Practice - Catalan Numbers - Derivation of Closed Form Formula
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Practice Questions
Test your understanding with targeted questions
Define Catalan numbers in your own words.
💡 Hint: Think about their connection to parentheses.
What is the cardinality of set A?
💡 Hint: Recalling the combination formula for selecting positions.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the closed-form formula for the nth Catalan number?
💡 Hint: Look for structure and combinatorial significance.
True or False: Set B contains all sequences that have only positive partial sums.
💡 Hint: Focus on the definition provided in the lecture.
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Challenge Problems
Push your limits with advanced challenges
Consider a sequence of n = 4. Calculate the individual possible valid parentheses configurations and show how they relate to C(4, 2).
💡 Hint: Try listing them to see how they form.
Using the reflection method, illustrate how you would transform a bad sequence of n = 2 (for example, 1, -1, 1, -1) to its valid form.
💡 Hint: Pay attention to how each sign change results in the surplus.
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Reference links
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