Practice Conclusion (21.1.16) - Catalan Numbers - Derivation of Closed Form Formula

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6 sample questions

Question 1.
What is the closed form formula for Catalan numbers?
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Consider the counts of valid sequences.
Question 2.
What is a valid parenthesis sequence for n=2?
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Think of pairs of parentheses.
3Question 3.
What is the closed form formula for Catalan numbers?
- C(n) = 2^n
- C(n) = C(2n
- n) / (n + 1)
- C(n) = n! * (n + 1)!
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Involves counting paths or matching parentheses.
4Question 4.
The reflection method is used to transform bad sequences into good ones.
- True
- False
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Think about what bad sequences need to be corrected.
Question 5.
Derive the Catalan number closed form for n=5 using combinatorial arguments.
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Utilize the patterns observed in smaller n values.
Question 6.
Explore two real-world applications of Catalan numbers
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Look towards programming contests or algorithm design.

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