Practice Recurrence Equation - 20.2.2 | 20. Catalan Numbers | Discrete Mathematics - Vol 2
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Recurrence Equation

20.2.2 - Recurrence Equation

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Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

List all valid parenthesizations for n = 1 (two numbers).

💡 Hint: Think about the basic requirement for two numbers.

Question 2 Easy

What is C(2)?

💡 Hint: Use the formula C(n) for small n values.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the formula for C(n)?

C(n) = C(n-1) + C(n-2)
C(n) = Σ C(k) * C(n-k-1)
C(n) = n!

💡 Hint: Think about how smaller instances contribute to the current one.

Question 2

True or False: The nth Catalan number represents valid parentheses strings.

True
False

💡 Hint: Reflect on previous discussions about counting parenthetical arrangements.

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Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

How many valid combinations exist for n = 5 using the recurrence relation?

💡 Hint: Break it down using smaller known values.

Challenge 2 Hard

Prove that C(n) corresponds to valid pairs of parentheses using an example.

💡 Hint: Construct examples for small n values to illustrate.

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Reference links

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