{};
+  detail::vertex_set_t vertices{};
+  detail::vertex_set_t excluded{};
 
-  std::vector<vertex_id_t> clique;
-  std::unordered_set<vertex_id_t> vertices, excluded;
-  for (const auto& [vertex, _] : graph.get_vertices()) {
-    vertices.insert(vertex);
+  for (const auto& [vertex_id, _] : graph.get_vertices()) {
+    vertices.insert(vertex_id);
   }
   detail::do_bron_kerbosch_maximal_clique(clique, vertices, excluded,
                                           maximal_cliques, graph);
diff --git a/test/graaflib/algorithm/clique/bron_kerbosch_test.cpp b/test/graaflib/algorithm/clique/bron_kerbosch_test.cpp
index 9bb9ba4e..cc70b90b 100644
--- a/test/graaflib/algorithm/clique/bron_kerbosch_test.cpp
+++ b/test/graaflib/algorithm/clique/bron_kerbosch_test.cpp
@@ -7,17 +7,6 @@
 #include <random>
 
 namespace graaf::algorithm {
-namespace {
-template <typename T>
-struct BronKerbosch : public testing::Test {
-  using graph_t = T;
-};
-
-using graph_types = testing::Types<undirected_graph<int, int>>;
-TYPED_TEST_SUITE(BronKerbosch, graph_types);
-
-};  // namespace
-
 void sort_vectors(std::vector<std::vector<vertex_id_t>>& vec1,
                   std::vector<std::vector<vertex_id_t>>& vec2) {
   // Sort 1D vectors
@@ -33,9 +22,18 @@ void sort_vectors(std::vector<std::vector<vertex_id_t>>& vec1,
   std::sort(vec2.begin(), vec2.end());
 }
 
+namespace {
+template <typename T>
+struct BronKerbosch : public testing::Test {
+  using graph_t = T;
+};
+using graph_types = testing::Types<undirected_graph<int, int>>;
+
+TYPED_TEST_SUITE(BronKerbosch, graph_types);
+}  // namespace
+
 TYPED_TEST(BronKerbosch, ThreeCliques) {
-  using graph_t = typename TestFixture::graph_t;
-  graph_t graph{};
+  undirected_graph<int, int> graph{};
 
   const auto vertex_1{graph.add_vertex(1)};
   const auto vertex_2{graph.add_vertex(2)};
@@ -58,8 +56,7 @@ TYPED_TEST(BronKerbosch, ThreeCliques) {
 }
 
 TYPED_TEST(BronKerbosch, OneClique) {
-  using graph_t = typename TestFixture::graph_t;
-  graph_t graph{};
+  undirected_graph<int, int> graph{};
 
   const auto vertex_1{graph.add_vertex(1)};
   const auto vertex_2{graph.add_vertex(2)};
@@ -82,8 +79,7 @@ TYPED_TEST(BronKerbosch, OneClique) {
 }
 
 TYPED_TEST(BronKerbosch, FourCliques) {
-  using graph_t = typename TestFixture::graph_t;
-  graph_t graph{};
+  undirected_graph<int, int> graph{};
 
   const auto vertex_1{graph.add_vertex(1)};
   const auto vertex_2{graph.add_vertex(2)};
@@ -113,8 +109,7 @@ TYPED_TEST(BronKerbosch, FourCliques) {
 }
 
 TYPED_TEST(BronKerbosch, GraphPentogram) {
-  using graph_t = typename TestFixture::graph_t;
-  graph_t graph{};
+  undirected_graph<int, int> graph{};
 
   const auto vertex_1{graph.add_vertex(1)};
   const auto vertex_2{graph.add_vertex(2)};
@@ -148,8 +143,7 @@ TYPED_TEST(BronKerbosch, GraphPentogram) {
 }
 
 TYPED_TEST(BronKerbosch, GraphTriangle) {
-  using graph_t = typename TestFixture::graph_t;
-  graph_t graph{};
+  undirected_graph<int, int> graph{};
 
   const auto vertex_1{graph.add_vertex(1)};
   const auto vertex_2{graph.add_vertex(2)};
@@ -172,8 +166,7 @@ TYPED_TEST(BronKerbosch, GraphTriangle) {
 }
 
 TYPED_TEST(BronKerbosch, GraphCone) {
-  using graph_t = typename TestFixture::graph_t;
-  graph_t graph{};
+  undirected_graph<int, int> graph{};
 
   const auto vertex_1{graph.add_vertex(1)};
   const auto vertex_2{graph.add_vertex(2)};
@@ -204,8 +197,7 @@ TYPED_TEST(BronKerbosch, GraphCone) {
 }
 
 TYPED_TEST(BronKerbosch, GraphEightSideStar) {
-  using graph_t = typename TestFixture::graph_t;
-  graph_t graph{};
+  undirected_graph<int, int> graph{};
 
   const auto vertex_1{graph.add_vertex(1)};
   const auto vertex_2{graph.add_vertex(2)};
@@ -268,32 +260,69 @@ TYPED_TEST(BronKerbosch, GraphEightSideStar) {
   ASSERT_EQ(cliques, expected_cliques);
 }
 
