Chapter 13: Recursion J ava P rogramming: From Problem Analysis to Program Design, From Problem Analysis to Program Design, Fourth Edition Fourth Edition.

Chapter 13: RecursionChapter 13: Recursion

JJavaava PProgramming:rogramming:

From Problem Analysis to Program From Problem Analysis to Program Design, Design,

Fourth EditionFourth Edition

Java Programming: From Problem Analysis to Program Design, Second Edition 2

Chapter Objectives

Learn about recursive definitions. Explore the base case and the general case of a

recursive definition. Learn about recursive algorithms. Learn about recursive methods. Become aware of direct and indirect recursion. Explore how to use recursive methods to implement

recursive algorithms.


Recursive Definitions Recursion:

Process of solving a problem by reducing it to smaller versions of itself.

Recursive definition:

Definition in which a problem is expressed in terms of a smaller version of itself.

Has one or more base cases.


Recursive Definitions Recursive algorithm:

Algorithm that finds the solution to a given problem by reducing the problem to smaller versions of itself.

Has one or more base cases. Implemented using recursive methods.

Recursive method: Method that calls itself.

Base case: Case in recursive definition in which the solution is

obtained directly. Stops the recursion.


Recursive Definitions General solution:

Breaks problem into smaller versions of itself.

General case:

Case in recursive definition in which a smaller version of itself is called.

Must eventually be reduced to a base case.


Tracing a Recursive Method

Recursive method:

Has unlimited copies of itself.

Every recursive call has its own:

Code

Set of parameters

Set of local variables


Tracing a Recursive Method

After completing a recursive call:

Control goes back to the calling environment.

Recursive call must execute completely before control goes back to previous call.

Execution in previous call begins from point immediately following recursive call.


Recursive Definitions

Directly recursive: A method that calls itself.

Indirectly recursive: A method that calls another method and eventually results in the original method call.

Tail recursive method: Recursive method in which the last statement executed is the recursive call.

Infinite recursion: The case where every recursive call results in another recursive call.


Designing Recursive Methods

Understand problem requirements.

Determine limiting conditions.

Identify base cases.


Designing Recursive Methods

Provide direct solution to each base case.

Identify general cases.

Provide solutions to general cases in terms of smaller versions of general cases.


Recursive Factorial Method

public static int fact(int num){ if (num = = 0) return 1; else return num * fact(num – 1);}


Recursive Factorial Method


Largest Value in Arraypublic static int largest(int[] list, int lowerIndex, int upperIndex){ int max; if (lowerIndex == upperIndex) return list[lowerIndex]; else { max = largest(list, lowerIndex + 1, upperIndex); if (list[lowerIndex] >= max) return list[lowerIndex]; else return max; }}


Largest Value in Array


Recursive Fibonacci


Recursive Fibonacci

public static int rFibNum(int a, int b, int n){ if(n = = 1) return a; else if (n = = 2) return b; else return rFibNum(a, b, n -1) + rFibNum(a, b, n - 2);}


Recursive Fibonacci


Towers of Hanoi: Three Disk Problem


Towers of Hanoi: Three Disk Solution


Towers of Hanoi: Three Disk Solution


Towers of Hanoi: Recursive Algorithm

public static void moveDisks(int count, int needle1, int needle3, int needle2){ if (count > 0) { moveDisks(count - 1, needle1, needle2, needle3); System.out.println("Move disk " + count + " from needle " + needle1 + " to needle " + needle3 + ". "); moveDisks(count - 1, needle2, needle3, needle1); }}


Recursion or Iteration?

Two ways to solve particular problem: Iteration

Recursion

Iterative control structures use looping to repeat a set of statements.

Tradeoffs between two options: Sometimes recursive solution is easier.

Recursive solution is often slower.


Programming Example: Decimal to Binary

public static void decToBin(int num, int base){ if (num > 0) { decToBin(num / base, base); System.out.print(num % base); }}


Programming Example: Decimal to Binary


Programming Example: Sierpinski Gasket


Programming Example:Sierpinski Gasket

Input: Non-negative integer that indicates level of Sierpinski gasket.

Output: Triangle shape that displays a Sierpinski gasket of the given order.

Solution includes:

Recursive method drawSierpinski.

Method to find midpoint of two points.


private void drawSierpinski(Graphics g, int lev, Point p1, Point p2, Point p3){ Point midP1P2; Point midP2P3; Point midP3P1; if (lev > 0) { g.drawLine(p1.x, p1.y, p2.x, p2.y); g.drawLine(p2.x, p2.y, p3.x, p3.y); g.drawLine(p3.x, p3.y, p1.x, p1.y); midP1P2 = midPoint(p1, p2); midP2P3 = midPoint(p2, p3); midP3P1 = midPoint(p3, p1); drawSierpinski(g, lev - 1, p1, midP1P2, midP3P1); drawSierpinski(g, lev - 1, p2, midP2P3, midP1P2); drawSierpinski(g, lev - 1, p3, midP3P1, midP2P3); }}





Chapter Summary

Recursive definitions

Recursive algorithms

Recursive methods

Base cases

General cases


Chapter Summary

Tracing recursive methods

Designing recursive methods

Varieties of recursive methods

Recursion vs. iteration

Various recursive functions

Chapter 13: Recursion J ava P rogramming: From Problem Analysis to Program Design, From Problem Analysis to Program Design, Fourth Edition Fourth Edition.

Documents

problem analysis

program design

recursive algorithms

recursive definitionsrecursion

recursive methodafter

recursive methodsunderstand

editionjava programming

tail recursive method