What is the difference between Θ(n) and O(n)?

Question

Sometimes I see Θ(n) with the strange Θ symbol with something in the middle of it, and sometimes just O(n). Is it just laziness of typing because nobody knows how to type th

Answer 1

Rather than provide a theoretical definition, which are beautifully summarized here already, I'll give a simple example:

Assume the run time of f(i) is O(1). Below is a code fragment whose asymptotic runtime is Θ(n). It always calls the function f(...) n times. Both the lower and the upper bound is n.

for(int i=0; i

The second code fragment below has the asymptotic runtime of O(n). It calls the function f(...) at most n times. The upper bound is n, but the lower bound could be Ω(1) or Ω(log(n)), depending on what happens inside f2(i).

for(int i=0; i