Question

3. Apply Topological sort algorithm on the following graph. Then, draw the sorted graph. 11 marvel

Answer 1

Topological Sort using DFS :-

  

Visited set. Set Sorted 3 * 5 7 11 10 2 2

Step 1: Select any node from which you want to start. So, suppose if I select 11.

Step2: Then we enter 11 into the visited set. Now, treverse all the nodes which can be reached from 11.

Step 3: From 11, I can reach 2. So, put 2 in the visited node. Now, from 2 can I reach any further node? No. So pop the node 2 and put it into a shorted set.

Step 4: Come back to 11, we again check from 11 which node can we reach i.e., 9 So, put it into a visited set & 9 has no further node. So we pop the node 9 and put it into a sorted set.  

Step 5: Repeat step 4. In this we get node 10 in the sorted set.

Step 6: Come back to 11 & check Is there any further node which can be visted from 11? The answer is No. So, we pop the node 11 and put it into a sorted set.

Step 7: Now I have to select one more node. So, suppose I select the node 7. So put it into the visted set & the check the node which can be reach from the node 7. From 7 we can reach 11 & 8 but we already visited the node 11 so we direct visit the node 8.

Step 8: Put the 8 into the visited set & then pop it and put it into the sorted set.

Step 9: Now I select one more node from 5 or 3. So suppose I select 5 so put it into visited set & from this all the node are already visited so we pop it & put it into a sorted set.

Step 10: Similarly the step 9, node 3 also has all visited node so we directly pop from the visited node & put it into a sorted node.

So, the final sorted set is 3,5,7,8,11,10,9,2

And the sorted graph will be: