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Practice Questions
Test your understanding with targeted questions related to the topic.
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.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
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.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Derive the Catalan number closed form for n=5 using combinatorial arguments.
💡 Hint: Utilize the patterns observed in smaller n values.
Question 2
Explore two real-world applications of Catalan numbers
💡 Hint: Look towards programming contests or algorithm design.
Challenge and get performance evaluation