Problem 3.1: Define "Big-O notation". [Solution]

Problem 3.2: Prove that the function f (n) = n² + 3n + 1 is O(n²). [Solution]

Problem 3.3: You are given two functions, one which has an average case running time of O(n²) and the other which has an average running time of O(nlogn). In general, which would you choose? [Solution]

Problem 3.4: True or false: A function with O(n) efficiency will always run faster than a function with O(n²) efficiency? [Solution]

Problem 3.5: Draw a graph showing how n, logn, n², and 2ⁿ compare as n increases. [Solution]