Chapter 6Iteration

Goals • To be able to program loops with the while ,

for , and do statements

• To avoid infinite loops and off-by-one errors

• To understand nested loops

• To learn how to process input

• To implement simulations

Investment with Compound Interest

Year Balance0 $10,000 1 $10,500 2 $11,025 3 $11,576.25

Invest $10,000, 5% interest, compounded annually

1. When will the balance be at least $20,000?

2. What is the new balance after 5 years?

Syntax 6.1. The while Statement• Syntax

while (condition)statement

repeats the statement while the condition is true

• Example:while (balance < targetBalance){ year++; double interest = balance * rate / 100; balance = balance + interest;}

• Purpose: To execute a statement while a condition is true

Flowchart for while Loop

Investment.java1 /** 2 A class to monitor the growth of an3 investment that accumulates interest at a

fixed annual rate 4 */ 5 public class Investment 6 { 7 /** 8 Constructs an Investment object from a9 starting balance and interest rate. 10 @param aBalance the starting balanece 11 @param aRate the interest rate in percent12 */ 13 public Investment(double aBalance,

double aRate) 14 { 15 balance = aBalance; 16 rate = aRate; 17 years = 0;18 } 20 /** 21 Keeps accumulating interest until a target

balance has been reached.

23 @param targetBalance the desired balance

24 */

25 public void waitForBalance(double targetBalance)

26 { 27 while (balance < targetBalance)

28 {

29 years++; 30 double interest = balance * rate / 100; 31 balance = balance + interest; 32 } 33 } 35 /** 36 Gets the current investment balance. 37 @return the current balance 38 */39 public double getBalance()40 { return balance; } 44 /** 45 Gets the number of years this investment 46 has accumulated interest. 47 @return the number of years since the 48 start of the investment 48 */ 49 public int getYears() 50 { 51 return years; 52 } 54 private double balance; 55 private double rate; 56 private int years; 57 }

InvestmentTest.java1/** 2 This program computes how

long it takes for an investment 3 to double. 4 */ 5 public class InvestmentTest 6 { 7 public static void main(String[]

args) 8 { 9 final double

INITIAL_BALANCE = 10000;

10 final double RATE = 5; 11 Investment invest = new

Investment(INITIAL_BALANCE, RATE);

12 invest.waitForBalance(2 * INITIAL_BALANCE);

13 int years = invest.getYears(); 14 System.out.println("The

investment doubled after " 15 + years + " years"); 16 } 17 }

Common Errors with while statement• Infinite Loop

– while (year < 20){

balance = balance + balance * rate / 100;

}while (year > 0){

year++; // oops, --

}– Loops run forever--must

kill program

Off-by-1 Error – year = 0;

while (balance < targetBalance){

year++;double

interest=balance*rate/100; balance = balance + interest;}System.out.println("Reached target after “ + year + " years.");

Should year start at 0 or 1? Should the test be < or <=? Avoiding Off-by-1 Error

Run through a simple example:target balance = $20,000, interest rate 50%after one year: balance = $15,000after two years: balance = $22,500Therefore: year must start at 0

interest rate 100%after one year: balance = $20,000loop should stopTherefore: must use <

Think, don't compile and try at random

do Statement• Syntax:

do statementwhile (condition);

• Purpose: Executes loop body at least once

Flowchart for Flowchart for do Loop

• Example: Validate inputdouble value;do {String input =JOptionPane.showInputDialog

("Please enter a positive number"); value =Integer.parseInt(input);} while (input <= 0);

Syntax 6.2. The for Statement Syntax:

for (initialization; condition; update)statement

Example: for (int i = 1; i <= n; i++){

double interest = balance * rate / 100;

balance = balance+interest;}

Equivalent toinitialization;while (condition){ statement; update; }

• Purpose: To execute an initialization, then keep executing a statement and updating an expression while a condition is true

Flowchart for for Loopfor Loop

Investment.java1 /**

2 A class to monitor the growth of an investment that

3 accumulates interest at a fixed annual rate

4 */

5 public class Investment

6 {

7 /**

8 Constructs an Investment object from a starting balance and

9 interest rate.

10 @param aBalance the starting balanece

11 @param aRate the interest rate in percent

12 */

13 public Investment(double aBalance, double aRate)

14 {

15 balance = aBalance;

16 rate = aRate; 17 years = 0; 18 } 19 20 /** 21 Keeps accumulating interest until a

target balance has 22 been reached. 23 @param targetBalance the desired

balance 24 */ 25 public void waitForBalance(double

targetBalance) 26 { 27 while (balance < targetBalance) 28 { 29 years++; 30 double interest = balance * rate / 100; 31 balance = balance + interest; 32 } 33 }

35 /**

36 Keeps accumulating interest for a given number of years.

37 @param n the number of years

38 */

39 public void waitYears(int n)

40 {

41 for (int i = 1; i <= n; i++)

