# combining big Oh with bit Theta

jay vas

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Posts: 407

posted 5 years ago

Hi guys : I've noticed that in some proofs, they combine big Oh notation with big Theta.... I'm not sure, in general, why you would want to express the Upper bound (big Oh) of an algorithm in terms of the lower bound (big theta).....

Any thoughts on the combination of big Oh, horseshoe Oh, and Theta Oh in algorithm analysis ?

Any thoughts on the combination of big Oh, horseshoe Oh, and Theta Oh in algorithm analysis ?

Stephan van Hulst

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Posts: 5599

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posted 5 years ago

Theta is not lower bound. Omega (or horseshoe, as you call it) is the lower bound. If an algorithm is in Theta for some function, it means that the lower bounds and the upper bound are both described by that function as well.

For instance, if an algorithm is in O(n log n), and it is in Omega(n log n) as well, we say the algorithm is in Theta(n log n).

For instance, if an algorithm is in O(n log n), and it is in Omega(n log n) as well, we say the algorithm is in Theta(n log n).

*The mind is a strange and wonderful thing. I'm not sure that it will ever be able to figure itself out, everything else, maybe. From the atom to the universe, everything, except itself.*

jay vas

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Posts: 407

Stephan van Hulst

Bartender

Posts: 5599

55