Recursion is one of the most fundamental concepts in computer science and a key programming technique that allows computations to be carried out repeatedly. Despite the importance of recursion for algorithm design, most programming books do not cover the topic in detail, despite the fact that numerous computer programming professors and researchers in the field of computer science education agree that recursion is difficult for novice students.
Introduction to Recursive Programming provides a detailed and comprehensive introduction to recursion. This text will serve as a useful guide for anyone who wants to learn how to think and program recursively, by analyzing a wide variety of computational problems of diverse difficulty.
It contains specific chapters on the most common types of recursion (linear, tail, and multiple), as well as on algorithm design paradigms in which recursion is prevalent (divide and conquer, and backtracking). Therefore, it can be used in introductory programming courses, and in more advanced classes on algorithm design. The book also covers lower-level topics related to iteration and program execution, and includes a rich chapter on the theoretical analysis of the computational cost of recursive programs, offering readers the possibility to learn some basic mathematics along the way.
It also incorporates several elements aimed at helping students master the material. First, it contains a larger collection of simple problems in order to provide a solid foundation of the core concepts, before diving into more complex material. In addition, one of the book's main assets is the use of a step-by-step methodology, together with specially designed diagrams, for guiding and illustrating the process of developing recursive algorithms. Furthermore, the book covers combinatorial problems and mutual recursion. These topics can broaden students' understanding of recursion by forcing them to apply the learned concepts differently, or in a more sophisticated manner.
The code examples have been written in Python 3, but should be straightforward to understand for students with experience in other programming languages. Finally, worked out solutions to over 120 end-of-chapter exercises are available for instructors.
Basic Concepts of Recursive Programming
Recognizing Recursion
Problem Decomposition
Recursive Code
Induction
Recursion Vs. Iteration
Types of Recursion
Exercises
Methodology for Recursive Thinking
Template for Designing Recursive Algorithms
Size of The Problem
Base Cases
Problem Decomposition
Recursive Cases, Induction, And Diagrams
Testing
Exercises
Runtime Analysis of Recursive Algorithms
Mathematical Preliminaries
Computational Time Complexity
Recurrence Relations
Exercises
Linear Recursion I
Arithmetic Operations
Digits, Bits, And Strings
Additional Problems
Exercises
Linear Recursion II: Tail Recursion
Searching Algorithms for Lists
Partitioning Schemes
The Quickselect Algorithm
Bisection AlgorithmfFor Root Finding
The Woodcutter Problem
Euclid's Algorithm
Exercises
Multiple Recursion I: Divide and Conquer
Is A List Sorted in Ascending Order?
Sorting
Majority Element in A List
Fast Integer Multiplication
Matrix Multiplication
The Tromino Tiling Problem
The Skyline Problem
Exercises
Multiple Recursion II: Puzzles and Fractals
Swamp Traversal
Towers of Hanoi
Longest Palindrome Substring
Fractals
EXERCISES
Counting Problems
Permutations
Variations with Repetition
Combinations
Staircase Climbing
Manhattan Paths
Convex Polygon Triangulations
Circle Pyramids
Exercises
Mutual Recursion
Parity of A Number
Strategic Games
Rabbit Population Growth
Water Treatment Plants Puzzle
Cyclic Towers of Hanoi
Grammars and Recursive Descent Parsers
Exercises
Program Execution
Control Flow Between Subroutines
Recursion Trees
The Program Stack
Memoization and Dynamic Programming
Exercises
Tail Recursion Revisited and Nested Recursion
Tail Recursion Vs. Iteration
Tail Recursion by Thinking Iteratively
Nested Recursion
Tail and Nested Recursion Through Function Generalization
Exercises
Backtracking
Introduction
Generating Combinatorial Entities
The N-Queens Problem
Subset Sum Problem
Path Through a Maze
The Sudoku Puzzle
Knapsack Problem
Exercises
Biography
Manuel Rubio-Sánchez received MS and PhD degrees in computer science from Universidad Politécnica de Madrid in 1997 and 2004, respectively. Since, he has had a faculty position at Universidad Rey Juan Carlos (Madrid, Spain), where he is currently an associate professor in the Superior Technical School of Computer Science. His teaching has focused on computer programming, ranging from introductory CS1 courses to more advanced courses on algorithms and data structures. He has published several research studies related to recursion in the computer science education conferences. His other research interests include machine learning, and exploratory data analysis and visualization. Finally, he has been a lecturer at St. Louis University (Madrid campus), and has carried out research visits at Université de Cergy-Pontoise (Paris), and the University of California, San Diego.
For more information on the author, please visit https://sites.google.com/view/recursiveprogrammingintro/.
Recursion is a fundamental topic in computer science, but one that is frequently taught in a fragmented way as part of an introductory course and then set aside for such electives as discrete programming and difference equations. Rubio-Sánchez (Universidad Rey Juan Carlos, Spain) believes that there are better ways to approach a concept so powerfully connected to computation. His book provides a comprehensive and approachable treatment of recursive programming. The text contains mathematical proofs, as well as clear methods that students can follow to derive new results and expand their knowledge in areas the book may not cover. Many of the fundamental problems that recursion can solve are presented and discussed; more advanced problems are addressed through decomposition and analysis. The book also contains a section on algorithm analysis, which helps form the basis for more advanced material on computational complexity. This book is useful as a textbook for introductory programming courses when an instructor adopts a more fundamental approach than imperative programming, but it can also serve as a useful reference for those who wish to explore recursive programming on their own, or for algorithm designers in the industry.
--L. Benedicenti, University of New Brunswick (CHOICE)