-TYPED_TEST(BronKerbosch, RandomGraphCheckRunTime) {
-  using graph_t = typename TestFixture::graph_t;
-  graph_t graph{};
+TYPED_TEST(BronKerbosch, DensePyramidGraph) {
+  undirected_graph<int, int> graph{};
 
-  std::vector<vertex_id_t> vertices;
+  const auto vertex_1 = graph.add_vertex(10);
+  const auto vertex_2 = graph.add_vertex(20);
+  const auto vertex_3 = graph.add_vertex(30);
+  const auto vertex_4 = graph.add_vertex(40);
+  const auto vertex_5 = graph.add_vertex(50);
+  const auto vertex_6 = graph.add_vertex(60);
+  const auto vertex_7 = graph.add_vertex(70);
 
-  for (int i = 1; i <= 70; ++i) {
-    vertices.push_back(graph.add_vertex(i));
-  }
+  graph.add_edge(vertex_1, vertex_2, 1);
+  graph.add_edge(vertex_6, vertex_7, 1);
+  graph.add_edge(vertex_1, vertex_7, 1);
+  graph.add_edge(vertex_2, vertex_7, 1);
+  graph.add_edge(vertex_1, vertex_6, 1);
+  graph.add_edge(vertex_2, vertex_6, 1);
 
-  std::random_device dev;
-  std::mt19937 rng(dev());
-  std::uniform_int_distribution<std::mt19937::result_type> rand_vertex(0, 69);
+  graph.add_edge(vertex_2, vertex_3, 1);
+  graph.add_edge(vertex_2, vertex_5, 1);
+  graph.add_edge(vertex_3, vertex_6, 1);
+  graph.add_edge(vertex_5, vertex_6, 1);
+  graph.add_edge(vertex_3, vertex_5, 1);
 
-  for (int i = 0; i < 1360; ++i) {
-    graph.add_edge(vertices[rand_vertex(rng)], vertices[rand_vertex(rng)], 1);
-  }
+  graph.add_edge(vertex_3, vertex_4, 1);
+  graph.add_edge(vertex_5, vertex_4, 1);
 
-  auto start = std::chrono::high_resolution_clock::now();
   auto cliques = bron_kerbosch(graph);
-  auto stop = std::chrono::high_resolution_clock::now();
-
-  int expected_time = 900;
+  std::vector<std::vector<vertex_id_t>> expected_cliques{
+      {vertex_1, vertex_2, vertex_6, vertex_7},
+      {vertex_2, vertex_6, vertex_3, vertex_5},
+      {vertex_3, vertex_4, vertex_5}};
+  sort_vectors(cliques, expected_cliques);
 
-  ASSERT_TRUE(expected_time >=
-              duration_cast<std::chrono::milliseconds>(stop - start).count());
+  ASSERT_EQ(cliques, expected_cliques);
 }
 
+TYPED_TEST(BronKerbosch, GraphTwoLines) {
+  undirected_graph<int, int> graph{};
+
+  const auto vertex_1 = graph.add_vertex(10);
+  const auto vertex_2 = graph.add_vertex(20);
+  const auto vertex_3 = graph.add_vertex(30);
+  const auto vertex_4 = graph.add_vertex(40);
+  const auto vertex_5 = graph.add_vertex(50);
+  const auto vertex_6 = graph.add_vertex(60);
+  const auto vertex_7 = graph.add_vertex(70);
+  const auto vertex_8 = graph.add_vertex(80);
+
+  graph.add_edge(vertex_2, vertex_1, 1);
+  graph.add_edge(vertex_2, vertex_3, 1);
+  graph.add_edge(vertex_3, vertex_4, 1);
+
+  graph.add_edge(vertex_5, vertex_6, 1);
+  graph.add_edge(vertex_6, vertex_7, 1);
+
+  auto cliques = bron_kerbosch(graph);
+  std::vector<std::vector<vertex_id_t>> expected_cliques{
+      {vertex_1, vertex_2}, {vertex_2, vertex_3}, {vertex_3, vertex_4},
+      {vertex_5, vertex_6}, {vertex_6, vertex_7}, {vertex_8}};
+
+  sort_vectors(cliques, expected_cliques);
+
+  ASSERT_EQ(cliques, expected_cliques);
+}
 };  // namespace graaf::algorithm
\ No newline at end of file

From 27e6894d554d31688bc007793d8f9dca695e1455 Mon Sep 17 00:00:00 2001
From: Aleksandr <hromizz@gmail.com>
Date: Mon, 9 Oct 2023 11:58:46 +0300
Subject: [PATCH 36/40] Update README.md

