Practicing Running Time Analysis of Recursive Algorithms

Educators teaching Algorithms and students taking the course consider running time analysis of recursive algorithms one of the most difficult topics in the course. The limited number of examples in the textbooks is not sufficient to grasp the topic for most of the learners. This text is designed to help students learn time performance analysis. It may be helpful for instructors teaching those courses as well by providing them a poll of test questions, or helping those to create projects that are variations of existing examples. The book provides 60 examples. They are grouped into decrease-by-constant, decrease-by-constant-factor, divide-and-conquer, and general-decrease type. Each example has a description of the problem, recursive algorithm implemented in Java, and full running time analysis consisting of problem size, basic operation, recurrence, and detailed derivation of solution for the recurrence. Most of the examples were given to students on tests, final exams, or were part of the assigned projects. The last chapter of the book provides templates for the following seven basic complexity categories: log n, n, n log n, n squared, n cubed, a raised to the power of n, and n!, together with a list of possible variations for each template that do not affect their asymptotic performance. In addition, we provide list of problems to illustrate each of the templates.