Practice Conclusion (21.1.16) - Catalan Numbers - Derivation of Closed Form Formula
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Practice - Conclusion

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Practice Questions

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Question 1 Easy

What is the closed form formula for Catalan numbers?

💡 Hint: Consider the counts of valid sequences.

Question 2 Easy

What is a valid parenthesis sequence for n=2?

💡 Hint: Think of pairs of parentheses.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the closed form formula for Catalan numbers?

C(n) = 2^n
C(n) = C(2n
n) / (n + 1)
C(n) = n! * (n + 1)!

💡 Hint: Involves counting paths or matching parentheses.

Question 2

The reflection method is used to transform bad sequences into good ones.

True
False

💡 Hint: Think about what bad sequences need to be corrected.

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Challenge Problems

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Challenge 1 Hard

Derive the Catalan number closed form for n=5 using combinatorial arguments.

💡 Hint: Utilize the patterns observed in smaller n values.

Challenge 2 Hard

Explore two real-world applications of Catalan numbers

💡 Hint: Look towards programming contests or algorithm design.

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