Win a copy of Svelte and Sapper in Action this week in the JavaScript forum!
programming forums Java Mobile Certification Databases Caching Books Engineering Micro Controllers OS Languages Paradigms IDEs Build Tools Frameworks Application Servers Open Source This Site Careers Other all forums
this forum made possible by our volunteer staff, including ...
Marshals:
• Campbell Ritchie
• Ron McLeod
• Paul Clapham
• Bear Bibeault
• Junilu Lacar
Sheriffs:
• Jeanne Boyarsky
• Tim Cooke
• Henry Wong
Saloon Keepers:
• Tim Moores
• Stephan van Hulst
• Tim Holloway
• salvin francis
• Frits Walraven
Bartenders:
• Scott Selikoff
• Piet Souris
• Carey Brown

# combining big Oh with bit Theta

Ranch Hand
Posts: 407
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 ?

Saloon Keeper
Posts: 12253
259
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).

jay vas
Ranch Hand
Posts: 407
Hmmm okay... So I guess a "tight" bound is when omega=theta ?

Stephan van Hulst
Saloon Keeper
Posts: 12253
259
A bound g(n) is tight if it's in O(f(n)) and Omega(f(n)) and thus in Theta(f(n)).

 Consider Paul's rocket mass heater.