I'm working out of a friend's textbook to try and prepare myself for a class I'll be taking in a month or so. I was wondering if someone could give me the answers to these problems so I have a better understanding of how to solve them? I'm going to be taking programming class too (Java and a couple others) and figured some of you guys are pretty good at this stuff.

1) How do you figure the degree of the table?

Let A_i, 1 ≤ i ≤ 5, be the domains for a table D ⊆ A_1 x A_2 x A_3 x A_4 x A_5, where A_1 = {U, V, W, X, Y, Z} (used as code names for different cereals in a test), and A_2 = A_3= A_4 = A_5 = Z^+.

Table D:

Code Name of Cereal / Grams of Sugar per 1-oz Serving / % of RDA^a of Vitamin A per 1-oz Serving / % of RDA Vitamin C per 1-oz Serving / % of RDA of Protein per 1-oz Serving

U 1 25 25 6

V 7 25 2 4

W 12 25 2 4

X 0 60 40 20

Y 3 25 40 10

Z 2 25 40 10

2) How do you determine the best "big-Oh" form?

Use the results of Table 1 to determine the best “big-Oh” form for the following function f: Z^+→ R.

f(n) = 3n + 7

Table 1 (I'm not sure how to write tables so I used the dash (-----):

Big-Oh Form ------------------------ Name

O(1) --------------------------------- Constant

O(log_2 n) -------------------------- Logarithmic

O(n) --------------------------------- Linear

O(n log_2 n) ------------------------ n log_2 n

O(n^2) ------------------------------ Quadratic

O(n^3) ------------------------------ Cubic

O(n^m), m = 0, 1, 2, 3,... ------- Polynomial

O(c^n), c > 1 ----------------------- Exponential