Add example of simple graph algorithms

+ Using pseudocode examples from MIT Intro to Algorithms

cpp/algorithms/graphs/simple/graph.cpp

@@ -0,0 +1,96 @@
+/*#############################################################################
+## Author: Shaun Reed                                                        ##
+## Legal: All Content (c) 2021 Shaun Reed, all rights reserved               ##
+## About: Driver program to test a simple graph implementation               ##
+##                                                                           ##
+## Contact: shaunrd0@gmail.com  | URL: www.shaunreed.com | GitHub: shaunrd0  ##
+###############################################################################
+*/
+
+#include "lib-graph.hpp"
+
+
+int main (const int argc, const char * argv[])
+{
+  // We could initialize the graph with some localNodes...
+  std::map<int, std::set<int>> localNodes{
+      {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}},
+  };
+//  Graph bfsGraph(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 (
+      {
+          {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
+  bfsGraph.BFS(2);
+
+
+  std::cout << "\n\n##### Depth First Search #####\n";
+  // Initialize an example graph for Depth First Search
+  Graph dfsGraph (
+      {
+          {1, {2, 4}},
+          {2, {5}},
+          {3, {5, 6}},
+          {4, {2}},
+          {5, {4}},
+          {6, {6}},
+      }
+  );
+  // The graph traversed in this example is seen in MIT Intro to Algorithms
+  // + Chapter 22, Figure 22.4 on DFS
+  dfsGraph.DFS();
+
+
+  std::cout << "\n\n##### Topological Sort #####\n";
+  // Initialize an example graph for Topological Sort
+  Graph topologicalGraph (
+      {
+          {1, {4, 5}},
+          {2, {5}},
+          {3, {}},
+          {4, {5, 7}},
+          {5, {}},
+          {6, {7, 8}},
+          {7, {9}},
+          {8, {9}},
+          {9, {}},
+      }
+  );
+  // The graph traversed in this example is seen in MIT Intro to Algorithms
+  // + Chapter 22, Figure 22.7 on Topological Sort
+  // + Each node was replaced with a value from left-to-right, top-to-bottom
+  // + Undershorts = 1, Socks = 2, Watch = 3, Pants = 4, etc...
+  std::vector<int> order = topologicalGraph.TopologicalSort();
+  // Because this is a simple graph with no objects to store finishing time
+  // + The result is only one example of valid topological order
+  // + There are other valid orders; Final result differs from one in the book
+  std::cout << "\n\nTopological order: ";
+  while (!order.empty()) {
+    std::cout << order.back() << " ";
+    order.pop_back();
+  }
+  std::cout << std::endl;
+
+}