6.19. Recursion
by Harvey M. Deitel, Abbey Deitel, Paul J. Deitel
C++11 for Programmers, Second Edition
- Title Page
- Copyright Page
- Dedication Page
- Contents
- Preface
- 1. Introduction
- 2. Introduction to C++ Programming, Input/Output and Operators
- 3. Introduction to Classes, Objects and Strings
- 3.1. Introduction
- 3.2. Defining a Class with a Member Function
- 3.3. Defining a Member Function with a Parameter
- 3.4. Data Members, set Member Functions and get Member Functions
- GradeBook Class with a Data Member, and set and get Member Functions
- Access Specifiers public and private
- Member Functions setCourseName and getCourseName
- Member Function displayMessage
- Testing Class GradeBook
- Software Engineering with Set and Get Functions
- GradeBook’s UML Class Diagram with a Data Member and set and get Functions
- 3.5. Initializing Objects with Constructors
- 3.6. Placing a Class in a Separate File for Reusability
- 3.7. Separating Interface from Implementation
- 3.8. Validating Data with set Functions
- 3.9. Wrap-Up
- 4. Control Statements: Part 1; Assignment, ++ and -- Operators
- 4.1. Introduction
- 4.2. Control Structures
- 4.3. if Selection Statement
- 4.4. if...else Double-Selection Statement
- 4.5. while Repetition Statement
- 4.6. Counter-Controlled Repetition
- 4.7. Sentinel-Controlled Repetition
- Implementing Sentinel-Controlled Repetition in Class GradeBook
- Program Logic for Sentinel-Controlled Repetition vs. Counter-Controlled Repetition
- Floating-Point Number Precision and Memory Requirements
- Converting Between Fundamental Types Explicitly and Implicitly
- Formatting for Floating-Point Numbers
- A Note About Unsigned Integers
- 4.8. Nested Control Statements
- 4.9. Assignment Operators
- 4.10. Increment and Decrement Operators
- 4.11. Wrap-Up
- 5. Control Statements: Part 2; Logical Operators
- 5.1. Introduction
- 5.2. Essentials of Counter-Controlled Repetition
- 5.3. for Repetition Statement
- for Statement Header Components
- Off-By-One Errors
- General Format of a for Statement
- Comma-Separated Lists of Expressions
- Expressions in the for Statement’s Header Are Optional
- Increment Expression Acts Like a Standalone Statement
- for Statement: Notes and Observations
- for Statement UML Activity Diagram
- 5.4. Examples Using the for Statement
- 5.5. do...while Repetition Statement
- 5.6. switch Multiple-Selection Statement
- GradeBook Class with switch Statement to Count A, B, C, D and F Grades
- GradeBook Class Header
- GradeBook Class Source-Code File
- Reading Character Input
- Entering the EOF Indicator
- switch Statement Details
- Providing a default Case
- Ignoring Newline, Tab and Blank Characters in Input
- Testing Class GradeBook
- switch Statement UML Activity Diagram
- Notes on Data Types
- C++11 In-Class Initializers
- 5.7. break and continue Statements
- 5.8. Logical Operators
- 5.9. Confusing the Equality (==) and Assignment (=) Operators
- 5.10. Wrap-Up
- 6. Functions and an Introduction to Recursion
- 6.1. Introduction
- 6.2. Math Library Functions
- 6.3. Function Definitions with Multiple Parameters
- 6.4. Function Prototypes and Argument Coercion
- 6.5. C++ Standard Library Headers
- 6.6. Case Study: Random Number Generation
- 6.7. Case Study: Game of Chance; Introducing enum
- 6.8. C++11 Random Numbers
- 6.9. Storage Classes and Storage Duration
- 6.10. Scope Rules
- 6.11. Function Call Stack and Activation Records
- 6.12. Functions with Empty Parameter Lists
- 6.13. Inline Functions
- 6.14. References and Reference Parameters
- 6.15. Default Arguments
- 6.16. Unary Scope Resolution Operator
- 6.17. Function Overloading
- 6.18. Function Templates
- 6.19. Recursion
- 6.20. Example Using Recursion: Fibonacci Series
- 6.21. Recursion vs. Iteration
- 6.22. Wrap-Up
- 7. Class Templates array and vector; Catching Exceptions
- 7.1. Introduction
- 7.2. arrays
- 7.3. Declaring arrays
- 7.4. Examples Using arrays
- 7.4.1. Declaring an array and Using a Loop to Initialize the array’s Elements
