Practice Valid Strings Of Parentheses (20.4) - Catalan Numbers - Discrete Mathematics

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8 questions

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6 questions · about 4 min · pass mark 70%. Hints available.
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2 questions · about 1 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
How many valid strings can we form with 2 pairs of parentheses?
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Draw out the pairs to visualize options.
Question 2.
If n equals 1, how many valid parenthesis strings are possible?
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Consider what it takes to open and close a bracket.
3Question 3.
How many valid strings can be formed with 3 pairs of parentheses?
- 3
- 5
- 12
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Use the formula of Catalan numbers.
4Question 4.
C(n) represents the number of valid parenthesis for n pairs. True or False?
- True
- False
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Think about the scenarios imagined in class.
Question 5.
Prove that the nth Catalan number can be also expressed as C(2n, n)/(n+1).
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Think combinatorically about choices of pairs in arrangements.
Question 6.
How many unique valid arrangements can you create with 5 pairs of parentheses?
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You can calculate using the recurrence relation iteratively.

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