9781111530532 ppt ch13

Java Programming: From Problem Analysis to Program Design, 5e

Chapter 13Recursion

Java Programming: From Problem Analysis to Program Design, 5e 2

Chapter Objectives

• Learn about recursive definitions

• Explore the base case and the general case of a recursive definition

• Learn about recursive algorithms


Chapter Objectives (continued)

• 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 (continued)


Recursive Definitions (continued)• 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 (continued)

• 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– Logically, you can think of a recursive method

having unlimited copies of itself– Every recursive call has its own:

• Code• Set of parameters• Set of local variables


Tracing a Recursive Method (continued)

• 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 (continued)

• Provide direct solution to each base case

• Identify general case(s)

• 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 (continued)


Largest Value in Array


• if the size of the list is 1 the largest element in the list is the only element in the list

• else to find the largest element in list[a]...list[b] a. find the largest element in list[a + 1]...list[b]

and call it max b. compare list[a] and max

if (list[a] >= max) the largest element in list[a]...list[b] is

list[a] else

the largest element in list[a]...list[b] is max

Largest Value in Array (continued)


public 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 (continued)


Execution of largest(list, 0, 3)


Execution of largest (list, 0, 3)


Recursive Fibonacci


Recursive Fibonacci (continued)

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 (continued)


Towers of Hanoi Problem with Three Disks


Towers of Hanoi: Three Disk Solution


Towers of Hanoi: Three Disk Solution (continued)


Towers of Hanoi: Recursive Algorithmpublic 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


Sierpinski Gaskets of Various Orders


Programming Example:Sierpinski Gasket

• Input: nonnegative integer indicating level of Sierpinski gasket

• Output: triangle shape displaying 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); }}

Programming Example:Sierpinski Gasket (continued)


Programming Example: Sierpinski Gasket (continued)


Chapter Summary

• Recursive definitions

• Recursive algorithms

• Recursive methods

• Base cases

• General cases


Chapter Summary (continued)

• Tracing recursive methods

• Designing recursive methods

• Varieties of recursive methods

• Recursion vs. iteration

• Various recursive functions explored

9781111530532 ppt ch13

Technology

problem analysis

program design

tail recursive method

recursion java programming

array java programming

disks java programming

problem requirements

base case java programming