42 {

43 double interest = balance * rate /

100;

44 balance = balance + interest;

45 }

46 years = years + n;

47 }

49 /**

50 Gets the current investment balance.

51 @return the current balance

52 */

53 public double getBalance()

54 {

55 return balance;

56 }

58 /**

59 Gets the number of years this investment has accumulated interest.

61 @return the number of years since the start of the investment

62 */

63 public int getYears()

64 {

65 return years;

66 }

68 private double balance;

69 private double rate;

70 private int years;

71 }

InvestmentTest.java1 /** 2 This program computes how

much an investment grows in 3 a given number of years. 4 */ 5 public class InvestmentTest 6 { 7 public static void

main(String[] args) 8 { 9 final double

INITIAL_BALANCE = 10000;

10 final double RATE = 5; 11 final int YEARS = 20; 12 Investment invest = new

Investment(INITIAL_BALANCE, RATE);

13 invest.waitYears(YEARS); 14 double balance =

invest.getBalance(); 15 System.out.println("The

balance after " + YEARS + 16 " years is " + balance); 17 } 18 }

Common Errors: Semicolons

• A semicolon that shouldn't be theresum = 0;for (i = 1; i <= 10; i++) ;

sum = sum + i;System.out.println(sum);

// A missing semicolon for (i = 1; i <= 10; sum = sum + i++)System.out.println(sum);

Make triangle row is another loopfor (int j = 1; j <= i; j++)

r = r + "[]";r = r + "\n";

Put loops together => Nested loops

Nested Loops

Create triangle pattern[][][][][][][][][][]

Loop through rowsfor (int i = 1; i <= n; i++){

// make triangle row}

Triangle.java1 /**

2 This class describes triangle objects that can be displayed as shapes like this:

4 []

5 [][]

6 [][][]

7 */

8 public class Triangle 9 { 10 /** 11 Constructs a triangle. 12 @param aWidth the number of []

in the last row of the triangle. 13 */ 14 public Triangle(int aWidth) 15 { 16 width = aWidth; 17 }

18 19 /** 20 Computes a string representing the

triangle. 21 @return a string consisting of [] and

newline characters 22 */ 23 public String toString() 24 { 25 String r = ""; 26 for (int i = 1; i <= width; i++) 27 { 28 // make triangle row 29 for (int j = 1; j <= i; j++) 30 r = r + "[]"; 31 r = r + "\n"; 32 } 33 return r; 34 } 35 36 private int width; 37 }

TriangleTest.java1 /** 2 This program tests the Triangle class. 3 */ 4 public class TriangleTest 5 { 6 public static void main(String[] args) 7 { 8 Triangle small = new Triangle(3); 9 System.out.println(small.toString()); 10 11 Triangle large = new Triangle(15); 12 System.out.println(large.toString()); 13 } 14 }

Reading Input Values• General pattern:

boolean done = false;while (!done){ String input = read input; if (end of input indicated) done = true; else { // process input }}

• "Loop and a half”:

The true test for loop termination is in the middle of the loop, not at the top

DataSet.java1 /**

2 Computes the average of a set of data values.

3 */

4 public class DataSet

5 {

6 /**

7 Constructs an empty data set.

8 */ 9 public DataSet() 10 { 11 sum = 0; 12 count = 0; 13 maximum = 0; 14 } 15 16 /** 17 Adds a data value to the data set 18 @param x a data value 19 */ 20 public void add(double x) 21 { 22 sum = sum + x; 26

23 if (count == 0 || maximum < x) maximum = x;

24 count++; 25 } 27 /** 28 Gets the average of the added data. 29 @return the average or 0 if no data has

been added 30 */ 31 public double getAverage() 32 { 33 if (count == 0) return 0; 34 else return sum / count; 35 } 37 /** 38 Gets the largest of the added data. 39 @return the maximum or 0 if no data has

been added 40 */ 41 public double getMaximum() 42 { 43 return maximum; 44 } 46 private double sum; 47 private double maximum; 48 private int count; 49 }

InputTest.java1 import javax.swing.JOptionPane;

3 /** 4 This program computes the

average and maximum of a set

5 of input values. 6 */ 7 public class InputTest 8 { 9 public static void

main(String[] args) 10 { 11 DataSet data = new

DataSet(); 12 13 boolean done = false; 14 while (!done) 15 {

16 String input = JOptionPane.showInputDialog("Enter value, Cancel to quit");

17 if (input == null) 18 done = true;19 else 20 { 21 double x =

Double.parseDouble(input);22 data.add(x); 23 } 24 } 25 26 System.out.println("Average = "

+ data.getAverage()); 27 System.out.println("Maximum =

" + data.getMaximum()); 28 } 29 }

String Tokenization StringTokenizer breaks up string into tokens By default, white space separates tokens "4.3 7 -2" breaks into three tokens:

