Practice Reflection Method (21.1.8) - Catalan Numbers - Derivation of Closed Form Formula
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Reflection Method

Practice - Reflection Method

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Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

Define a bad sequence in terms of 1s and -1s.

💡 Hint: Think about what happens to the total if it dips below zero.

Question 2 Easy

What is the cardinality of set A?

💡 Hint: Consider how many ways you can arrange n 1s and n -1s.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is a requisite condition for a sequence to be valid?

All sums are positive
All sums are non-negative
All sums are negative

💡 Hint: Remember, we discussed partial sums' behavior extensively.

Question 2

True or False: The reflection method results in a sequence having more elements than the original bad sequence.

True
False

💡 Hint: Think about the reflection mechanism.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Given the sequence [1, 1, -1, -1, 1], identify the first negative partial sum and reflect it. What does the new sequence look like?

💡 Hint: Draw the partial sums to visualize.

Challenge 2 Hard

Consider a sequence with 4 1s and 4 -1s. What would be the total valid sequences using the reflection method without calculating directly?

💡 Hint: Remember the derived formula for valid sequences we discussed!

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