Comp 2140 Algorithm Analysis / Asymptotic Notation

List the common function growth rates from slowest to fastest growing

1. Constant 2. Logarithmic 3. Linear 4. N-log-N 5. Quadratic 6. Cubic 7. Exponential

Lower bound

A function f(N) that is ≤ the best case T(N)

Upper bound

A function f(N) that is ≥ the worst case T(N)

Asymptotic notation

Classification of runtime complexity that uses functions that indicate only the growth rate of a bounding function.

O notation

Growth rate for algorithm's upper bound

Ω notation

Growth rate for an algorithm's lower bound

Θ notation

Growth rate for an algorithm's upper and lower bound

T(N)

The function (notation for runtime complexity). T = time, N = space (eg space on disk)

Bounded Function

the function has an upper AND lower bound