"4.3", "7", "-2" • StringTokenizer tokenizer

= new StringTokenizer();while (tokenizer.hasMoreTokens()){ String token = tokenizer.nextToken(); // process token}

InputTest.java1 import java.util.StringTokenizer; 2 import javax.swing.JOptionPane;3 4 /** 5 This program computes the

average and maximum of a set 6 of input values that are entered

on a single line. 7 */ 8 public class InputTest 9 { 10 public static void main(String[]

args) 11 { 12 DataSet data = new DataSet(); 13 14 String input =

JOptionPane.showInputDialog("Enter values:");

15 StringTokenizer tokenizer = new StringTokenizer(input);

16 while (tokenizer.hasMoreTokens())

17 { 18 String token =

tokenizer.nextToken(); 19 double x =

Double.parseDouble(token);21 data.add(x); 22 } 23 24 System.out.println("Average =

" + data.getAverage()); 25 System.out.println("Maximum

= " + data.getMaximum()); 26 } 27 }

Traversing Characters in String s.charAt(i) is the ith

character of the string s – for (int i = 0; i <

s.length(); i++){ char ch = s.charAt(i); process ch}

Example: Count vowels s.indexOf(ch) is the

index of the first occurrence of ch in s, or -1 if ch doesn't occur in s

int vowelCount = 0;String vowels = "aeiouy";for (int i = 0; i < s.length();

i++){ char ch = s.charAt(i); if (vowels.indexOf(ch)

>= 0) vowelCount++;}

Random Numbers

Random number generatorRandom generator = new Random();int n = generator.nextInt(a); // 0 <= n < adouble x = generator.nextDouble();// 0 <= x < 1

Throw die (random number between 1 and 6)int d = 1 + generator.nextInt(6);

Die.java1 import java.util.Random; 2 3 /** 4 This class models a die that, when

cast, lands on a random 5 face. 6 */ 7 public class Die 8 { 9 /** 10 Constructs a die with a given

number of sides 11 @param s the number of sides, e.g.

6 for a normal die 12 */ 13 public Die(int s) 14 { 15 sides = s; 16 generator = new Random(); 17 }

18

19 /**

20 Simulates a throw of the die

21 @return the face of the die

22 */

23 public int cast()

24 {

25 return 1 + generator.nextInt(sides);

26 }

27

28

29 private Random generator;

30 private int sides;

31 }

DieTest.java1 /** 2 This program simulates casting a die ten times. 3 */ 4 public class DieTest 5 { 6 public static void main(String[] args) 7 { 8 Die d = new Die(6); 9 final int TRIES = 10; 10 for (int i = 1; i <= TRIES; i++) 11 { 12 int n = d.cast(); 13 System.out.print(n + " "); 14 } 15 System.out.println(); 16 } 17 }

Buffon Needle Experiment

Needle Position Needle length = 1, distance

between lines = 2 Generate random ylow

between 0 and 2 Generate random angle a

between 0 and 180 degrees yhigh = ylow + sin( a) Hit if yhigh >= 2

• Simulating of random events• On each try, a needle, of length 1

is dropped onto a paper ruled with lines of length 2

• If needles drops onto a line, hit• Conjecture: ties/hitsπ

Needle.java1 import java.util.Random; 3 /** 4 This class simulates a needle in

the Buffon needle experiment. 5 */ 6 public class Needle 7 { 8 /** 9 Constructs a needle. 10 */ 11 public Needle() 12 { 13 hits = 0; 14 generator = new Random(); 15 } 17 /** 18 Drops the needle on the grid of

lines and remembers whether the needle hit a line.

20 */ 21 public void drop() 22 { 23 double ylow = 2 *

generator.nextDouble();

24 double angle = 180 * generator.nextDouble();

26 // compute high point of needle 28 double yhigh = ylow +

Math.sin(Math.toRadians(angle)); 29 if (yhigh >= 2) hits++; 30 tries++; 31 } 33 /** 34 Gets the number of times the needle hit a

line. 35 @return the hit count 36 */37 public int getHits() 38 { return hits; } 42 /** 43 Gets the total number of times the needle was

dropped. 44 @return the try count 45 */ 46 public int getTries() 47 { return tries; } 51 private Random generator; 52 private int hits; 53 private int tries; 54 }

NeedleTest.java1 /** 2 This program simulates the

Buffon needle experiment and prints the resulting approximations of pi.

4 */ 5 public class NeedleTest 6 { 7 public static void

main(String[] args) 8 {

9 Needle n = new Needle(); 10 final int TRIES1 = 10000; 11 final int TRIES2 = 100000; 12

13 for (int i = 1; i <= TRIES1; i++) 14 n.drop(); 15 System.out.println("Tries / Hits

= " + (double)n.getTries() / n.getHits());

17 18 for (int i = TRIES1 + 1; i <=

TRIES2; i++) 19 n.drop(); 20 System.out.println("Tries / Hits

= " + (double)n.getTries() / n.getHits());

22 } 23 }