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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the total number of valid sequences of 1's and -1's?
💡 Hint: Think about how many places you can choose for the 1's.
Question 2
Easy
Define a bad sequence in your own words.
💡 Hint: Consider sequences with parentheses or ladder-like paths.
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
What is the formula for Catalan numbers?
- C(2n
- n)/(n+1)
- C(2n
- n+1)
- C(n
- 2n)
💡 Hint: Recall the conclusion at the end of our session.
Question 2
True or False: Set A is defined to include all legitimate sequences with no restrictions.
- True
- False
💡 Hint: Think about the restrictions we talked about.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given n = 4, find all valid sequences of 1's and -1's, and verify using the Catalan number formula.
💡 Hint: Write out the sequences; account for each by ensuring partial sums are valid.
Question 2
If the first two positive indices yield a negative sum, demonstrate the reflection method with an example.
💡 Hint: Ask yourself how you can visualize the switch in numbers.
Challenge and get performance evaluation