---
 README.md | 3 +--
 1 file changed, 1 insertion(+), 2 deletions(-)

diff --git a/README.md b/README.md
index 17da09eb..fc9b5d2e 100644
--- a/README.md
+++ b/README.md
@@ -103,8 +103,7 @@ take a look at the [docs](https://bobluppes.github.io/graaf/docs/algorithms/intr
     - BFS-Based Shortest Path
     - Dijkstra
     - Bellman-Ford
-5. [**Strongly Connected Components Algorithms
-   **](https://bobluppes.github.io/graaf/docs/category/strongly-connected-components):
+5. [**Strongly Connected Components Algorithms**](https://bobluppes.github.io/graaf/docs/category/strongly-connected-components):
     - Tarjan's Strongly Connected Components
 6. [**Topological Sorting Algorithms**](https://bobluppes.github.io/graaf/docs/category/topological-sorting):
     - Topological sorting DFS-based

From 696983932b77668446030e77d9ce17675519a99a Mon Sep 17 00:00:00 2001
From: Hromz <hromizz@gmail.com>
Date: Mon, 9 Oct 2023 12:14:55 +0300
Subject: [PATCH 37/40] folder name correction, added json to docs

---
 docs/docs/algorithms/clique-detection/_category_.json       | 6 ++++++
 .../{clique => clique-detection}/bron_kerbosch.md           | 0
 .../{clique => clique_detection}/bron_kerbosch_test.cpp     | 0
 3 files changed, 6 insertions(+)
 create mode 100644 docs/docs/algorithms/clique-detection/_category_.json
 rename docs/docs/algorithms/{clique => clique-detection}/bron_kerbosch.md (100%)
 rename test/graaflib/algorithm/{clique => clique_detection}/bron_kerbosch_test.cpp (100%)

diff --git a/docs/docs/algorithms/clique-detection/_category_.json b/docs/docs/algorithms/clique-detection/_category_.json
new file mode 100644
index 00000000..26b2ac70
--- /dev/null
+++ b/docs/docs/algorithms/clique-detection/_category_.json
@@ -0,0 +1,6 @@
+{
+  "label": "Clique Detection",
+  "link": {
+    "type": "generated-index"
+  }
+}
\ No newline at end of file
diff --git a/docs/docs/algorithms/clique/bron_kerbosch.md b/docs/docs/algorithms/clique-detection/bron_kerbosch.md
similarity index 100%
rename from docs/docs/algorithms/clique/bron_kerbosch.md
rename to docs/docs/algorithms/clique-detection/bron_kerbosch.md
diff --git a/test/graaflib/algorithm/clique/bron_kerbosch_test.cpp b/test/graaflib/algorithm/clique_detection/bron_kerbosch_test.cpp
similarity index 100%
rename from test/graaflib/algorithm/clique/bron_kerbosch_test.cpp
rename to test/graaflib/algorithm/clique_detection/bron_kerbosch_test.cpp

From 0f9ffe89102042cc47291c6ad7a929841b04c12e Mon Sep 17 00:00:00 2001
From: Hromz <hromizz@gmail.com>
Date: Mon, 9 Oct 2023 12:25:23 +0300
Subject: [PATCH 38/40] small correction in name and headers

---
 .../algorithm/{clique => clique_detection}/bron_kerbosch.h  | 6 +++---
 .../{clique => clique_detection}/bron_kerbosch.tpp          | 2 +-
 .../algorithm/clique_detection/bron_kerbosch_test.cpp       | 2 +-
 3 files changed, 5 insertions(+), 5 deletions(-)
 rename include/graaflib/algorithm/{clique => clique_detection}/bron_kerbosch.h (76%)
 rename include/graaflib/algorithm/{clique => clique_detection}/bron_kerbosch.tpp (98%)

diff --git a/include/graaflib/algorithm/clique/bron_kerbosch.h b/include/graaflib/algorithm/clique_detection/bron_kerbosch.h
similarity index 76%
rename from include/graaflib/algorithm/clique/bron_kerbosch.h
rename to include/graaflib/algorithm/clique_detection/bron_kerbosch.h
index 9547e040..01e4ca57 100644
--- a/include/graaflib/algorithm/clique/bron_kerbosch.h
+++ b/include/graaflib/algorithm/clique_detection/bron_kerbosch.h
@@ -8,9 +8,9 @@ namespace graaf::algorithm {
  * algorithm.
  *
  * The Bron-Kerbosch algorithm is used for finding all cliques in an undirected
- * graph. A clique is a subset of vertices such that every two distinct vertices
- * are adjacent. This function returns a list of all cliques, each represented
- * as a vector of vertex identifiers.
+ * graph. A clique_detection is a subset of vertices such that every two
+ * distinct vertices are adjacent. This function returns a list of all cliques,
+ * each represented as a vector of vertex identifiers.
  *
  * @tparam V The vertex type of the graph.
  * @tparam E The edge type of the graph.
diff --git a/include/graaflib/algorithm/clique/bron_kerbosch.tpp b/include/graaflib/algorithm/clique_detection/bron_kerbosch.tpp
similarity index 98%
rename from include/graaflib/algorithm/clique/bron_kerbosch.tpp
rename to include/graaflib/algorithm/clique_detection/bron_kerbosch.tpp
index 3a55196a..5ecb8df6 100644
--- a/include/graaflib/algorithm/clique/bron_kerbosch.tpp
+++ b/include/graaflib/algorithm/clique_detection/bron_kerbosch.tpp
@@ -1,6 +1,6 @@
 #pragma once
 
