The.Algorithm.Design.Manual.Springer-Verlag.1998

Exercises
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Modeling
Exercises
1. Let P be a problem. The worst-case time complexity of P is . The worst-case time
complexity of P is also . Let A be an algorithm that solves P. Which subset of the
following statements are consistent with this information about the complexity of P?
❍ A has worst-case time complexity .
❍ A has worst-case time complexity .
❍ A has worst-case time complexity O(n).
❍ A has worst-case time complexity .
❍ A has worst-case time complexity .
2. Suppose that an algorithm A runs in worst-case time f(n) and that algorithm B runs in worst-case
time g(n). For each of the following questions, answer either yes, no, or can't tell and explain
why.
(a) Is A faster than B for all n greater than some if ?
(b) Is A faster than B for all n greater than some if ?
(c) Is A faster than B for all n greater than some if ?
(d) Is B faster than A for all n greater than some if ?
(e) Is B faster than A for all n greater than some if ?
(f) Is B faster than A for all n greater than some if ?
3. For each of these questions, briefly explain your answer.
(a) If I prove that an algorithm takes worst-case time, is it possible that it takes O(n) on
some inputs?
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