Prove max(O(f(n)), O(g(n)))=O(max(f(n), g(n))
It does make sense, but so far I don't have any idea how to actually prove it.
Any input would be appreciated.
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Mahesh Velaga
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EatEmAll
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What is the commas meaning in O(f(n), g(n))? I only know O(f(n)). – Micha Wiedenmann May 02 '13 at 20:00
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It was my mistake. It should have been max(O(f(n), O(g(n))). – EatEmAll May 02 '13 at 20:16
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f(n) <= max(f(n), g(n))
g(n) <= max(f(n), g(n))
max(O(f(n)), O(g(n))) <= O(max(f(n), g(n)), max(f(n), g(n))) = O(max(f(n), g(n)))
Note that the in-equalities used are not strict.
Mahesh Velaga
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Thank. Just to note that the last expression should be max(O(f(n)), O(g(n))) = O(max(f(n), g(n)) – EatEmAll May 02 '13 at 20:08
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Edited to fix the brackets as well as to make it more explicit to derive RHS from LHS – Mahesh Velaga May 06 '13 at 21:19