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Practice Questions
Test your understanding with targeted questions related to the topic.
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.
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 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.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
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.
Question 2
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!
Challenge and get performance evaluation