-#include <graaflib/algorithm/clique/bron_kerbosch.h>
+#include <graaflib/algorithm/clique_detection/bron_kerbosch.h>
 
 #include <algorithm>
 #include <iostream>
diff --git a/test/graaflib/algorithm/clique_detection/bron_kerbosch_test.cpp b/test/graaflib/algorithm/clique_detection/bron_kerbosch_test.cpp
index cc70b90b..2aabc4aa 100644
--- a/test/graaflib/algorithm/clique_detection/bron_kerbosch_test.cpp
+++ b/test/graaflib/algorithm/clique_detection/bron_kerbosch_test.cpp
@@ -1,5 +1,5 @@
 #include <fmt/core.h>
-#include <graaflib/algorithm/clique/bron_kerbosch.h>
+#include <graaflib/algorithm/clique_detection/bron_kerbosch.h>
 #include <graaflib/graph.h>
 #include <graaflib/types.h>
 #include <gtest/gtest.h>

From ef490b8feb4abc85f5f4d10456659fcbdeafb567 Mon Sep 17 00:00:00 2001
From: Hromz <hromizz@gmail.com>
Date: Fri, 13 Oct 2023 00:08:23 +0300
Subject: [PATCH 39/40] benchmark test Bron-Kerbosch

---
 perf/graaflib/bron_kerbosch_benchmark.cpp | 245 ++++++++++++++++++++++
 1 file changed, 245 insertions(+)
 create mode 100644 perf/graaflib/bron_kerbosch_benchmark.cpp

