25.1.5. Computing Longest Path Using Topological Order

Try these first

1. 1.

   Define a Directed Acyclic Graph (DAG).

   Hint

   Focus on the terms 'directed' and 'acyclic'.

2. 2.

   What does topological sorting help us achieve?

   Hint

   Think about ordering tasks based on requirements.

3. 3.

   Which of the following best defines a Directed Acyclic Graph (DAG)?

   • A cyclic directed graph
   • A directed graph with cycles
   • A directed graph without cycles

   Hint

   Focus on what 'acyclic' implies.

4. 4.

   True or False: Topological sorting can be applied to any type of graph.

   • True
   • False

   Hint

   Consider the implications of cycles.

5. 5.

   Construct a DAG for a project consisting of six tasks where specific tasks cannot start until others are finished. Identify the longest path.

   Hint

   Visualize the dependency flow and compute paths straightforwardly.

6. 6.

   Explain in depth how the complexity of finding the longest path changes in DAGs vs. arbitrary graphs.

   Hint

   Refer back to algorithms and their computational limits.