20.2. Formulating the Problem

Try these first

1. 1.

   How many unique ways can you parenthesize three numbers?

   Hint

   Think of the number of combinations for arranging multiplications.

2. 2.

   What is the recurrence relation formula for C(n)?

   Hint

   Recall how we divide the sequences.

3. 3.

   What does C(n) represent?

   • The number of ways to multiply n numbers.
   • The number of valid parenthesis strings for n pairs.
   • Both of the above.

   Hint

   Remember the key applications of Catalan numbers.

4. 4.

   True or False: C(n) can be calculated directly without recursion.

   • True
   • False

   Hint

   Consider the formula you may learn about next.

5. 5.

   Determine how many distinct binary trees can be created using n nodes. Relate this to Catalan numbers.

   Hint

   Think about how parenthesis configurations symbolize binary structures.

6. 6.

   Create a valid sequence with n pairs of parentheses and find out how it corresponds to C(n).

   Hint

   Utilize the rules of valid pairing consistently.