diff --git a/perf/graaflib/bron_kerbosch_benchmark.cpp b/perf/graaflib/bron_kerbosch_benchmark.cpp
new file mode 100644
index 00000000..dede051d
--- /dev/null
+++ b/perf/graaflib/bron_kerbosch_benchmark.cpp
@@ -0,0 +1,245 @@
+#include <benchmark/benchmark.h>
+#include <graaflib/algorithm/clique_detection/bron_kerbosch.h>
+#include <graaflib/graph.h>
+
+#include <random>
+#include <vector>
+
+namespace {
+
+// Generating random number of vertices (1- 30) for a clique
+std::random_device dev;
+std::mt19937 rng(dev());
+std::uniform_int_distribution<std::mt19937::result_type> random_clique_size(1,
+                                                                            30);
+
+template <typename EDGE_T>
+[[nodiscard]] std::vector<graaf::vertex_id_t> create_vertices(
+    graaf::undirected_graph<int, EDGE_T>& graph, size_t n) {
+  std::vector<graaf::vertex_id_t> vertices{};
+  vertices.reserve(n);
+
+  for (size_t i{0}; i < n; ++i) {
+    vertices.push_back(graph.add_vertex(i));
+  }
+
+  return vertices;
+}
+
+template <typename EDGE_T>
+void add_clique(graaf::undirected_graph<int, EDGE_T>& graph,
+                const std::vector<graaf::vertex_id_t>& vertices,
+                size_t start_vertex, size_t clique_size) {
+  // We are in range of vector of vertices
+  size_t end_vertex = std::min(start_vertex + clique_size, vertices.size());
+  std::vector<graaf::edge_id_t> clique{};
+  clique.reserve((clique_size * (clique_size - 1)) / 2);
+
+  // Constructing a clique
+  for (size_t i{start_vertex}; i < end_vertex; ++i) {
+    for (size_t j{i + 1}; j < end_vertex; ++j) {
+      clique.emplace_back(vertices[i], vertices[j]);
+    }
+  }
+
+  for (auto& edge_t : clique) {
+    graph.add_edge(edge_t.first, edge_t.second, 1);
+  }
+}
+}  // namespace
+
+static void bron_kerbosh_two_vertices_cliques(benchmark::State& state) {
+  const auto number_of_edges{static_cast<size_t>(state.range(0))};
+
+  graaf::undirected_graph<int, int> graph{};
+
+  // We create enough vertices to construct the requested number of edges
+  const auto number_of_vertices{number_of_edges + 1};
+  const auto vertices{create_vertices(graph, number_of_vertices)};
+
+  for (auto _ : state) {
+    for (size_t i{0}; i < number_of_edges; ++i) {
+      graph.add_edge(vertices[i], vertices[i + 1], 1);
+    }
+  }
+
+  graaf::algorithm::bron_kerbosch(graph);
+  state.SetComplexityN(state.range(0));
+}
+
+static void bron_kerbosh_dense_graph(benchmark::State& state) {
+  const auto number_of_edges{static_cast<size_t>(state.range(0))};
+
+  graaf::undirected_graph<int, int> graph{};
+
+  // We create enough vertices to construct the requested number of edges
+  const auto number_of_vertices{number_of_edges + 1};
+  const auto vertices{create_vertices(graph, number_of_vertices)};
+
+  for (auto _ : state) {
+    for (size_t i{0}; i < number_of_edges; ++i) {
+      for (size_t j{i + 1}; j < number_of_edges; ++j) {
+        if (i != j && !graph.has_edge(vertices[i], vertices[j]))
+          graph.add_edge(vertices[i], vertices[j], 1);
+      }
+    }
+  }
+
+  graaf::algorithm::bron_kerbosch(graph);
+  state.SetComplexityN(state.range(0));
+}
+
+static void bron_kerbosh_graph_triangle_cliques(benchmark::State& state) {
+  const auto number_of_edges{static_cast<size_t>(state.range(0))};
+
+  graaf::undirected_graph<int, int> graph{};
+
+  // We create enough vertices to construct the requested number of edges
+  const auto number_of_vertices{number_of_edges + 1};
+  const auto vertices{create_vertices(graph, number_of_vertices)};
+
+  size_t clique_size = 4;
+
+  for (auto _ : state) {
+    for (size_t i{0}; i < number_of_edges; i += clique_size) {
+      std::vector<graaf::edge_id_t> clique{};
+      add_clique(graph, vertices, i, clique_size);
+    }
+  }
+
+  graaf::algorithm::bron_kerbosch(graph);
+  state.SetComplexityN(state.range(0));
+}
+
+static void bron_kerbosh_graph_connected_triangle_cliques(
+    benchmark::State& state) {
+  const auto number_of_edges{static_cast<size_t>(state.range(0))};
+
+  graaf::undirected_graph<int, int> graph{};
+
+  // We create enough vertices to construct the requested number of edges
+  const auto number_of_vertices{number_of_edges + 1};
+  const auto vertices{create_vertices(graph, number_of_vertices)};
+
+  size_t clique_size = 4;
+
+  for (auto _ : state) {
+    // Connecting all cliques
+    for (size_t i{0}; i + clique_size < number_of_edges; i += clique_size) {
+      graph.add_edge(vertices[i], vertices[i + clique_size], 1);
+    }
+
+    for (size_t i{0}; i < number_of_edges; i += clique_size) {
+      std::vector<graaf::edge_id_t> clique{};
+      add_clique(graph, vertices, i, clique_size);
+    }
+  }
+
+  graaf::algorithm::bron_kerbosch(graph);
+  state.SetComplexityN(state.range(0));
+}
+
+static void bron_kerbosh_graph_large_cliques(benchmark::State& state) {
+  const auto number_of_edges{static_cast<size_t>(state.range(0))};
+
+  graaf::undirected_graph<int, int> graph{};
+
+  // We create enough vertices to construct the requested number of edges
+  const auto number_of_vertices{number_of_edges + 1};
+  const auto vertices{create_vertices(graph, number_of_vertices)};
+
+  size_t clique_size = 25;
+
+  for (auto _ : state) {
+    for (size_t i{0}; i < number_of_edges; i += clique_size) {
+      std::vector<graaf::edge_id_t> clique{};
+      add_clique(graph, vertices, i, clique_size);
+    }
+  }
+
+  graaf::algorithm::bron_kerbosch(graph);
+  state.SetComplexityN(state.range(0));
+}
+
+static void bron_kerbosh_graph_mixed_random_cliques(benchmark::State& state) {
+  const auto number_of_edges{static_cast<size_t>(state.range(0))};
+
+  graaf::undirected_graph<int, int> graph{};
+
+  // We create enough vertices to construct the requested number of edges
+  const auto number_of_vertices{number_of_edges + 1};
+  const auto vertices{create_vertices(graph, number_of_vertices)};
+
+  size_t clique_size = 3;
+
+  for (auto _ : state) {
+    for (size_t i{0}; i + clique_size < number_of_edges; i += clique_size) {
+      std::vector<graaf::edge_id_t> clique{};
+      add_clique(graph, vertices, i, clique_size++);
+
+      clique_size = random_clique_size(rng);
+    }
+  }
+
+  graaf::algorithm::bron_kerbosch(graph);
+  state.SetComplexityN(state.range(0));
+}
+
+static void bron_kerbosh_graph_connected_mixed_random_cliques(
+    benchmark::State& state) {
+  const auto number_of_edges{static_cast<size_t>(state.range(0))};
+
+  graaf::undirected_graph<int, int> graph{};
+
+  // We create enough vertices to construct the requested number of edges
+  const auto number_of_vertices{number_of_edges + 1};
+  const auto vertices{create_vertices(graph, number_of_vertices)};
+
+  size_t clique_size = 3;
+
+  for (auto _ : state) {
+    // Connecting all cliques
+    for (size_t i{0}; i < number_of_edges; ++i) {
+      graph.add_edge(vertices[i], vertices[i + 1], 1);
+    }
+
+    for (size_t i{0}; i + clique_size < number_of_edges; i += clique_size) {
+      std::vector<graaf::edge_id_t> clique{};
+      add_clique(graph, vertices, i, clique_size++);
+
+      clique_size = random_clique_size(rng);
+    }
+  }
+
+  graaf::algorithm::bron_kerbosch(graph);
+  state.SetComplexityN(state.range(0));
+}
+
+BENCHMARK(bron_kerbosh_two_vertices_cliques)
+    ->Range(100, 10000)
+    ->Unit(benchmark::kMillisecond)
+    ->Complexity();
+BENCHMARK(bron_kerbosh_dense_graph) /* large amount of vertices to process */
+    ->Range(100, 1000)
+    ->Unit(benchmark::kMillisecond)
+    ->Complexity();
+BENCHMARK(bron_kerbosh_graph_triangle_cliques)
+    ->Range(100, 10000)
+    ->Unit(benchmark::kMillisecond)
+    ->Complexity();
+BENCHMARK(bron_kerbosh_graph_connected_triangle_cliques)
+    ->Range(100, 10000)
+    ->Unit(benchmark::kMillisecond)
+    ->Complexity();
+BENCHMARK(bron_kerbosh_graph_large_cliques)
+    ->Range(100, 10000)
+    ->Unit(benchmark::kMillisecond)
+    ->Complexity();
+BENCHMARK(bron_kerbosh_graph_mixed_random_cliques)
+    ->Range(100, 10000)
+    ->Unit(benchmark::kMillisecond)
+    ->Complexity();
+BENCHMARK(bron_kerbosh_graph_connected_mixed_random_cliques)
+    ->Range(100, 10000)
+    ->Unit(benchmark::kMillisecond)
+    ->Complexity();
\ No newline at end of file

