Let h(n) = n mod 3. Next, let f(n) = n and g(n) = nh(n). What...

Question

Question

Let h(n) = n mod 3. Next, let f(n) = n and g(n) = n^h(n). What is the order relationship between f and g?

Please explain with complete sentences!

Answer 1

Answer #1

Clearly, the possible value of h(n) = 0, 1 or 2

This means that the possible values of g(n) could be 0, n or 2n.

In all the cases, f(n) = Θ(g(n)) since both f(n) and g(n) grow in the order of n as n increases.

Answer 2

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