C++ Program to Find the Shortest Path Between Two Vertices Using Dijkstra’s Algorithm

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This is a C++ Program to check whether path exists between two given nodes. The idea is to run the depth first search algorithm with the given source node, if during dfs we visit destination node, path exists, not otherwise.

Here is source code of the C++ Program to Find Whether a Path Exists Between 2 Given Nodes. The C++ program is successfully compiled and run on a Linux system. The program output is also shown below.

  1. #include <iostream>
  2. #include <list>
  3.  
  4. using namespace std;
  5.  
  6. // This class represents a directed graph using adjacency list representation
  7. class Graph
  8. {
  9.         int V; // No. of vertices
  10.         list<int> *adj; // Pointer to an array containing adjacency lists
  11.     public:
  12.         Graph(int V); // Constructor
  13.         void addEdge(int v, int w); // function to add an edge to graph
  14.         bool isReachable(int s, int d); // returns true if there is a path from s to d
  15. };
  16.  
  17. Graph::Graph(int V)
  18. {
  19.     this->V = V;
  20.     adj = new list<int> [V];
  21. }
  22.  
  23. void Graph::addEdge(int v, int w)
  24. {
  25.     adj[v].push_back(w); // Add w to v’s list.
  26. }
  27.  
  28. // A BFS based function to check whether d is reachable from s.
  29. bool Graph::isReachable(int s, int d)
  30. {
  31.     // Base case
  32.     if (s == d)
  33.         return true;
  34.  
  35.     // Mark all the vertices as not visited
  36.     bool *visited = new bool[V];
  37.     for (int i = 0; i < V; i++)
  38.         visited[i] = false;
  39.  
  40.     // Create a queue for BFS
  41.     list<int> queue;
  42.  
  43.     // Mark the current node as visited and enqueue it
  44.     visited[s] = true;
  45.     queue.push_back(s);
  46.  
  47.     // it will be used to get all adjacent vertices of a vertex
  48.     list<int>::iterator i;
  49.  
  50.     while (!queue.empty())
  51.     {
  52.         // Dequeue a vertex from queue and print it
  53.         s = queue.front();
  54.         queue.pop_front();
  55.  
  56.         // Get all adjacent vertices of the dequeued vertex s
  57.         // If a adjacent has not been visited, then mark it visited
  58.         // and enqueue it
  59.         for (i = adj[s].begin(); i != adj[s].end(); ++i)
  60.         {
  61.             // If this adjacent node is the destination node, then return true
  62.             if (*i == d)
  63.                 return true;
  64.  
  65.             // Else, continue to do BFS
  66.             if (!visited[*i])
  67.             {
  68.                 visited[*i] = true;
  69.                 queue.push_back(*i);
  70.             }
  71.         }
  72.     }
  73.  
  74.     return false;
  75. }
  76.  
  77. // Driver program to test methods of graph class
  78. int main()
  79. {
  80.     // Create a graph given in the above diagram
  81.     Graph g(4);
  82.     g.addEdge(0, 1);
  83.     g.addEdge(0, 2);
  84.     g.addEdge(1, 2);
  85.     g.addEdge(2, 0);
  86.     g.addEdge(2, 3);
  87.     g.addEdge(3, 3);
  88.  
  89.     cout << "Enter the source and destination vertices: (0-3)";
  90.     int u, v;
  91.     cin >> u >> v;
  92.     if (g.isReachable(u, v))
  93.         cout << "\nThere is a path from " << u << " to " << v;
  94.     else
  95.         cout << "\nThere is no path from " << u << " to " << v;
  96.  
  97.     int temp;
  98.     temp = u;
  99.     u = v;
  100.     v = temp;
  101.     if (g.isReachable(u, v))
  102.         cout << "\nThere is a path from " << u << " to " << v;
  103.     else
  104.         cout << "\nThere is no path from " << u << " to " << v;
  105.  
  106.     return 0;
  107. }

Output:

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$ g++ PathBetweenNodes.cpp
$ a.out
 
Enter the source and destination vertices: (0-3)
1 3
 
There is a path from 1 to 3
There is no path from 3 to 1
 
Enter the source and destination vertices: (0-3)
2 3
 
There is a path from 2 to 3
There is no path from 3 to 2
 
------------------
(program exited with code: 0)
Press return to continue

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