CODEWITHSUNDEEP
algorithmcomplexity-theory
Hadiqa Khan
Hadiqa Khan

Reputation: 1

Asymptotic Notation Properties - proof?

I am trying to solve these problems. In the first property it seems it is transpose symmetry but there is difference of notation in f(n).

For all positive f(n), g(n) and h(n)

  1. If f(n) = O(g(n)) and f(n) = Ω(h(n)), then g(n) + h(n) = (f(n)).

  2. If f(n) = O(g(n)) and f(n) = Ω(g(n)), then we have (f(n))3 = Θ((g(n))3)

  3. If f(n) = O(g(n)) and f(n) = Ω(g(n)), then we have (f(n))2 = (g(n))2

Upvotes: 0

Views: 212

Answers (1)

Vishal Prakash
Vishal Prakash

Reputation: 11

You are correct this is transpose of function h(n), g(n),h(n).And all the function has same growth at all in first case. Theta f(n)=Theta g(n)+Theta h(n)

Upvotes: 1

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