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Art of Computer Programming, The: Volume 1: Fundamental Algorithms by Donald E. Knuth

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Exercises

1. [HM01] What is limn→∞ O(n− 1/3)?

Image    2. [M10] Mr. B. C. Dull obtained astonishing results by using the “self-evident” formula O(f (n)) − O(f (n)) = 0. What was his mistake, and what should the righthand side of his formula have been?

3. [M15] Multiply (ln n + γ + O(1/n)) by Image, and express your answer in O-notation.

Image    4. [M15] Give an asymptotic expansion of , if a > 0, to terms O(1/n3).

5. [M20] Prove or disprove: O(f (n) + g(n)) =

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