From 7b42950bf4ccc3ef1e2b68cdbb3e46f63819d24a Mon Sep 17 00:00:00 2001
From: Hromz <hromizz@gmail.com>
Date: Mon, 16 Oct 2023 20:51:39 +0300
Subject: [PATCH 40/40] Changed according to comments

---
 perf/graaflib/bron_kerbosch_benchmark.cpp | 178 +++++++---------------
 1 file changed, 53 insertions(+), 125 deletions(-)

diff --git a/perf/graaflib/bron_kerbosch_benchmark.cpp b/perf/graaflib/bron_kerbosch_benchmark.cpp
index dede051d..c27c8fbc 100644
--- a/perf/graaflib/bron_kerbosch_benchmark.cpp
+++ b/perf/graaflib/bron_kerbosch_benchmark.cpp
@@ -6,13 +6,11 @@
 #include <vector>
 
 namespace {
-
 // Generating random number of vertices (1- 30) for a clique
 std::random_device dev;
 std::mt19937 rng(dev());
 std::uniform_int_distribution<std::mt19937::result_type> random_clique_size(1,
                                                                             30);
-
 template <typename EDGE_T>
 [[nodiscard]] std::vector<graaf::vertex_id_t> create_vertices(
     graaf::undirected_graph<int, EDGE_T>& graph, size_t n) {
@@ -32,23 +30,17 @@ void add_clique(graaf::undirected_graph<int, EDGE_T>& graph,
                 size_t start_vertex, size_t clique_size) {
   // We are in range of vector of vertices
   size_t end_vertex = std::min(start_vertex + clique_size, vertices.size());
-  std::vector<graaf::edge_id_t> clique{};
-  clique.reserve((clique_size * (clique_size - 1)) / 2);
 
   // Constructing a clique
   for (size_t i{start_vertex}; i < end_vertex; ++i) {
     for (size_t j{i + 1}; j < end_vertex; ++j) {
-      clique.emplace_back(vertices[i], vertices[j]);
+      graph.add_edge(vertices[i], vertices[j], 1);
     }
   }
-
-  for (auto& edge_t : clique) {
-    graph.add_edge(edge_t.first, edge_t.second, 1);
-  }
 }
 }  // namespace
 
-static void bron_kerbosh_two_vertices_cliques(benchmark::State& state) {
+static void bron_kerbosh_cliques(benchmark::State& state) {
   const auto number_of_edges{static_cast<size_t>(state.range(0))};
 
   graaf::undirected_graph<int, int> graph{};
@@ -56,40 +48,21 @@ static void bron_kerbosh_two_vertices_cliques(benchmark::State& state) {
   // We create enough vertices to construct the requested number of edges
   const auto number_of_vertices{number_of_edges + 1};
   const auto vertices{create_vertices(graph, number_of_vertices)};
+  const auto clique_size = static_cast<size_t>(state.range(1));
 
-  for (auto _ : state) {
-    for (size_t i{0}; i < number_of_edges; ++i) {
-      graph.add_edge(vertices[i], vertices[i + 1], 1);
-    }
+  for (size_t i{0}; i < number_of_edges; i += clique_size) {
+    add_clique(graph, vertices, i, clique_size);
   }
 
