Create KahnTopologicalSort.java

Author: 17tanya

GraphsDFS&BFS/KahnTopologicalSort.java

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+//Reference - https://www.geeksforgeeks.org/topological-sorting-indegree-based-solution/
+
+/*Algorithm - 
+Step-1: Compute in-degree (number of incoming edges) for each of the vertex present in the DAG and initialize the count of visited nodes as 0.
+
+Step-2: Pick all the vertices with in-degree as 0 and add them into a queue (Enqueue operation)
+
+Step-3: Remove a vertex from the queue (Dequeue operation) and then.
+
+    Increment count of visited nodes by 1.
+    Decrease in-degree by 1 for all its neighboring nodes.
+    If in-degree of a neighboring nodes is reduced to zero, then add it to the queue.
+
+Step 5: Repeat Step 3 until the queue is empty.
+
+Step 5: If count of visited nodes is not equal to the number of nodes in the graph then the topological sort is not possible for the given graph.
+*/
+
+class TopologicalSort{
+    int vertices;
+    ArrayList<Integer> adjList[];
+    //adjList[2] signifies all the neighbours of vertex 2. The edge is directed from 2 ==> (all elements in adjList[2])
+    
+    topologicalSort(int n){
+        vertices = n;
+        adjList = new ArrayList[n];
+        for(int i=0;i<n;i++) adjList[i] = new ArrayList<Integer>();
+    }
+    
+    void topologicalSort(){
+        int inDegree[] = new int[vertices]; 
+        ArrayList<Integer> sortOrder = new ArrayList<>();
+        Arrays.fill(inDegree,0);
+        
+        for(int i=0 ; i<vertices ; i++){
+            ArrayList<Integer> neighbours = adjList[i];
+            for(int neighbour : neighbours){
+                inDegree[neighbour]++;
+            }
+        }
+        
+        Queue<Integer> inDegree0 = new LinkedList<>();
+        for(int i=0;i<vertices;i++){
+            if(inDegree[i]==0) inDegree0.add(i);
+        }
+        
+        int vertexCnt = 0;
+        while(!inDegree0.isEmpty()){
+            int curr = inDegree0.poll();
+            sortOrder.add(curr);
+            ArrayList<Integer> neighbours = adjList[curr];
+            for(int neighbour : neighbours){
+                if(--inDegree[neighbour]==0) inDegree0.add(neighbour);
+            }
+            vertexCnt++;
+        }
+        
+        if(vertexCnt!=vertices) System.out.println("Cycles in the graph");
+        else{
+            for(int i=0;i<vertices;i++) System.out.println(sortOrder.get(i));
+        }
+    }
+    
+}