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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
How many valid strings can we form with 2 pairs of parentheses?
💡 Hint: Draw out the pairs to visualize options.
Question 2
Easy
If n equals 1, how many valid parenthesis strings are possible?
💡 Hint: Consider what it takes to open and close a bracket.
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
How many valid strings can be formed with 3 pairs of parentheses?
- 3
- 5
- 12
💡 Hint: Use the formula of Catalan numbers.
Question 2
C(n) represents the number of valid parenthesis for n pairs. True or False?
- True
- False
💡 Hint: Think about the scenarios imagined in class.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Prove that the nth Catalan number can be also expressed as C(2n, n)/(n+1).
💡 Hint: Think combinatorically about choices of pairs in arrangements.
Question 2
How many unique valid arrangements can you create with 5 pairs of parentheses?
💡 Hint: You can calculate using the recurrence relation iteratively.
Challenge and get performance evaluation