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Practice Questions
Test your understanding with targeted questions related to the topic.
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.
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 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.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
How many valid combinations exist for n = 5 using the recurrence relation?
💡 Hint: Break it down using smaller known values.
Question 2
Prove that C(n) corresponds to valid pairs of parentheses using an example.
💡 Hint: Construct examples for small n values to illustrate.
Challenge and get performance evaluation