Practice Lower Bound Examples (7.7.2) - Design and Analysis of Algorithms

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6 sample questions

Question 1.
Define what a lower bound is in algorithm analysis.
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Think about the 'worst possible case' scenarios.
Question 2.
Give an example of a function that is both upper and lower bounded.
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Consider consistent linear functions.
3Question 3.
What notation is used to express lower bounds?
- Big O
- Big Ω
- Theta
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Remember the letters associated with upper bounds versus lower bounds.
4Question 4.
True or False: An algorithm that runs in O(n) time is also Ω(n).
- True
- False
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Consider the definitions of upper and lower bounds.
Question 5.
Can you derive a lower bound of Ω(n^2) for any sorting algorithm? Discuss your thought process.
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Think carefully about the capacity of data manipulations.
Question 6.
Construct an algorithm with a known lower bound and explain why it's significant.
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Reflect more on the known characteristics of existing algorithms.

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