Practice Introduction To Counting Problems (13.1) - Counting Using Recurrence Equations

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6 sample questions

Question 1.
What is the base condition for counting strings of length 1 and 2?
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Think of the possible strings.
Question 2.
Write the recurrence relation for counting bit strings with no consecutive zeros.
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Think about where a string can start.
3Question 3.
What is a recurrence equation?
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Consider how terms can be calculated based on earlier values.
4Question 4.
True or False: The Fibonacci sequence is an example of a recurrence relation.
- True
- False
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Think of how Fibonacci is traditionally defined.
Question 5.
Given C(1) = 2, C(2) = 3. Using the derived relation, calculate C(8) and provide the reasoning for each step.
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Draw out or visualize a tree for each sequence.
Question 6.
Construct a different counting function that also uses a recurrence relation and compare its properties with our strings without consecutive zeros.
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Identify how many strings might be invalid and adjust the relations accordingly.

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