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Practice Questions
Test your understanding with targeted questions related to the topic.
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.
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 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.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Prove that the number of valid parenthesis sequences increases exponentially as n rises.
💡 Hint: Reflect on how factorial numbers grow.
Question 2
If you add a ‘bad’ sequence to a valid sequence, what type of sequence is produced?
💡 Hint: Check how the sums behave post addition.
Challenge and get performance evaluation