20.3.1. Final Dot Interpretation

Try these first

1. 1.

   What is the value of C(1)?

   Hint

   Think about one opening and one closing parenthesis.

2. 2.

   List three valid arrangements for 2 pairs of parentheses.

   Hint

   Remember that pairs must match.

3. 3.

   What does C(3) equal?

   • 3
   • 5
   • 7

   Hint

   Count valid arrangements.

4. 4.

   True or False: Catalan numbers are always positive.

   • True
   • False

   Hint

   Think about the function definition.

5. 5.

   Create a function that counts valid parenthesis strings of length 2n.

   Hint

   Think of how C(n) builds from C(k).

6. 6.

   Analyze a real-world scenario using Catalan numbers.

   Hint

   Consider how binary trees mirror the parenthesis structure.