Computers and Technology, 20.03.2020 03:23 mchillery1028
Formally prove that n^2 + n + 1 is in O(n^2).
Solution:
Let T(n) = n^2 + n + 1. Let f(n) = n^2.
Choose c = 3, and N = 1. Then, we know T(n) is in O(n^2) if we can prove
T(n) <= c f(n),
or equivalently, n^2 + n + 1 <= 3 n^2, for all n >= 1.
Is this inequality true? Well, for any n >= 1, we know that 1 <= n <= n^2.
Hence, all of the following are true:
1 <= n^2
n <= n^2
n^2 = n^2
Adding the left and right sides of these inequalities together, we have
n^2 + n + 1 <= 3 n^2, which completes the proof.
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Formally prove that n^2 + n + 1 is in O(n^2).
Solution:
Let T(n) = n^2 + n + 1. Let f(n)...
Solution:
Let T(n) = n^2 + n + 1. Let f(n)...
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