Chapter 6 Iteration Chapter Goals To be able

Chapter 6 Iteration

Chapter 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 Invest $10, 000, 5% interest, compounded annually When will the balance be at least $20, 000?

while Statement while (condition) statement; repeats the statement while the condition is true while (balance < target. Balance) { year++; double interest = balance * rate / 100; balance = balance + interest; }

File 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 a. Balance the starting balanece 11 @param a. Rate the interest rate in percent 12 */ 13 public Investment(double a. Balance, double a. Rate) 14 { 15 balance = a. Balance; 16 rate = a. Rate; 17 years = 0; 18 } 19

20 /** 21 Keeps accumulating interest until a target balance has 22 been reached. 23 @param target. Balance the desired balance 24 */ 25 public void wait. For. Balance(double target. Balance) 26 { 27 while (balance < target. Balance)

28 { 29 years++; 30 double interest = balance * rate / 100; 31 balance = balance + interest; 32 } 33 } 34 35 /** 36 Gets the current investment balance. 37 @return the current balance 38 */

39 public double get. Balance() 40 { 41 return balance; 42 } 43 44 /** 45 Gets the number of years this investment has accumulated 46 interest.

47 @return the number of years since the start of the investment 48 */ 49 public int get. Years() 50 { 51 return years; 52 } 53 54 private double balance; 55 private double rate; 56 private int years; 57 }

File Investment. Test. java 1/** 2 This program computes how long it takes for an investment 3 to double. 4 */ 5 public class Investment. Test 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. wait. For. Balance(2 * INITIAL_BALANCE); 13 int years = invest. get. Years(); 14 System. out. println("The investment doubled after " 15 + years + " years"); 16 } 17 }

Flowchart for while Loop

Syntax 6. 1. The while Statement • while (condition) statement Example: • while (balance < target. Balance) • { • year++; • double interest = balance * rate / 100; • balance = balance + interest; • } – Purpose: • To execute a statement while a condition is true

Common Error: Infinite Loop while (year < 20) { balance = balance + balance * rate / 100; } while (year > 0) { year++; // oops, meant -} Loops run forever--must kill program

Common Error: Off-by-1 Error · year = 0; while (balance < target. Balance) { 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

do Statement • Executes loop body at least once: • do statement while (condition); • Example: Validate input • double value; do { String input = JOption. Pane. show. Input. Dialog( "Please enter a positive number"); value = Integer. parse. Int(input); } while (input <= 0);

Flowchart for do Loop

for Statement · 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; }

Flowchart for Loop

File 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 a. Balance the starting balanece 11 @param a. Rate the interest rate in percent 12 */ 13 public Investment(double a. Balance, double a. Rate) 14 { 15 balance = a. Balance;

16 rate = a. Rate; 17 years = 0; 18 } 19 20 /** 21 Keeps accumulating interest until a target balance has 22 been reached. 23 @param target. Balance the desired balance 24 */

25 public void wait. For. Balance(double target. Balance) 26 { 27 while (balance < target. Balance) 28 { 29 years++; 30 double interest = balance * rate / 100; 31 balance = balance + interest; 32 } 33 }

34 35 /** 36 Keeps accumulating interest for a given number of years. 37 @param n the number of years 38 */ 39 public void wait. Years(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 } 48

49 /** 50 Gets the current investment balance. 51 @return the current balance 52 */ 53 public double get. Balance() 54 { 55 return balance; 56 } 57

58 /** 59 Gets the number of years this investment has accumulated 60 interest. 61 @return the number of years since the start of the investment 62 */ 63 public int get. Years() 64 { 65 return years; 66 }

67 68 private double balance; 69 private double rate; 70 private int years; 71 }

File Investment. Test. java 1 /** 2 This program computes how much an investment grows in 3 a given number of years. 4 */ 5 public class Investment. Test 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. wait. Years(YEARS); 14 double balance = invest. get. Balance(); 15 System. out. println("The balance after " + YEARS + 16 " years is " + balance); 17 } 18 }

Syntax 6. 2. The for Statement • for (initialization; condition; update ) statement – Example: • for (int i = 1; i <= n; i++) { double interest = balance * rate / 100; balance = balance + interest; } – Purpose: • To execute an initialization, then keep executing a statement and updating an expression while a condition is true

