24.4. Topological Sorting

Try these first

1. 1.

   What is a cover in a poset?

   Hint

   Think about how one element can lead to another directly.

2. 2.

   Define a minimal element in a poset.

   Hint

   Look at the bottom layer of the Hasse diagram.

3. 3.

   What defines a cover relationship in a poset?

   • A direct relationship with intermediates
   • A direct relationship without intermediates
   • A relationship with equal elements

   Hint

   Think about direct pathways in a Hasse diagram.

4. 4.

   True or False: Every poset has a greatest element.

   • True
   • False

   Hint

   Consider posets with incomparable elements.

5. 5.

   Given a set of tasks A, B, C, and D with dependencies (A -> B, A -> C, B -> D), create a proper Hasse diagram and perform a topological sort.

   Hint

   Once you visualize it, look for minimal elements for sorting.

6. 6.

   Illustrate a scenario where there are three tasks that can be done in any order but depend on a fourth completion. How would that look in both a Hasse diagram and via topological sorting?

   Hint

   Draw connections and analyze the flow of dependencies.