Add pathing using BFS within the simple-graph example

cpp/algorithms/graphs/simple/graph.cpp

@@ -13,6 +13,9 @@
 int main (const int argc, const char * argv[])
 {
   // We could initialize the graph with some localNodes...
+  // This graph uses an unordered_(map/set), so initialization is reversed
+  // + So the final order of initialization is 1,2,3,4,5,6,7,8
+  // + Similarly, adjacent nodes are inserted at front (6,4 initializes to 4,6)
   std::unordered_map<int, std::unordered_set<int>> localNodes{
       {8, {6, 4}},
       {7, {8, 6, 4, 3}},
@@ -45,6 +48,17 @@ int main (const int argc, const char * argv[])
   // + Chapter 22, Figure 22.3 on BFS
   bfsGraph.BFS(2);
 
+  std::cout << "\nTesting finding a path between two nodes using BFS...\n";
+  auto path = bfsGraph.PathBFS(1, 7);
+  if (path.empty()) std::cout << "No valid path found!\n";
+  else {
+    std::cout << "\nValid path from " << path.front() << " to "
+              << path.back() << ": ";
+    for (const auto &node : path) {
+      std::cout << node << " ";
+    }
+    std::cout << std::endl;
+  }
 
   std::cout << "\n\n##### Depth First Search #####\n";
   // Initialize an example graph for Depth First Search
@@ -64,18 +78,22 @@ int main (const int argc, const char * argv[])
 
 
   std::cout << "\n\n##### Topological Sort #####\n";
+  // The graph traversed in this example is seen in MIT Intro to Algorithms
+  // + Chapter 22, Figure 22.4 on DFS
   // Initialize an example graph for Topological Sort
+  // + The final result will place node 3 (watch) at the beginning of the order
+  // + This is because node 3 has no connecting node
   Graph topologicalGraph (
       {
-          {9, {}},
-          {8, {9}},
-          {7, {9}},
-          {6, {7, 8}},
-          {5, {}},
-          {4, {7, 5}},
-          {3, {}},
-          {2, {5}},
-          {1, {5, 4}},
+          {9, {}},     // jacket
+          {8, {9}},    // tie
+          {7, {9}},    // belt
+          {6, {7, 8}}, // shirt
+          {5, {}},     // shoes
+          {4, {7, 5}}, // pants
+          {3, {}},     // watch
+          {2, {5}},    // socks
+          {1, {5, 4}}, // undershorts
       }
   );
   auto order = topologicalGraph.TopologicalSort(topologicalGraph.GetNode(6));
@@ -86,9 +104,9 @@ int main (const int argc, const char * argv[])
   }
   std::cout << std::endl << std::endl;
 
-  //   If we want the topological order to match what is seen in the book
+  // If we want the topological order to exactly match what is seen in the book
   // + We have to initialize the graph carefully to get this result -
-  // Because this is an unordered_(map/set) initialization is reversed
+  // This graph uses an unordered_(map/set), so initialization is reversed
   // + So the order of nodes on the container below is 6,7,8,9,3,1,4,5,2
   // + The same concept applies to their adjacent nodes (7,8 initializes to 8,7)
   // + In object-graph implementation, I use vectors this does not apply there
@@ -122,7 +140,5 @@ int main (const int argc, const char * argv[])
   }
   std::cout << std::endl;
 
-  std::cout << std::endl;
-
   return 0;
 }

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

@@ -16,6 +16,9 @@ void Graph::BFS(int startNode)
 {
   // Track the nodes we have discovered
   std::vector<bool> discovered(nodes_.size(), false);
+  // Reset values of predecessor and distance JIC there was a previous traversal
+  for (auto &p : predecessor) p = std::make_pair(0, INT32_MIN);
+  for (auto &d : distance) d = std::make_pair(0, 0);
 
   // Create a queue to visit discovered nodes in FIFO order
   std::queue<int> visitQueue;
@@ -37,6 +40,14 @@ void Graph::BFS(int startNode)
     for (const auto &adjacent : nodes_[thisNode]) {
       if (!discovered[adjacent - 1]) {
         std::cout << "Found undiscovered adjacentNode: " << adjacent << "\n";
+
+        // Update the distance from the start node
+        distance[adjacent - 1] =
+            std::make_pair(adjacent, distance[thisNode - 1].second + 1);
+        // Update the predecessor for the adjacent node when we discover it
+        // + The node that first discovers the adjacent is the predecessor
+        predecessor[adjacent - 1] = std::make_pair(adjacent, thisNode);
+
         // Mark the adjacent node as discovered
         // + If this were done out of the for loop we could discover nodes twice
         // + This would result in visiting the node twice, since it appears
@@ -52,6 +63,32 @@ void Graph::BFS(int startNode)
 
 }
 
+std::deque<int> Graph::PathBFS(int start, int finish)
+{
+  // Store the path as a deque of integers so we can push to the front and back
+  std::deque<int> path;
+  // Perform BFS on the start node, updating all possible predecessors
+  BFS(start);
+  // Begin at the finish node's predecessor
+  int next = predecessor[finish - 1].second;
+  bool isValid = false;
+  do {
+    // If the next node is the start node, we have found a valid path
+    if (next == start) isValid = true;
+    // Add the next node to the path
+    path.push_front(next);
+    // Move to the predecessor of the next node
+    next = predecessor[next - 1].second;
+  } while (next != INT32_MIN); // If we hit a node with no predecessor, break
+  // Push the finish node the end of the path
+  // + We could do this prior to the loop with push_front.. but, deques :)
+  path.push_back(finish);
+  // If we never found a valid path, erase the path
+  if (!isValid) path.erase(path.begin(), path.end());
+  // Return the path, the caller should handle the case where the path is empty
+  return path;
+}
+
 void Graph::DFS()
 {
   // Track the nodes we have discovered

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

@@ -11,9 +11,7 @@
 #define LIB_GRAPH_HPP
 
 #include <iostream>
-#include <map>
 #include <queue>
-#include <set>
 #include <vector>
 #include <unordered_map>
 #include <unordered_set>
@@ -26,9 +24,12 @@ public:
   {
     discoveryTime.resize(nodes_.size());
     finishTime.resize(nodes_.size(), std::make_pair(0,0));
+    predecessor.resize(nodes_.size(), std::make_pair(0, INT32_MIN));
+    distance.resize(nodes_.size(), std::make_pair(0, 0));
   }
 
   void BFS(int startNode);
+  std::deque<int> PathBFS(int start, int finish);
 
   void DFS();
   void DFS(Node::iterator startNode);
@@ -52,6 +53,8 @@ private:
   // Unordered to avoid container reorganizing elements
   // + Since this would alter the order nodes are traversed in
   Node nodes_;
+  std::vector<std::pair<int, int>> distance;
+  std::vector<std::pair<int, int>> predecessor;
 
   // Where the first element in the following two pairs is the node number
   // And the second element is the discovery / finish time