For the given functions below, place them into proper classes : 10^(-3) n^(3) +

Question

For the given functions below, place them into proper classes :

10^(-3) n^(3) + 10^(3) n^(2) + 10n + 10^(5)
2^(n+1) + (n+1)^2 + n + 1
p+3
nlgn+n^2
n+5+nlgn+vn

Explanation / Answer

O(2^(n+1)+(n+1)^2+n+1) > O(10^(-3)n^(3)+10^(3)n^(2)+10n+10^(5)) > O(n^2+nlogn) > O(nlogn+n+vn+5) > O(p+3) If v & p are assumed to be constants. Logic : First(highest order) has exponential order due to one of it's terms. Second has cubic polynomial order, Third has square polynomial order, Fourth has nlogn order, Fifth has constant order. Please ask in case of doubts, I'll respond by comments.

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