Update simple-graph implementation to track discovery and finish time

+ Allows result of topological sort to match examples shown in MIT Algorithms
+ Correct order of initialization for all graphs and adjacent nodes in graph.cpp
+ Provide overloaded DFS for beginning at a specific node within the graph

cpp/algorithms/graphs/simple/lib-graph.hpp

@@ -15,22 +15,48 @@
 #include <queue>
 #include <set>
 #include <vector>
+#include <unordered_map>
+#include <unordered_set>
 
 
 class Graph {
 public:
-  explicit Graph(std::map<int, std::set<int>> nodes) : nodes_(std::move(nodes)) {}
-  std::map<int, std::set<int>> nodes_;
+  using Node = std::unordered_map<int, std::unordered_set<int>>;
+  explicit Graph(Node nodes) : nodes_(std::move(nodes))
+  {
+    discoveryTime.resize(nodes_.size());
+    finishTime.resize(nodes_.size(), std::make_pair(0,0));
+  }
 
   void BFS(int startNode);
 
   void DFS();
-  void DFSVisit(int startNode, std::vector<bool> &discovered);
+  void DFS(Node::iterator startNode);
+  void DFSVisit(int &time, int startNode, std::vector<bool> &discovered);
 
-  std::vector<int> TopologicalSort();
+  std::vector<int> TopologicalSort(Node::iterator startNode);
   void TopologicalVisit(
       int startNode, std::vector<bool> &discovered, std::vector<int> &order
   );
+
+  // Define a comparator for std::sort
+  // + This will help to sort nodes by finished time after traversal
+  static bool FinishedSort(std::pair<int, int> &node1, decltype(node1) &node2)
+  { return node1.second < node2.second;}
+
+  inline Node::iterator NodeBegin() { return nodes_.begin();}
+  // A non-const accessor for direct access to a node with the number value i
+  inline Node::iterator GetNode(int i) { return nodes_.find(i);}
+
+private:
+  // Unordered to avoid container reorganizing elements
+  // + Since this would alter the order nodes are traversed in
+  Node nodes_;
+
+  // Where the first element in the following two pairs is the node number
+  // And the second element is the discovery / finish time
+  std::vector<std::pair<int, int>> discoveryTime;
+  std::vector<std::pair<int, int>> finishTime;
 };
 
 #endif // LIB_GRAPH_HPP