## >Big Theta Binary Relation on Functions

1. Big Theta growth rates compared visually. Sorry, but to see 8! or 9! you would need a movie screen sized computer monitor! Not that Visual Basic could even handle 8 factorial.
Smaller sized version, courtesy of PhotoShop.
Smaller sized version, courtesy of HTML. Notice the difference in clarity Photoshop achieved compared to HTML and browser.

2. Excel spreadsheet and chart of two functions that are the same order of magnitude. For functions f and g, (f, g) element of BigTheta binary relation. Big Theta question #7

More Big Theta analysis of programs and functions. Why is it called the FIND THREE NUMBERS GAME?

3. Big Theta is a binary relation on functions and is used to categorize programs and functions into equivalent groups, according to how much work they have to do for problems of size n.

4. Logarithmic, Exponential, Quadratic, Cubic, n log n, linear, constant are the names used for some of the most common categories.

5. The Heap Sort is an n log n order of magnitude sorting alrorithm. The selection sort is order n squared or quadratic in its order of magnitude.

6. The sequential search is linear, but the binary search is logarithmic.

7. What are the categories or orders of magnitude of the two different algorithms that are presented for finding the sum of 1 + 2 + 3 + ... + n?