20.4 - Valid Strings of Parentheses
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Practice Questions
Test your understanding with targeted questions
How many valid strings can we form with 2 pairs of parentheses?
💡 Hint: Draw out the pairs to visualize options.
If n equals 1, how many valid parenthesis strings are possible?
💡 Hint: Consider what it takes to open and close a bracket.
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Interactive Quizzes
Quick quizzes to reinforce your learning
How many valid strings can be formed with 3 pairs of parentheses?
💡 Hint: Use the formula of Catalan numbers.
C(n) represents the number of valid parenthesis for n pairs. True or False?
💡 Hint: Think about the scenarios imagined in class.
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Challenge Problems
Push your limits with advanced challenges
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.
How many unique valid arrangements can you create with 5 pairs of parentheses?
💡 Hint: You can calculate using the recurrence relation iteratively.
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