Growth of functions, classes.
- f(x) = 1
- f(x) = log2(x)
- f(x) = sqrt(x)
- f(x) = x
- f(x) = x*log2(x)
- f(x) = x^2
- f(x) = x^3
- f(x) = 2^x
Why do we throw away constants and lower-order terms? Which constants and terms?
Formally:
- Big O (bounded above)
- Big Omega (bounded below)
- Big Theta (both)
Counting operations.
Which operations?
- Machine instructions?
- We really want time. How does that relate to instructions?
- => Whichever thing happens the most, the rest is constants and lower order terms.
Which N?
- Size of a collection.
- What if there are two collections with different sizes?
- Assume the same size?
- One is asymptotically bigger.
