Practice Bit Strings With Substring '01' (16.3) - Valid Sequences Analysis

Practice: Bit Strings with Substring '01'

Lesson 16.3Valid Sequences Analysis

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10 questions

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4 questions · about 3 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
What is S(2)?
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Think about the minimal string that contains '01'.
Question 2.
List valid bit strings of length 3 containing '01'.
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Consider where '01' can appear in a string of length 3.
3Question 3.
Which category of strings does S(n) incorporate when starting with '1'?
- Only strings with two 1's
- Strings with at least one '01'
- Only strings of length n-1
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Think about what must hold true if the first bit is '1'.
4Question 4.
True or False: S(n) considers both cases of leading zeros and starting with '1'.
- True
- False
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Reflect on how both categories are defined and their contributions to S(n).
Question 5.
Determine the values of S(6) based on the established recurrence. Then, describe the logic.
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Use previously computed values and step through the relation incrementally.
Question 6.
If the concept of leading zeros is modified to allow a fixed number (like 2) before a 1 appears, reformulate S(n) to accommodate this.
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Explore how variations in leading zero lengths adjust our recurrence.

6 more questions in this section. Enroll free to practise them all.