- 7.4.2. Initializing an array in a Declaration with an Initializer List
- 7.4.3. Specifying an array’s Size with a Constant Variable and Setting array Elements with Calculations
- 7.4.4. Summing the Elements of an array
- 7.4.5. Using Bar Charts to Display array Data Graphically
- 7.4.6. Using the Elements of an array as Counters
- 7.4.7. Using arrays to Summarize Survey Results
- 7.4.8. Static Local arrays and Automatic Local arrays
- 7.5. Range-Based for Statement
- 7.6. Case Study: Class GradeBook Using an array to Store Grades
- 7.7. Sorting and Searching arrays
- 7.8. Multidimensional arrays
- 7.9. Case Study: Class GradeBook Using a Two-Dimensional array
- 7.10. Introduction to C++ Standard Library Class Template vector
- Creating vector Objects
- vector Member Function size; Function outputVector
- Function inputVector
- Comparing vector Objects for Inequality
- Initializing One vector with the Contents of Another
- Assigning vectors and Comparing vectors for Equality
- Using the [] Operator to Access and Modify vector Elements
- Exception Handling: Processing an Out-of-Range Subscript
- The try Statement
- Executing the catch Block
- what Member Function of the Exception Parameter
- Changing the Size of a vector
- C++11: List Initializing a vector
- 7.11. Wrap-Up
- 8. Pointers
- 8.1. Introduction
- 8.2. Pointer Variable Declarations and Initialization
- 8.3. Pointer Operators
- 8.4. Pass-by-Reference with Pointers
- 8.5. Built-In Arrays
- 8.6. Using const with Pointers
- 8.7. sizeof Operator
- 8.8. Pointer Expressions and Pointer Arithmetic
- 8.9. Relationship Between Pointers and Built-In Arrays
- 8.10. Pointer-Based Strings
- Characters and Character Constants
- Strings
- Pointer-Based Strings
- String Literals as Initializers
- Character Constants as Initializers
- Accessing Characters in a C String
- Reading Strings into char Built-In Arrays with cin
- Reading Lines of Text into char Built-In Arrays with cin.getline
- Displaying C Strings
- 8.11. Wrap-Up
- 9. Classes: A Deeper Look; Throwing Exceptions
- 9.1. Introduction
- 9.2. Time Class Case Study
- Time Class Definition
- Time Class Member Functions
- Time Class Member Function setTime and Throwing Exceptions
- Time Class Member Function printUniversal
- Time Class Member Function printStandard
- Defining Member Functions Outside the Class Definition; Class Scope
- Member Functions vs. Global Functions (Also Called Free Functions)
- Using Class Time
- Calling setTime with Invalid Values
- Looking Ahead to Composition and Inheritance
- Object Size
- 9.3. Class Scope and Accessing Class Members
- 9.4. Access Functions and Utility Functions
- 9.5. Time Class Case Study: Constructors with Default Arguments
- 9.6. Destructors
- 9.7. When Constructors and Destructors Are Called
- 9.8. Time Class Case Study: A Subtle Trap—Returning a Reference or a Pointer to a private Data Member
- 9.9. Default Memberwise Assignment
- 9.10. const Objects and const Member Functions
- 9.11. Composition: Objects as Members of Classes
- 9.12. friend Functions and friend Classes
- 9.13. Using the this Pointer
- 9.14. static Class Members
- 9.15. Wrap-Up
- 10. Operator Overloading; Class string
- 10.1. Introduction
- 10.2. Using the Overloaded Operators of Standard Library Class string
- 10.3. Fundamentals of Operator Overloading
- 10.4. Overloading Binary Operators
- 10.5. Overloading the Binary Stream Insertion and Stream Extraction Operators
- 10.6. Overloading Unary Operators
- 10.7. Overloading the Unary Prefix and Postfix ++ and -- Operators
- 10.8. Case Study: A Date Class
- 10.9. Dynamic Memory Management
- Obtaining Dynamic Memory with new
- Releasing Dynamic Memory with delete
- Initializing Dynamic Memory
- Dynamically Allocating Built-In Arrays with new []
- C++11: Using a List Initializer with a Dynamically Allocated Built-In Array
- Releasing Dynamically Allocated Built-In Arrays with delete []
- C++11: Managing Dynamically Allocated Memory with unique_ptr
- 10.10. Case Study: Array Class
- 10.11. Operators as Member vs. Non-Member Functions
