1. Chapter 6 Iteration 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

2. Investment with Compound Interest 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?

3. 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

4. Flowchart for while Loop

5. Investment.java 1 /** 2 A class to monitor the growth of an 3 investment that accumulates interest at a fixed annual rate 4 */ 5 public class Investment 6 { 7 /** 8 Constructs an Investment object from a 9 starting balance and 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 } 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 /** 45Gets the number of years this investment 46has accumulated interest. 47@return the number of years since the 48start 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 }

6. InvestmentTest.java 1/** 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_BAL ANCE, 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 }

7. 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 = $15,000 after two years: balance = $22,500 Therefore: year must start at 0  interest rate 100% after one year: balance = $20,000 loop should stop Therefore: must use <  Think, don't compile and try at random

8. do Statement Syntax: do statement while (condition); Purpose: Executes loop body at least once Flowchart for Flowchart for do Loop Example: Validate input double value; do { String input =JOptionPane.showInputDialog ("Please enter a positive number"); value =Integer.parseInt(input); } while (input <= 0);

9. 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 to initialization; while (condition) { statement; update; } Purpose: To execute an initialization, then keep executing a statement and updating an expression while a condition is true for Loop Flowchart for for Loop

10. Investment.java 1 /** 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 }

11. 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 }

12. InvestmentTest.java 1 /** 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_BALAN CE, RATE); 13 invest.waitYears(YEARS); 14 double balance = invest.getBalance(); 15 System.out.println("The balance after " + YEARS + 16 " years is " + balance); 17 } 18 }

13. Common Errors: Semicolons A semicolon that shouldn't be there sum = 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);

14.  Make triangle row is another loop for (int j = 1; j <= i; j++) r = r + "[]"; r = r + "\n";  Put loops together => Nested loops Nested Loops  Create triangle pattern [] [][] [][][] [][][][]  Loop through rows for (int i = 1; i <= n; i++) { // make triangle row }

15. Triangle.java 1 /** 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 }

16. TriangleTest.java 1 /** 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 }

17. 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

18. DataSet.java 1 /** 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 }

19. InputTest.java 1 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 { 21double x = Double.parseDouble(input); 22data.add(x); 23 } 24 } 25 26 System.out.println("Average = " + data.getAverage()); 27 System.out.println("Maximum = " + data.getMaximum()); 28 } 29 }

20. 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 }

21. InputTest.java 1 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 }

22. 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++; }

23. Random Numbers  Random number generator Random generator = new Random(); int n = generator.nextInt(a); // 0 <= n < a double x = generator.nextDouble(); // 0 <= x < 1  Throw die (random number between 1 and 6) int d = 1 + generator.nextInt(6);

24. Die.java 1 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 }

25. DieTest.java 1 /** 2 This program simulates casting a die ten times. 3 */ 4public 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 }

26. Buffon Needle Experiment Needle Position  Needle length = 1, distance between lines = 2  Generate random y low between 0 and 2  Generate random angle a between 0 and 180 degrees  y high = y low + sin( a)  Hit if y high >= 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/hits  π

27. Needle.java 1 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 }

28. NeedleTest.java 1 /** 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 }