Practice Recap Of Previous Lecture (21.1.1) - Catalan Numbers - Derivation of Closed Form Formula
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Recap of Previous Lecture

Practice - Recap of Previous Lecture

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Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What is the formula for Catalan numbers?

💡 Hint: Think about the number of valid structures divided by n+1.

Question 2 Easy

How many valid parenthesis combinations are there for n = 2?

💡 Hint: Try to visualize the arrangements.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What are Catalan numbers commonly used to count?

Valid sequences of parentheses
Prime numbers
Fibonacci sequences

💡 Hint: Think about the structures you’ve learned.

Question 2

True or False: The number of valid sequences of 1s and -1s equals the number of valid parentheses strings.

True
False

💡 Hint: Refer to the connections discussed.

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Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Prove that the number of valid parenthesis sequences increases exponentially as n rises.

💡 Hint: Reflect on how factorial numbers grow.

Challenge 2 Hard

If you add a ‘bad’ sequence to a valid sequence, what type of sequence is produced?

💡 Hint: Check how the sums behave post addition.

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