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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define Catalan numbers in your own words.
💡 Hint: Think about their connection to parentheses.
Question 2
Easy
What is the cardinality of set A?
💡 Hint: Recalling the combination formula for selecting positions.
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 the nth Catalan number?
- C(n) = C(2n
- n)/(n + 1)
- C(n) = C(2n
- n)/n
- C(n) = C(n + 1
- 2n)
💡 Hint: Look for structure and combinatorial significance.
Question 2
True or False: Set B contains all sequences that have only positive partial sums.
- True
- False
💡 Hint: Focus on the definition provided in the lecture.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
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.
Question 2
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.
Challenge and get performance evaluation