FAQ Database Discussion Community

## How can we prove that the running time bound of an algorithm is tight?

algorithm,big-o,computer-science,big-theta
Suppose we can prove that an algorithm, invoked with an input of size n, runs in time O(f(n)). I want to prove that this running time bound is tight. Two questions: Wouldn't it suffice to give a special input and show that the running time is at least f(n)? I've...

## How to get Omega(n)

algorithm,big-o,complexity-theory,big-theta
I have the formula a(n) = n * a(n-1) +1 ; a(0) = 0 How can i get the Omega, Theta or O Notation from this without the Master Theorem or did anyone have a good site to understand the explanation...

## What is the time complexity of the given algorthm?

algorithm,time-complexity,complexity-theory,asymptotic-complexity,big-theta
x=0 for i=1 to ceiling(log(n)) for j=1 to i for k=1 to 10 x=x+1 I've included the answer I've come up with here: I think the time complexity is θ(n^2 log(n)), but I am not sure my logic is correct. I would really appreciate any help understanding how to do...

## Theta Runtime of a triple loop that essentially much less than n^3

algorithm,loops,runtime,analysis,big-theta
I was looking at a programming question today and I had an issues finding the theta runtime of it. Basically, within my question, I form the following loop structure: for(int i = 0; i < n; i++) for(int j = i + 1; j < n; j++) for(int k =...

## What is the Difference between T(n) (reccurence relations), Big O and Big Theta

algorithm,big-o,analysis,recurrence-relation,big-theta
I am wondering about this for my Algorithm class. It seems to be unclear what the difference is between BigO, Big Theta, and Recurrence relations (T(n)) For example: T(n) = 4T(n/3) + O(1)