# 05 - Chapter 5 Recursion Data Structures and Algorithms in...

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Data Structures and Algorithms in Java Chapter 5 Recursion

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Data Structures and Algorithms in Java 2 Objectives Discuss the following topics: Recursive Definitions Method Calls and Recursion Implementation Anatomy of a Recursive Call Tail Recursion Nontail Recursion Indirect Recursion
Data Structures and Algorithms in Java 3 Objectives (continued) Discuss the following topics: Nested Recursion Excessive Recursion Backtracking Case Study: A Recursive Descent Interpreter

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Data Structures and Algorithms in Java 4
Data Structures and Algorithms in Java 5 Recursive Definitions Recursive definitions are programming concepts that define themselves A recursive definition consists of two parts: The anchor or ground case , the basic elements that are the building blocks of all other elements of the set Rules that allow for the construction of new objects out of basic elements or objects that have already been constructed

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Data Structures and Algorithms in Java 6 Recursive Definitions Examples: 1 ) 2 ( ) 1 ( 1 1 0 0 ) ( n if n Fib n Fib n if n if n Fib 1 )! 1 ( * 0 1 ! n if n n n if n 1 * 0 1 1 n if x x n if x n n
Data Structures and Algorithms in Java 7 Recursive Definitions (continued) Recursive definitions serve two purposes: Generating new elements Testing whether an element belongs to a set Recursive definitions are frequently used to define functions and sequences of numbers

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Data Structures and Algorithms in Java Recursive Definitions (continued) 8 1 )! 1 ( * 0 1 ! n if n n n if n
Data Structures and Algorithms in Java Recursive Definitions (continued) 9 1 ) 2 ( ) 1 ( 1 1 0 0 ) ( n if n Fib n Fib n if n if n Fib

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Data Structures and Algorithms in Java Recursive Definitions (continued) Exercises: 1. 2. Write a recursive method that for a positive integer n calculate sum of numbers from 1 to n. 3. Write a recursive method that for a positive integer n prints numbers a. between 1 and n b. between n and 1 10 1 * 0 1 1 n if x x n if x n n
Data Structures and Algorithms in Java 11 Method Calls and Recursion Implementation Activation records contain the following: Values for all parameters to the method, location of the first cell if an array is passed or a variable is passed by reference, and copies of all other data items Local (automatic) variables that can be stored elsewhere The return address to resume control by the caller, the address of the caller’s instruction immediately following the call

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Data Structures and Algorithms in Java 12 Method Calls and Recursion Implementation (continued) A dynamic link, which is a pointer to the caller’s activation record The returned value for a method not declared as void
Data Structures and Algorithms in Java 13 Method Calls and Recursion Implementation (continued) Figure 5-1 Contents of the run-time stack when main() calls method f1() , f1() calls f2() , and f2() calls f3()

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Data Structures and Algorithms in Java Anatomy of a Recursive Call 14
Data Structures and Algorithms in Java Anatomy of a Recursive Call 15

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Data Structures and Algorithms in Java Anatomy of a Recursive Call 16
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• Fall '16
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• Data Structures, Backtracking, Eight queens puzzle, helge von koch

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