Add example of object graph traversal algorithms

+ Using pseudocode examples from MIT Intro to Algorithms

cpp/algorithms/graphs/object/CMakeLists.txt

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+################################################################################
+## Author: Shaun Reed                                                         ##
+## Legal: All Content (c) 2021 Shaun Reed, all rights reserved                ##
+## About: A basic CMakeLists configuration to test RBT implementation         ##
+##                                                                            ##
+## Contact: shaunrd0@gmail.com  | URL: www.shaunreed.com | GitHub: shaunrd0   ##
+################################################################################
+#
+
+cmake_minimum_required(VERSION 3.15)
+
+project(
+    #[[NAME]]   ObjectGraph
+    VERSION     1.0
+    DESCRIPTION "Practice implementing and using object graphs in C++"
+    LANGUAGES CXX
+)
+
+add_library(lib-graph-object "lib-graph.cpp")
+
+add_executable(graph-test-object "graph.cpp")
+target_link_libraries(graph-test-object lib-graph-object)

cpp/algorithms/graphs/object/graph.cpp

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+/*##############################################################################
+## Author: Shaun Reed                                                         ##
+## Legal: All Content (c) 2021 Shaun Reed, all rights reserved                ##
+## About: An example of an object graph implementation                        ##
+##        Algorithms in this example are found in MIT Intro to Algorithms     ##
+##                                                                            ##
+## 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);
+
+//  Graph testGraph(
+//      {
+//          {Node(1, {2, 5})},
+////          {Node(1, {2, 5})},
+//       }
+//  )
+
+
+  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 (
+      {
+          {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})},
+      }
+  );
+  // 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);
+
+
+  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 Depth First Search
+  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 22.4 on DFS
+  std::vector<Node> order = topologicalGraph.TopologicalSort();
+  std::cout << "\n\nTopological order: ";
+  while (!order.empty()) {
+    std::cout << order.back().number << " ";
+    order.pop_back();
+  }
+  std::cout << std::endl;
+
+}