-  graaf::algorithm::bron_kerbosch(graph);
-  state.SetComplexityN(state.range(0));
-}
-
-static void bron_kerbosh_dense_graph(benchmark::State& state) {
-  const auto number_of_edges{static_cast<size_t>(state.range(0))};
-
-  graaf::undirected_graph<int, int> graph{};
-
-  // We create enough vertices to construct the requested number of edges
-  const auto number_of_vertices{number_of_edges + 1};
-  const auto vertices{create_vertices(graph, number_of_vertices)};
-
   for (auto _ : state) {
-    for (size_t i{0}; i < number_of_edges; ++i) {
-      for (size_t j{i + 1}; j < number_of_edges; ++j) {
-        if (i != j && !graph.has_edge(vertices[i], vertices[j]))
-          graph.add_edge(vertices[i], vertices[j], 1);
-      }
-    }
+    auto result = graaf::algorithm::bron_kerbosch(graph);
+    benchmark::DoNotOptimize(result);
   }
 
-  graaf::algorithm::bron_kerbosch(graph);
-  state.SetComplexityN(state.range(0));
+  state.SetComplexityN(state.range(1));
 }
 
-static void bron_kerbosh_graph_triangle_cliques(benchmark::State& state) {
+static void bron_kerbosh_connected_cliques(benchmark::State& state) {
   const auto number_of_edges{static_cast<size_t>(state.range(0))};
 
   graaf::undirected_graph<int, int> graph{};
@@ -97,49 +70,26 @@ static void bron_kerbosh_graph_triangle_cliques(benchmark::State& state) {
   // We create enough vertices to construct the requested number of edges
   const auto number_of_vertices{number_of_edges + 1};
   const auto vertices{create_vertices(graph, number_of_vertices)};
+  const auto clique_size = static_cast<size_t>(state.range(1));
 
-  size_t clique_size = 4;
-
-  for (auto _ : state) {
-    for (size_t i{0}; i < number_of_edges; i += clique_size) {
-      std::vector<graaf::edge_id_t> clique{};
-      add_clique(graph, vertices, i, clique_size);
-    }
+  // Connecting all cliques
+  for (size_t i{0}; i + clique_size < number_of_edges; i += clique_size) {
+    graph.add_edge(vertices[i], vertices[i + clique_size], 1);
   }
 
-  graaf::algorithm::bron_kerbosch(graph);
-  state.SetComplexityN(state.range(0));
-}
-
-static void bron_kerbosh_graph_connected_triangle_cliques(
-    benchmark::State& state) {
-  const auto number_of_edges{static_cast<size_t>(state.range(0))};
-
-  graaf::undirected_graph<int, int> graph{};
-
-  // We create enough vertices to construct the requested number of edges
-  const auto number_of_vertices{number_of_edges + 1};
-  const auto vertices{create_vertices(graph, number_of_vertices)};
-
-  size_t clique_size = 4;
+  for (size_t i{0}; i < number_of_edges; i += clique_size) {
+    add_clique(graph, vertices, i, clique_size);
+  }
 
   for (auto _ : state) {
-    // Connecting all cliques
-    for (size_t i{0}; i + clique_size < number_of_edges; i += clique_size) {
-      graph.add_edge(vertices[i], vertices[i + clique_size], 1);
-    }
-
-    for (size_t i{0}; i < number_of_edges; i += clique_size) {
-      std::vector<graaf::edge_id_t> clique{};
-      add_clique(graph, vertices, i, clique_size);
-    }
+    auto result = graaf::algorithm::bron_kerbosch(graph);
+    benchmark::DoNotOptimize(result);
   }
 
-  graaf::algorithm::bron_kerbosch(graph);
-  state.SetComplexityN(state.range(0));
+  state.SetComplexityN(state.range(1));
 }
 
-static void bron_kerbosh_graph_large_cliques(benchmark::State& state) {
+static void bron_kerbosh_random_cliques(benchmark::State& state) {
   const auto number_of_edges{static_cast<size_t>(state.range(0))};
 
   graaf::undirected_graph<int, int> graph{};
@@ -147,21 +97,22 @@ static void bron_kerbosh_graph_large_cliques(benchmark::State& state) {
   // We create enough vertices to construct the requested number of edges
   const auto number_of_vertices{number_of_edges + 1};
   const auto vertices{create_vertices(graph, number_of_vertices)};
+  size_t clique_size = random_clique_size(rng);
 
-  size_t clique_size = 25;
+  for (size_t i{0}; i + clique_size < number_of_edges; i += clique_size) {
+    add_clique(graph, vertices, i, clique_size++);
+    clique_size = random_clique_size(rng);
+  }
 
   for (auto _ : state) {
-    for (size_t i{0}; i < number_of_edges; i += clique_size) {
-      std::vector<graaf::edge_id_t> clique{};
-      add_clique(graph, vertices, i, clique_size);
-    }
+    auto result = graaf::algorithm::bron_kerbosch(graph);
+    benchmark::DoNotOptimize(result);
   }
 
-  graaf::algorithm::bron_kerbosch(graph);
   state.SetComplexityN(state.range(0));
 }
 
