CS 361: Algorithms and Data Structures
Homework 1
Due date: Monday 9/5 by 2:00pm

Usually, assignments will be collected at the beginning of the class period. However, Monday the 5th is Labor Day so we do not have class. For this assignment only, please bring a hardcopy of your assignment to my office. There will be an envelope on the front door. Your assignment can be hand-written or typed.

The first two questions ask you to either disprove a claim using a counterexample or (if you believe it is true) give a short explanation. Please see "A Listing of Some Mathematical Notation and Terminology" for an explanation of what a counterexample is. A counterexample has a precise mathematical meaning and is more than just words.

1. Algorithm Design 1.1, 1.2


2. Write by hand the definition for Big-Θ five times. Your definition should begin with, "A function T(n) is Θ(f(n))..."


3. Algorithm Design 2.2. (Please be sure to show all of your work.)


4. Use your answers from AD 2.2 to fill in the following table:
   
   

   Running Times (in ascending order)	Largest input size (in 1 hour)

   
   Note: The first column should be the functions from AD 2.2 arranged in ascending order of growth rate. That is, if function g(n) immediately follows function f(n) in the table, then it should be the case that f(n) is O(g(n)). The second column should be the results you computed in AD 2.2