Question

How would I traverse through this graph? Provide example code, please!

class Edge {
   int src, dest;

   Edge(int src, int dest)
   {
       this.src = src;
       this.dest = dest;
   }
};

// class to represent a graph object
class Graph
{
   // A list of lists to represent adjacency list
   List<List<Integer>> adj = new ArrayList<>();

   // Constructor to construct graph
   public Graph(List<Edge> edges)
   {
       // allocate memory for adjacency list
       for (int i = 0; i < edges.size(); i++) {
           adj.add(i, new ArrayList<>());
       }

       // add edges to the undirected graph
       for (Edge current : edges)
       {
           // allocate new node in adjacency List from src to dest
           adj.get(current.src).add(current.dest);

           // Uncomment line 39 for undirected graph

           // allocate new node in adjacency List from dest to src
           // adj.get(current.dest).add(current.src);
       }
   }
}

class Main
{
   // print adjacency list representation of graph
   private static void printGraph(Graph graph)
   {
       int src = 0;
       int n = graph.adj.size();

       while (src < n)
       {
           // print current vertex and all its neighboring vertices
           for (int dest : graph.adj.get(src)) {
               System.out.print("(" + src + " --> " + dest + ")\t");
           }

           System.out.println();
           src++;
       }
   }

   // Directed Graph Implementation in Java
   public static void main (String[] args)
   {
       // Input: List of edges in a directed graph (as per above diagram)
       List<Edge> edges = Arrays.asList(new Edge(0, 1), new Edge(1, 2),
                                   new Edge(2, 0), new Edge(2, 1),new Edge(3, 2),
                                   new Edge(4, 5), new Edge(5, 4));

       // construct graph from given list of edges
       Graph graph = new Graph(edges);

       // print adjacency list representation of the graph
       printGraph(graph);
   }
}

Answer 1

In the given code, the graph is saved as an adjecency list. There are in total two ways of representing a graph in an algorithm. An adjacency list is a collection of unordered lists used to represent a finite graph. Each list describes the set of neighbors of a vertex in the graph.

Think of the data structure as a list of list of integers. See this line: List<List<Integer>> adj = new ArrayList<>();

This means we have a list (linked list) of many sources and each of those sources have various destinations in the graph. Have a look at this adjecency list (a vertical stack of source nodes and a list of other nodes which are connected to this particular node):

Now, you have (b) which is an adjecency list. (c) denotes an adjecency matrix.

For traversing through the graph you can use the following process:

Let's say you are trying to reach node 3 from node 2 from node 1. In a gist 1 -> 2 -> 3

step 1: select a starting node (may be 1)

step 2: in the List, search for the first node (node 1) and then search the list associated with (1) if node (2) exists there. The nodes associated with (1) are 2 and 5 so you are sure that 2 exists.

step 3: since 2 was there in list of node 1, you can be sure that you can reach 2, now try searching node 3 in the second node's list. in the List, search for the second node (node 2) and then search the list associated with (2) if node (3) exists there.

since 3 exists, we have traversed from 1 to 3

The code will look as follows:

private static void goFrom1To3Graph(Graph graph)
   {
       int src = 1;
       int n = graph.adj.size();
       for (int dest : graph.adj.get(src)) {
           System.out.print("(" + src + " --> " + dest + ")\t");

if (dest == 2) {

for(int dest2 : graph.adj.get((2)) {

  System.out.print("(" + 2 + " --> " + dest + ")\t");

if (dest2 == 3)

System.out.println("reached 3 through 2 through 1");

}

}
       }
   }