-static void bron_kerbosh_graph_mixed_random_cliques(benchmark::State& state) {
+static void bron_kerbosh_connected_random_cliques(benchmark::State& state) {
   const auto number_of_edges{static_cast<size_t>(state.range(0))};
 
   graaf::undirected_graph<int, int> graph{};
@@ -169,77 +120,54 @@ static void bron_kerbosh_graph_mixed_random_cliques(benchmark::State& state) {
   // We create enough vertices to construct the requested number of edges
   const auto number_of_vertices{number_of_edges + 1};
   const auto vertices{create_vertices(graph, number_of_vertices)};
+  size_t clique_size = random_clique_size(rng);
 
-  size_t clique_size = 3;
-
-  for (auto _ : state) {
-    for (size_t i{0}; i + clique_size < number_of_edges; i += clique_size) {
-      std::vector<graaf::edge_id_t> clique{};
-      add_clique(graph, vertices, i, clique_size++);
-
-      clique_size = random_clique_size(rng);
-    }
+  // Connecting all cliques
+  for (size_t i{0}; i < number_of_edges; ++i) {
+    graph.add_edge(vertices[i], vertices[i + 1], 1);
   }
 
-  graaf::algorithm::bron_kerbosch(graph);
-  state.SetComplexityN(state.range(0));
-}
-
-static void bron_kerbosh_graph_connected_mixed_random_cliques(
-    benchmark::State& state) {
-  const auto number_of_edges{static_cast<size_t>(state.range(0))};
-
-  graaf::undirected_graph<int, int> graph{};
-
-  // We create enough vertices to construct the requested number of edges
-  const auto number_of_vertices{number_of_edges + 1};
-  const auto vertices{create_vertices(graph, number_of_vertices)};
-
-  size_t clique_size = 3;
+  for (size_t i{0}; i + clique_size < number_of_edges; i += clique_size) {
+    add_clique(graph, vertices, i, clique_size++);
+    clique_size = random_clique_size(rng);
+  }
 
   for (auto _ : state) {
-    // Connecting all cliques
-    for (size_t i{0}; i < number_of_edges; ++i) {
-      graph.add_edge(vertices[i], vertices[i + 1], 1);
-    }
-
-    for (size_t i{0}; i + clique_size < number_of_edges; i += clique_size) {
-      std::vector<graaf::edge_id_t> clique{};
-      add_clique(graph, vertices, i, clique_size++);
-
-      clique_size = random_clique_size(rng);
-    }
+    auto result = graaf::algorithm::bron_kerbosch(graph);
+    benchmark::DoNotOptimize(result);
   }
 
-  graaf::algorithm::bron_kerbosch(graph);
   state.SetComplexityN(state.range(0));
 }
 
-BENCHMARK(bron_kerbosh_two_vertices_cliques)
-    ->Range(100, 10000)
+BENCHMARK(bron_kerbosh_cliques)
+    ->Ranges({{100, 10000}, {2, 32}}) /* clique size 2 ^ n */
     ->Unit(benchmark::kMillisecond)
     ->Complexity();
-BENCHMARK(bron_kerbosh_dense_graph) /* large amount of vertices to process */
-    ->Range(100, 1000)
+BENCHMARK(bron_kerbosh_connected_cliques)
+    ->Ranges({{100, 10000}, {2, 32}}) /* clique size 2 ^ n */
     ->Unit(benchmark::kMillisecond)
     ->Complexity();
-BENCHMARK(bron_kerbosh_graph_triangle_cliques)
-    ->Range(100, 10000)
+BENCHMARK(bron_kerbosh_cliques)
+    ->Ranges({{100, 1000},
+              {1000, 1000}}) /* Dense graph, number of vertices are
+                                min(state.range(1), vertex.size()) */
     ->Unit(benchmark::kMillisecond)
     ->Complexity();
-BENCHMARK(bron_kerbosh_graph_connected_triangle_cliques)
-    ->Range(100, 10000)
+BENCHMARK(bron_kerbosh_cliques)
+    ->Ranges({{100, 10000}, {10, 60}}) /* large cliques */
     ->Unit(benchmark::kMillisecond)
     ->Complexity();
-BENCHMARK(bron_kerbosh_graph_large_cliques)
-    ->Range(100, 10000)
+BENCHMARK(bron_kerbosh_connected_cliques)
+    ->Ranges({{100, 10000}, {10, 60}}) /* large cliques */
     ->Unit(benchmark::kMillisecond)
     ->Complexity();
-BENCHMARK(bron_kerbosh_graph_mixed_random_cliques)
+BENCHMARK(bron_kerbosh_random_cliques) /* random clique size between 1-30 */
     ->Range(100, 10000)
     ->Unit(benchmark::kMillisecond)
     ->Complexity();
-BENCHMARK(bron_kerbosh_graph_connected_mixed_random_cliques)
+BENCHMARK(
+    bron_kerbosh_connected_random_cliques) /* random clique size between 1-30 */
     ->Range(100, 10000)
     ->Unit(benchmark::kMillisecond)
     ->Complexity();
\ No newline at end of file