- 10.12. Converting Between Types
- 10.13. explicit Constructors and Conversion Operators
- 10.14. Overloading the Function Call Operator ()
- 10.15. Wrap-Up
- 11. Object-Oriented Programming: Inheritance
- 11.1. Introduction
- 11.2. Base Classes and Derived Classes
- 11.3. Relationship between Base and Derived Classes
- 11.3.1. Creating and Using a CommissionEmployee Class
- 11.3.2. Creating a BasePlusCommissionEmployee Class Without Using Inheritance
- 11.3.3. Creating a CommissionEmployee–BasePlusCommissionEmployee Inheritance Hierarchy
- 11.3.4. CommissionEmployee–BasePlusCommissionEmployee Inheritance Hierarchy Using protected Data
- 11.3.5. CommissionEmployee–BasePlusCommissionEmployee Inheritance Hierarchy Using private Data
- 11.4. Constructors and Destructors in Derived Classes
- 11.5. public, protected and private Inheritance
- 11.6. Software Engineering with Inheritance
- 11.7. Wrap-Up
- 12. Object-Oriented Programming: Polymorphism
- 12.1. Introduction
- 12.2. Introduction to Polymorphism: Polymorphic Video Game
- 12.3. Relationships Among Objects in an Inheritance Hierarchy
- 12.4. Type Fields and switch Statements
- 12.5. Abstract Classes and Pure virtual Functions
- 12.6. Case Study: Payroll System Using Polymorphism
- 12.7. (Optional) Polymorphism, Virtual Functions and Dynamic Binding “Under the Hood”
- 12.8. Case Study: Payroll System Using Polymorphism and Runtime Type Information with Downcasting, dynamic_cast, typeid and type_info
- 12.9. Wrap-Up
- 13. Stream Input/Output: A Deeper Look
- 13.1. Introduction
- 13.2. Streams
- 13.3. Stream Output
- 13.4. Stream Input
- 13.5. Unformatted I/O Using read, write and gcount
- 13.6. Introduction to Stream Manipulators
- 13.7. Stream Format States and Stream Manipulators
- 13.7.1. Trailing Zeros and Decimal Points (showpoint)
- 13.7.2. Justification (left, right and internal)
- 13.7.3. Padding (fill, setfill)
- 13.7.4. Integral Stream Base (dec, oct, hex, showbase)
- 13.7.5. Floating-Point Numbers; Scientific and Fixed Notation (scientific, fixed)
- 13.7.6. Uppercase/Lowercase Control (uppercase)
- 13.7.7. Specifying Boolean Format (boolalpha)
- 13.7.8. Setting and Resetting the Format State via Member Function flags
- 13.8. Stream Error States
- 13.9. Tying an Output Stream to an Input Stream
- 13.10. Wrap-Up
- 14. File Processing
- 14.1. Introduction
- 14.2. Files and Streams
- 14.3. Creating a Sequential File
- 14.4. Reading Data from a Sequential File
- 14.5. Updating Sequential Files
- 14.6. Random-Access Files
- 14.7. Creating a Random-Access File
- 14.8. Writing Data Randomly to a Random-Access File
- 14.9. Reading from a Random-Access File Sequentially
- 14.10. Case Study: A Transaction-Processing Program
- 14.11. Object Serialization
- 14.12. Wrap-Up
- 15. Standard Library Containers and Iterators
- 16. Standard Library Algorithms
- 16.1. Introduction
- 16.2. Minimum Iterator Requirements
- 16.3. Algorithms
- 16.3.1. fill, fill_n, generate and generate_n
- 16.3.2. equal, mismatch and lexicographical_compare
- 16.3.3. remove, remove_if, remove_copy and remove_copy_if
- 16.3.4. replace, replace_if, replace_copy and replace_copy_if
- 16.3.5. Mathematical Algorithms
- 16.3.6. Basic Searching and Sorting Algorithms
- 16.3.7. swap, iter_swap and swap_ranges
- 16.3.8. copy_backward, merge, unique and reverse
- 16.3.9. inplace_merge, unique_copy and reverse_copy
- 16.3.10. Set Operations
- 16.3.11. lower_bound, upper_bound and equal_range
- 16.3.12. Heapsort
- 16.3.13. min, max, minmax and minmax_element
- 16.4. Function Objects
- 16.5. Lambda Expressions
- 16.6. Standard Library Algorithm Summary
- 16.7. Wrap-Up
- 17. Exception Handling: A Deeper Look
- 17.1. Introduction
- 17.2. Example: Handling an Attempt to Divide by Zero
- Defining an Exception Class to Represent the Type of Problem That Might Occur
- Demonstrating Exception Handling
- Enclosing Code in a try Block
- Defining a catch Handler to Process a DivideByZeroException
- Termination Model of Exception Handling
