Big Oh notation

Aug 2009
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Give a classification of T(n) as O(f(n)) for a suitable function f in the hierarchy of Big Oh.

T(n) = 5 + T(n - 1) (n > 0) *THIS IS PART OF THE RECURRENCE SYSTEM.
T(n) = 5 + 5N. *THIS IS THE FORMULA FOR THE TIME COMPLEXITY FUNCTION. WORKED OUT BY SOLVING THE RECURRENCE SYSTEM.

I've got confused, not sure if I give a classification of the formula that I worked out by solving the recurrence system or of the recurrence system.
I think it is the formula T(n) = 5 + 5n. In which case I *think* it's a no brainer because the only term is 5n and so,

T(n) = 5n is (O^2) and also it is O(n). Thus T(n) = 5n is of order n. Which means 5n is BIG THETA O(n).

Would appreciate ir if someone could verify I'm on the right track with this.
 

CaptainBlack

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Give a classification of T(n) as O(f(n)) for a suitable function f in the hierarchy of Big Oh.

T(n) = 5 + T(n - 1) (n > 0) *THIS IS PART OF THE RECURRENCE SYSTEM.
T(n) = 5 + 5N. *THIS IS THE FORMULA FOR THE TIME COMPLEXITY FUNCTION. WORKED OUT BY SOLVING THE RECURRENCE SYSTEM.

I've got confused, not sure if I give a classification of the formula that I worked out by solving the recurrence system or of the recurrence system.
I think it is the formula T(n) = 5 + 5n. In which case I *think* it's a no brainer because the only term is 5n and so,

T(n) = 5n is (O^2) and also it is O(n). Thus T(n) = 5n is of order n. Which means 5n is BIG THETA O(n).

Would appreciate ir if someone could verify I'm on the right track with this.
Yes \(\displaystyle T(n)=5+5n \in \Theta(n)\)

CB
 
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