Practice - Claims About Bad Sequence
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Practice Questions
Test your understanding with targeted questions
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.
Define a bad sequence in your own words.
💡 Hint: Consider sequences with parentheses or ladder-like paths.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the formula for Catalan numbers?
💡 Hint: Recall the conclusion at the end of our session.
True or False: Set A is defined to include all legitimate sequences with no restrictions.
💡 Hint: Think about the restrictions we talked about.
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Challenge Problems
Push your limits with advanced challenges
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.
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.
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Reference links
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