Practice - Recap of Previous Lecture
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Practice Questions
Test your understanding with targeted questions
What is the formula for Catalan numbers?
💡 Hint: Think about the number of valid structures divided by n+1.
How many valid parenthesis combinations are there for n = 2?
💡 Hint: Try to visualize the arrangements.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What are Catalan numbers commonly used to count?
💡 Hint: Think about the structures you’ve learned.
True or False: The number of valid sequences of 1s and -1s equals the number of valid parentheses strings.
💡 Hint: Refer to the connections discussed.
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Challenge Problems
Push your limits with advanced challenges
Prove that the number of valid parenthesis sequences increases exponentially as n rises.
💡 Hint: Reflect on how factorial numbers grow.
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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Reference links
Supplementary resources to enhance your learning experience.