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3 cards from this section. Quick, good the night before a test.
Define a bad sequence in terms of 1s and -1s.
Think about what happens to the total if it dips below zero.
What is the cardinality of set A?
Consider how many ways you can arrange n 1s and n -1s.
What is a requisite condition for a sequence to be valid?
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.
Think about the reflection mechanism.
Given the sequence [1, 1, -1, -1, 1], identify the first negative partial sum and reflect it. What does the new sequence look like?
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?
Remember the derived formula for valid sequences we discussed!
5 more questions in this section. Enroll free to practise them all.
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