Update object-graph example to add path finding between nodes using BFS

+ Clean code, add overloaded functions and helper functions for common tasks

cpp/algorithms/graphs/object/graph.cpp

@@ -14,7 +14,7 @@
 int main (const int argc, const char * argv[])
 {
   // We could initialize the graph with some localNodes...
-  std::map<int, std::vector<int>> localNodes{
+  std::vector<Node> localNodes{
       {1, {2, 5}}, // Node 1
       {2, {1, 6}}, // Node 2
       {3, {4, 6, 7}},
@@ -24,34 +24,50 @@ int main (const int argc, const char * argv[])
       {7, {3, 4, 6, 8}},
       {8, {4, 6}},
   };
-//  Graph bfsGraph(localNodes);
+  Graph bfsGraphInit(localNodes);
 
 
   std::cout << "\n\n##### Breadth First Search #####\n";
   // Or we could use an initializer list...
   // Initialize a example graph for Breadth First Search
-  Graph bfsGraph (
+  Graph bfsGraph(
       {
-          {Node(1, {2, 5})}, // Node 1
-          {Node(2, {1, 6})}, // Node 2...
-          {Node(3, {4, 6, 7})},
-          {Node(4, {3, 7, 8})},
-          {Node(5, {1})},
-          {Node(6, {2, 3, 7})},
-          {Node(7, {3, 4, 6, 8})},
-          {Node(8, {4, 6})},
+          {1, {2, 5}}, // Node 1
+          {2, {1, 6}}, // Node 2...
+          {3, {4, 6, 7}},
+          {4, {3, 7, 8}},
+          {5, {1}},
+          {6, {2, 3, 7}},
+          {7, {3, 4, 6, 8}},
+          {8, {4, 6}},
       }
   );
   // The graph traversed in this example is seen in MIT Intro to Algorithms
   // + Chapter 22, Figure 22.3 on BFS
-  auto iter = bfsGraph.nodes_.begin();
-  std::advance(iter, 1);
-  bfsGraph.BFS(*iter);
+  bfsGraph.BFS(bfsGraph.GetNodeCopy(2));
+  Node test = bfsGraph.GetNodeCopy(3);
+
+  std::cout << "\nTesting finding a path between two nodes using BFS...\n";
+  // Test finding a path between two nodes using BFS
+  auto path = bfsGraph.PathBFS(
+      bfsGraph.GetNodeCopy(1), bfsGraph.GetNodeCopy(7)
+      );
+  // If we were returned an empty path, it doesn't exist
+  if (path.empty()) std::cout << "No valid path found!\n";
+  else {
+    // If we were returned a path, print it
+    std::cout << "\nValid path from " << path.front()->number
+              << " to " << path.back()->number << ": ";
+    for (const auto &node : path) {
+      std::cout << node->number << " ";
+    }
+    std::cout << std::endl;
+  }
 
 
   std::cout << "\n\n##### Depth First Search #####\n";
   // Initialize an example graph for Depth First Search
-  Graph dfsGraph (
+  Graph dfsGraph(
       {
           {1, {2, 4}},
           {2, {5}},
@@ -68,7 +84,41 @@ int main (const int argc, const char * argv[])
 
   std::cout << "\n\n##### Topological Sort #####\n";
   // Initialize an example graph for Depth First Search
+  // + The order of initialization is important
+  // + To produce the same result as seen in the book
+  // ++ If the order is changed, other valid topological orders will be found
+  // The book starts on the 'shirt' node (with the number 6, in this example)
   Graph topologicalGraph (
+      {
+          {1, {4, 5}}, // undershorts
+          {2, {5}},    // socks
+          {3, {}},     // watch
+          {4, {5, 7}}, // pants
+          {5, {}},     // shoes
+          {6, {8, 7}}, // shirt
+          {7, {9}},    // belt
+          {8, {9}},    // tie
+          {9, {}},     // jacket
+      }
+  );
+
+  // The graph traversed in this example is seen in MIT Intro to Algorithms
+  // + Chapter 22, Figure 22.4 on DFS
+  // Unlike the simple-graph example, this final result matches MIT Algorithms
+  // + Aside from the placement of the watch node, which is not connected
+  // +  This is because the node is visited after all other nodes are finished
+  std::vector<Node> order =
+      topologicalGraph.TopologicalSort(topologicalGraph.GetNodeCopy(6));
+  std::cout << "\n\nTopological order: ";
+  while (!order.empty()) {
+    std::cout << order.back().number << " ";
+    order.pop_back();
+  }
+  std::cout << std::endl;
+
+  // If we want the topological order to match what is seen in the book
+  // + We have to initialize the graph carefully to get this result -
+  Graph topologicalGraph2 (
       {
           {6, {8, 7}}, // shirt
           {8, {9}},    // tie
@@ -81,15 +131,11 @@ int main (const int argc, const char * argv[])
           {2, {5}},    // socks
       }
   );
-  // The graph traversed in this example is seen in MIT Intro to Algorithms
-  // + Chapter 22, Figure 22.4 on DFS
-  // Unlike the simple-graph example, this final result matches MIT Algorithms
-  std::vector<Node> order = topologicalGraph.TopologicalSort();
+  auto order2 = topologicalGraph2.TopologicalSort(*topologicalGraph2.NodeBegin());
   std::cout << "\n\nTopological order: ";
-  while (!order.empty()) {
-    std::cout << order.back().number << " ";
-    order.pop_back();
+  while (!order2.empty()) {
+    std::cout << order2.back().number << " ";
+    order2.pop_back();
   }
   std::cout << std::endl;
-
-}
+}