Practice Recap Of Previous Lecture (21.1.1) - Catalan Numbers

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8 questions

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6 sample questions

Question 1.
What is the formula for Catalan numbers?
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Think about the number of valid structures divided by n+1.
Question 2.
How many valid parenthesis combinations are there for n = 2?
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Try to visualize the arrangements.
3Question 3.
What are Catalan numbers commonly used to count?
- Valid sequences of parentheses
- Prime numbers
- Fibonacci sequences
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Think about the structures you’ve learned.
4Question 4.
True or False: The number of valid sequences of 1s and -1s equals the number of valid parentheses strings.
- True
- False
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Refer to the connections discussed.
Question 5.
Prove that the number of valid parenthesis sequences increases exponentially as n rises.
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Reflect on how factorial numbers grow.
Question 6.
If you add a ‘bad’ sequence to a valid sequence, what type of sequence is produced?
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Check how the sums behave post addition.

4 more questions in this section. Enroll free to practise them all.