11/8: Recursion

• About Scoping.java

• Recursion

• Program of the Day

Scoping.java pt.1//Fig. 6.10: Scoping.java -- A scoping exampleimport java.awt.Container;import javax.swing.*;

public class Scoping extends JApplet { JTextArea outputArea; int x = 1; //note: an instance variable public void init () { outputArea = new JTextArea(); Container c = getContentPane(); c.add ( outputArea ); }

Scoping.java pt.2 public void start () { int x = 5; //note: a local variable with the same name. outputArea.append ( "local x in start is " + x ); methodA(); //methodA has automatic local x methodB(); //methodB uses instance variable x methodA(); //methodA reinitializes automatic local x methodB(); //instance variable x retains its value outputArea.append ( "\n\nlocal x in start is " + x ); }

Scoping.java pt.3 public void methodA() { int x = 25; //initialized each time methodA is called. outputArea.append( "\n\nlocal x in methodA is " + x + " after entering methodA" ); ++x; outputArea.append( "\nlocal x in methodA is " + x + " before exiting methodA" ); }

Scoping.java pt.4 public void methodB() { outputArea.append ( "\n\ninstance variable x is " + x + " on entering methodB" ); x *= 10; outputArea.append ( "\ninstance variable x is " + x + " on exiting methodB" ); }}

Recursion

• Somewhat like iteration

• A recursive method calls itself.

• EX from math: factorial: n! = n * ( n - 1 ) !

• EX: finding a name in phone book– go to the middle of the phone book.– if name is before that page, go to middle of front half– if name is before that page, go to middle of front half

of front half– if name is before that page, go to middle of front half

of front half of front half...

Example: countZeros.java pt. 1//Counting zeros: a recursion exampleimport javax.swing.JOptionPane;public class CountZeros { public static void main ( String args [] ) { int number, zeros; number = Integer.parseInt ( JOptionPane.showInputDialog ( "Give me an integer. I'll count the zeros for you." ) ); zeros = count0s( number ); JOptionPane.showMessageDialog ( null , "The number " +

number + " has " + zeros + " zeros in it." ); System.exit ( 0 ); }

Example: countZeros.java pt. 2 public static int count0s ( int n ) //called by the method above { if ( n == 0 ) return 1;

else if ( n < 10 ) //and not zero, mind you return 0;

else if ( n % 10 == 0 ) //remainder of n/10 return ( count0s ( n / 10 ) + 1 );

else //n%10 is not = to zero return ( count0s ( n / 10 ) ); }}

Notes about Recursive Methods

• base case (or stopping case)– last one to be evaluated– must exist for recursion to end. Without it, the

recursion is endless (and the program won’t stop.)– EX: factorial: n! = n * ( n - 1 ) !– the base case would be 2 * 1– factorials, by definition, stop at 1: 0! = 1, 1! = 1

Memory Issue: Recursive Methods

• Java stores all values generated along the way:– Java calculating factorial of 6 :

6! = 6 * (6 - 1 )! = 720 = 5 * ( 5 - 1 )! = 120 = 4 * ( 4 - 1 )! = 24 = 3 * ( 3 - 1 )! = 6

= 2 * ( 2 - 1 )! = 2 = 1

• Java stores these values in a stack.

Recursive vs. Iterative Methods

• Any recursive method can be rewritten as an iterative method.

• Why use recursion, then?– recursion may mimic the problem at hand better.– iterative solutions may not be obvious.

Program of the day

• pg. 239 FibonacciTest.java

• After you get it to work, follow through with an input of 7 to see what the program flow looks like.