25.1.10. Importance of DAGs and Efficiency in Longest Path

Try these first

1. 1.

   What does 'acyclic' mean in the context of a graph?

   Hint

   Think about if you could loop back in a graph.

2. 2.

   What is the primary use of topological sorting?

   Hint

   Remember the order of tasks depends on dependencies.

3. 3.

   Which of the following statements about DAGs is true?

   • A DAG can have cycles.
   • A DAG is a directed graph with no cycles.
   • A DAG can have multiple paths.

   Hint

   Recall the term DAG itself.

4. 4.

   True or False: Topological sorting can result in multiple valid orderings.

   • True
   • False

   Hint

   Think about scenarios with multiple paths.

5. 5.

   Given a complex DAG of tasks, determine the longest path while justifying each step taken in your reasoning.

   Hint

   Trace the paths paying close attention to resource requirements.

6. 6.

   Create a real-life scenario using DAG concepts to illustrate task management. What challenges arise, and how would you solve them using a longest path calculation?

   Hint

   Draw connections between tasks and their prerequisites to showcase interactions.