cpp/algorithms/graphs/object/lib-graph.cpp

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+/*##############################################################################
+## Author: Shaun Reed                                                         ##
+## Legal: All Content (c) 2021 Shaun Reed, all rights reserved                ##
+## About: Driver program to test object graph implementation                  ##
+##                                                                            ##
+## Contact: shaunrd0@gmail.com  | URL: www.shaunreed.com | GitHub: shaunrd0   ##
+################################################################################
+*/
+
+#include "lib-graph.hpp"
+
+
+void Graph::BFS(const Node& startNode) const
+{
+  // Track the nodes we have discovered
+  //  TODO: Do this at the end to maintain the state instead of at beginning?
+  for (const auto &node : nodes_) node.color = White;
+
+  // Create a queue to visit discovered nodes in FIFO order
+  std::queue<Node> visitQueue;
+
+  // Mark the startNode as in progress until we finish checking adjacent nodes
+  startNode.color = Gray;
+
+  // Visit the startNode
+  visitQueue.push(startNode);
+
+  // Continue to visit nodes until there are none left in the graph
+  while (!visitQueue.empty()) {
+    // Remove thisNode from the visitQueue, storing its vertex locally
+    Node thisNode = visitQueue.front();
+    visitQueue.pop();
+    std::cout << "Visiting node " << thisNode.number << std::endl;
+
+    // Check if we have already discovered all the adjacentNodes to thisNode
+    for (const auto &adjacent : thisNode.adjacent) {
+      if (nodes_[adjacent - 1].color == White) {
+        std::cout << "Found undiscovered adjacentNode: " << adjacent << "\n";
+        // Mark the adjacent node as in progress
+        nodes_[adjacent - 1].color = Gray;
+        // Add the discovered node the the visitQueue
+        visitQueue.push(nodes_[adjacent - 1]);
+      }
+    }
+    // We are finished with this node and the adjacent nodes; Mark it discovered
+    thisNode.color = Black;
+  }
+
+}
+
+void Graph::DFS() const
+{
+  // Track the nodes we have discovered
+  for (const auto &node : nodes_) node.color = White;
+
+  // Visit each node in the graph
+  for (const auto& node : nodes_) {
+    std::cout << "Visiting node " << node.number << std::endl;
+    // If the node is undiscovered, visit it
+    if (node.color == White) {
+      std::cout << "Found undiscovered node: " << node.number << std::endl;
+      // Visiting the undiscovered node will check it's adjacent nodes
+      DFSVisit(node);
+    }
+  }
+
+}
+
+void Graph::DFSVisit(const Node& startNode) const
+{
+  startNode.color = Gray;
+  // Check the adjacent nodes of the startNode
+  for (const auto &adjacent : startNode.adjacent) {
+    // If the adjacentNode is undiscovered, visit it
+    // + Offset by 1 to account for 0 index of discovered vector
+    if (nodes_[adjacent - 1].color == White) {
+      std::cout << "Found undiscovered adjacentNode: "
+                << nodes_[adjacent - 1].number << std::endl;
+      // Visiting the undiscovered node will check it's adjacent nodes
+      DFSVisit(nodes_[adjacent - 1]);
+    }
+  }
+  startNode.color = Black;
+}
+
+std::vector<Node> Graph::TopologicalSort() const
+{
+  std::vector<Node> topologicalOrder;
+
+  // Track the nodes we have discovered
+  for (const auto &node : nodes_) node.color = White;
+
+  // Visit each node in the graph
+  for (const auto &node : nodes_) {
+    std::cout << "Visiting node " << node.number << std::endl;
+    // If the node is undiscovered, visit it
+    if (node.color == White) {
+      std::cout << "Found undiscovered node: " << node.number << std::endl;
+      // Visiting the undiscovered node will check it's adjacent nodes
+      TopologicalVisit(node, topologicalOrder);
+    }
+  }
+
+  // The topologicalOrder is read right-to-left in the final result
+  // + Output is handled in main as FILO, similar to a stack
+  return topologicalOrder;
+}
+
+void Graph::TopologicalVisit(const Node &startNode,
+                             std::vector<Node> &order) const
+{
+  // Mark the node as visited so we don't visit it twice
+  startNode.color = Gray;
+
+  // Check the adjacent nodes of the startNode
+  for (const auto& adjacent : startNode.adjacent) {
+    // If the adjacentNode is undiscovered, visit it
+    if (nodes_[adjacent - 1].color == White) {
+      std::cout << "Found undiscovered adjacentNode: " << adjacent << std::endl;
+      // Visiting the undiscovered node will check it's adjacent nodes
+      TopologicalVisit(nodes_[adjacent - 1], order);
+    }
+  }
+  startNode.color = Black;
+
+  // Add startNode to the topologicalOrder
+  order.push_back(startNode);
+}

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

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+/*##############################################################################
+## Author: Shaun Reed                                                         ##
+## Legal: All Content (c) 2021 Shaun Reed, all rights reserved                ##
+## About: An example of an object graph implementation                        ##
+##        Algorithms in this example are found in MIT Intro to Algorithms     ##
+##                                                                            ##
+## Contact: shaunrd0@gmail.com  | URL: www.shaunreed.com | GitHub: shaunrd0   ##
+################################################################################
+*/
+#ifndef LIB_GRAPH_HPP
+#define LIB_GRAPH_HPP
+
+#include <iostream>
+#include <algorithm>
+#include <map>
+#include <set>
+#include <utility>
+#include <vector>
+#include <queue>
+
+// A vertex can also be referred to as a node
+// + ... Unless you are a mathematician ^.^
+struct Vertex {
+  // This vertex's number
+  int number;
+  // A set of all vertices adjacent to this vertex
+  std::set<int> adjacent;
+};
+
+enum Color {White, Gray, Black};
+
+struct Node {
+public:
+  Node(int num, std::set<int> adj) : number(num), adjacent(std::move(adj)) {}
+  int number;
+  std::set<int> adjacent;
+  // Mutable so we can update the color of the nodes during traversal
+  mutable Color color = White;
+  std::vector<int> predecessors;
+
+//  bool operator<(const Node &node1) const { return number < node1.number;}
+  inline void setColor(Color newColor) const { color = newColor;}
+};
+
+class Graph {
+public:
+  explicit Graph(std::vector<Node> nodes) : nodes_(std::move(nodes)) {}
+  std::vector<Node> nodes_;
+
+  void BFS(const Node& startNode) const;
+  void DFS() const;
+  void DFSVisit(const Node& startNode) const;
+  std::vector<Node> TopologicalSort() const;
+  void TopologicalVisit(const Node &startNode, std::vector<Node> &order) const;
+
+};
+
+#endif // LIB_GRAPH_HPP