ALGORITHM ENGINEERING HOMEWORK Let g(n) = n. Is it true that g(n) 2 O(n2)? Why or...

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ALGORITHM ENGINEERING HOMEWORK Let g(n) = n. Is it true that g(n) 2 O(n2)? Why or...

ALGORITHM ENGINEERING HOMEWORK

Let g(n) = n. Is it true that g(n) 2 O(n2)? Why or why not?

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Answer 1

Answer #1

f(n) = O(g(n)) means there are positive constants c and n0, such that 0 ≤ f(n) ≤ cg(n) for all n ≥ n0

g(n) = O(n^2)
n    = O(n^2)

=>  n <= c*n^2

Let's assume c = 1

=>  n <= c*n^2
=>  n <= n^2
=>  0 <= n

so, g(n) = O(n^2) given c = 1 and n0 = 0

Please let me know if you need me to make any changes.

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Answer 2

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