CSCI 580 Homework Assignment #1 (Due: Mon. Feb. 2)

1. [10 point] Problem 2-2, Page 38.
2. [20 point] (A) Group the following so that f and g are in the same group if and only if f=Θ(g). (List the groups formed from the lowest to highest rank.)
   (B) List all the functions that are O(n²) but not O(n).
   n+2n/lg n+lg n, 3lg lg n, 2n+n/lg n, lg lg(n²), (3 lg lg n)², n³-n²lg n, 2ⁿ, 12 n lg(n²)-4n, n^16/3, 4n+12nlg n, 2ⁿ+n³⁵, n2ⁿ.
3. [10 point] Exercises 4.1-6, Page 67.
4. [20 point] Exercise 4.4-2, Page 84.
5. [30 point] Problem 4-4 (a,c--f,h), Page 86.
6. [10 point] Prove Σ _i=0..d a_inⁱ =Θ(n^d) where a_i are constants and a_d>0. (Note: you need to find c₁, c₂, and n₀).