- Flow of Program Control When the User Enters a Nonzero Denominator
- Flow of Program Control When the User Enters a Denominator of Zero
- 17.3. Rethrowing an Exception
- 17.4. Stack Unwinding
- 17.5. When to Use Exception Handling
- 17.6. Constructors, Destructors and Exception Handling
- 17.7. Exceptions and Inheritance
- 17.8. Processing new Failures
- 17.9. Class unique_ptr and Dynamic Memory Allocation
- 17.10. Standard Library Exception Hierarchy
- 17.11. Wrap-Up
- 18. Introduction to Custom Templates
- 19. Class string and String Stream Processing: A Deeper Look
- 19.1. Introduction
- 19.2. string Assignment and Concatenation
- 19.3. Comparing strings
- 19.4. Substrings
- 19.5. Swapping strings
- 19.6. string Characteristics
- 19.7. Finding Substrings and Characters in a string
- 19.8. Replacing Characters in a string
- 19.9. Inserting Characters into a string
- 19.10. Conversion to Pointer-Based char * Strings
- 19.11. Iterators
- 19.12. String Stream Processing
- 19.13. C++11 Numeric Conversion Functions
- 19.14. Wrap-Up
- 20. Bits, Characters, C Strings and structs
- 20.1. Introduction
- 20.2. Structure Definitions
- 20.3. typedef
- 20.4. Example: Card Shuffling and Dealing Simulation
- 20.5. Bitwise Operators
- 20.6. Bit Fields
- 20.7. Character-Handling Library
- 20.8. C String-Manipulation Functions
- 20.9. C String-Conversion Functions
- 20.10. Search Functions of the C String-Handling Library
- 20.11. Memory Functions of the C String-Handling Library
- 20.12. Wrap-Up
- 21. Other Topics
- 22. ATM Case Study, Part 1: Object-Oriented Design with the UML
- 22.1. Introduction
- 22.2. Introduction to Object-Oriented Analysis and Design
- 22.3. Examining the ATM Requirements Document
- 22.4. Identifying the Classes in the ATM Requirements Document
- 22.5. Identifying Class Attributes
- 22.6. Identifying Objects’ States and Activities
- 22.7. Identifying Class Operations
- Identifying Operations
- Modeling Operations
- Operations of Class BankDatabase and Class Account
- Operations of Class Screen
- Operations of Class Keypad
- Operations of Class CashDispenser and Class DepositSlot
- Operations of Class ATM
- Identifying and Modeling Operation Parameters
- Self-Review Exercises for Section 22.7
- 22.8. Indicating Collaboration Among Objects
- 22.9. Wrap-Up
- 23. ATM Case Study, Part 2: Implementing an Object-Oriented Design
- 23.1. Introduction
- 23.2. Starting to Program the Classes of the ATM System
- 23.3. Incorporating Inheritance into the ATM System
- 23.4. ATM Case Study Implementation
- 23.4.1. Class ATM
- 23.4.2. Class Screen
- 23.4.3. Class Keypad
- 23.4.4. Class CashDispenser
- 23.4.5. Class DepositSlot
- 23.4.6. Class Account
- 23.4.7. Class BankDatabase
- 23.4.8. Class Transaction
- 23.4.9. Class BalanceInquiry
- 23.4.10. Class Withdrawal
- 23.4.11. Class Deposit
- 23.4.12. Test Program ATMCaseStudy.cpp
- 23.5. Wrap-Up
- A. Operator Precedence and Associativity
- B. ASCII Character Set
- C. Fundamental Types
- D. Number Systems
- D.1. Introduction
- D.2. Abbreviating Binary Numbers as Octal and Hexadecimal Numbers
- D.3. Converting Octal and Hexadecimal Numbers to Binary Numbers
- D.4. Converting from Binary, Octal or Hexadecimal to Decimal
- D.5. Converting from Decimal to Binary, Octal or Hexadecimal
- D.6. Negative Binary Numbers: Two’s Complement Notation
- E. Preprocessor
- E.1. Introduction
- E.2. #include Preprocessing Directive
- E.3. #define Preprocessing Directive: Symbolic Constants
- E.4. #define Preprocessing Directive: Macros
- E.5. Conditional Compilation
- E.6. #error and #pragma Preprocessing Directives
- E.7. Operators # and ##
- E.8. Predefined Symbolic Constants
- E.9. Assertions
- E.10. Wrap-Up
- Index
6.19. Recursion
A recursive function is a function that calls itself, either directly, or indirectly (through another function). [Note: The C++ standard document indicates that main should not be called within a program or recursively. Its sole purpose is to be the starting point for program execution.]
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