This document discusses the running time of algorithms. It states that an efficient algorithm has a polynomial running time, meaning that when the input size doubles the algorithm slows down by a constant factor. It also notes that most basic operations take constant time and that the worst case running time is described using Big O notation while the best case is described using Big Omega notation. Big-Theta notation describes algorithms whose running time is bounded both above and below by a polynomial.

1. CSC 391

2. Polynomials in running time
Desirable scaling property.
When the input size doubles, the algorithm should only slow
down by some constant factor C.
We say that an algorithm is efficient if has a polynomial
running time.

3. Cost of basic operations
Observation. Most primitive operations take constant time

9. Factors affecting running time

19. ** The difference between Big O notation
and Big Omega notation is that Big O is
used to describe the worst case running
time for an algorithm. But,
Big Omega notation, on the other hand, is
used to describe the best case running time
for a given algorithm.

20. Big-Theta notation