20.5.1. New Problem of Sequences

Try these first

1. 1.

   What does C(2) equal?

   Hint

   Think about how parentheses can be arranged for two pairs.

2. 2.

   Define a valid parentheses string.

   Hint

   Consider how you ensure that every '(' is matched.

3. 3.

   What does C(3) represent?

   • 3
   • 5
   • 1

   Hint

   Recall the examples discussed in class.

4. 4.

   Is the string '(()()())' valid?

   • True
   • False

   Hint

   Count the parentheses and check for matches.

5. 5.

   Determine the number of valid parenthesis sequences for n = 4, and list them.

   Hint

   Use your understanding of valid sequences and recursive definitions.

6. 6.

   Using the recurrence relation, calculate C(5) based on previous values.

   Hint

   Execute the summation for all k values from 0 to 4.