Practice Tighter Upper Bounds (7.6.4) - Design and Analysis of Algorithms

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6 sample questions

Question 1.
What does Big O notation represent?
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Think about limits in performance.
Question 2.
In which scenario would we use O(n) as an upper bound?
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Consider simple loops.
3Question 3.
What does it mean when we say t(n) is O(g(n))?
- t(n) grows faster than g(n)
- t(n) is less than or equal to c·g(n) beyond some n₀
- t(n) and g(n) are equal
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Think about performance limits.
4Question 4.
True or False: Big O notation can be affected by constant factors.
- True
- False
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Remember how we simplify when analyzing algorithms.
Question 5.
Given a complex function t(n) = 3n² + 2n logarithm + n, find an upper bound using Big O notation and justify your answer.
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Identify the term that increases the fastest.
Question 6.
Prove that for any constant c, n³ is not O(n²).
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Use limits or consider what happens as n grows large.

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