Practice - Reflection Method
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Practice Questions
Test your understanding with targeted questions
Define a bad sequence in terms of 1s and -1s.
💡 Hint: Think about what happens to the total if it dips below zero.
What is the cardinality of set A?
💡 Hint: Consider how many ways you can arrange n 1s and n -1s.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is a requisite condition for a sequence to be valid?
💡 Hint: Remember, we discussed partial sums' behavior extensively.
True or False: The reflection method results in a sequence having more elements than the original bad sequence.
💡 Hint: Think about the reflection mechanism.
1 more question available
Challenge Problems
Push your limits with advanced challenges
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.
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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