Counting, Recurrences, and Trees

Abstract

Section 3.1 introduces a number of principles useful in counting complicated sets of objects. These principles include the rule of sum, the rule of product, and the pigeonhole principle. The section also introduces permutations and combinations, and the binomial theorem. Section 3.2 extends the formal study of trees, which were briefly encountered in Chapter 2, and explores ways of counting and computing based on recurrence relations. The final section has a different flavor but is still devoted to counting — this time to counting the number of steps taken by an algorithm to process data. It thus introduces the reader to the important topic of “analysis of algorithms” which enables us to compare the efficiency of different approaches to solve a given problem.