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);

Nested Loops · Create triangle pattern [] [][][] · Loop through rows for (int i = 1; i <= n; i++) { // make triangle row }

· Make triangle row is another loop for (int j = 1; j <= i; j++) r = r + "[]"; r = r + "n"; · Put loops together => Nested loops

File Triangle. java 1 /** 2 This class describes triangle objects that can be displayed 3 as shapes like this: 4 [] 5 [][] 6 [][][] 7 */

8 public class Triangle 9{ 10 /** 11 Constructs a triangle. 12 @param a. Width the number of [] in the last row of the triangle. 13 */ 14 public Triangle(int a. Width) 15 { 16 width = a. Width; 17 }

18 19 /** 20 Computes a string representing the triangle. 21 @return a string consisting of [] and newline characters 22 */ 23 public String to. String() 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 }

File Triangle. Test. java 1 /** 2 This program tests the Triangle class. 3 */ 4 public class Triangle. Test 5{ 6 public static void main(String[] args) 7{ 8 Triangle small = new Triangle(3); 9 System. out. println(small. to. String());

10 11 Triangle large = new Triangle(15); 12 System. out. println(large. to. String()); 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"

File Data. Set. java 1 /** 2 Computes the average of a set of data values. 3 */ 4 public class Data. Set 5{ 6 /** 7 Constructs an empty data set. 8 */

9 public Data. Set() 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; 23 if (count == 0 || maximum < x) maximum = x; 24 count++; 25 } 26 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 get. Average() 32 { 33 if (count == 0) return 0; 34 else return sum / count; 35 } 36 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 get. Maximum() 42 { 43 return maximum; 44 } 45 46 private double sum; 47 private double maximum; 48 private int count; 49 }

File Input. Test. java 1 import javax. swing. JOption. Pane; 2 3 /** 4 This program computes the average and maximum of a set 5 of input values. 6 */ 7 public class Input. Test 8{

9 public static void main(String[] args) 10 { 11 Data. Set data = new Data. Set(); 12 13 boolean done = false; 14 while (!done) 15 { 16 String input = JOption. Pane. show. Input. Dialog("Enter value, Cancel to quit"); 17 if (input == null) 18 done = true;

19 else 20 { 21 double x = Double. parse. Double(input); 22 data. add(x); 23 } 24 } 25 26 System. out. println("Average = " + data. get. Average()); 27 System. out. println("Maximum = " + data. get. Maximum()); 28 } 29 }

String Tokenization · String. Tokenizer breaks up string into tokens · By default, white space separates tokens · "4. 3 7 -2" breaks into three tokens: "4. 3", "7", "-2" – String. Tokenizer tokenizer = new String. Tokenizer(); while (tokenizer. has. More. Tokens()) { String token = tokenizer. next. Token(); process token }

File Input. Test. java 1 import java. util. String. Tokenizer; 2 import javax. swing. JOption. Pane; 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 Input. Test 9{

10 public static void main(String[] args) 11 { 12 Data. Set data = new Data. Set(); 13 14 String input = JOption. Pane. show. Input. Dialog("Enter values: "); 15 String. Tokenizer tokenizer = new String. Tokenizer(input); 16 while (tokenizer. has. More. Tokens()) 17 { 18 String token = tokenizer. next. Token();

19 20 double x = Double. parse. Double(token); 21 data. add(x); 22 } 23 24 System. out. println("Average = " + data. get. Average()); 25 System. out. println("Maximum = " + data. get. Maximum()); 26 } 27 }

Traversing Characters in String · s. char. At(i) is the ith character of the string s – for (int i = 0; i < s. length(); i++) { char ch = s. char. At(i); process ch }

· Example: Count vowels – int vowel. Count = 0; String vowels = "aeiouy"; for (int i = 0; i < s. length(); i++) { char ch = s. char. At(i); if (vowels. index. Of(ch) >= 0) vowel. Count++; } · s. index. Of(ch) is the index of the first occurrence of ch in s, or -1 if ch doesn't occur in s

Random Numbers · Random number generator Random generator = new Random(); int n = generator. next. Int(a); // 0 <= n < a double x = generator. next. Double(); // 0 <= x < 1 · Throw die (random number between 1 and 6) int d = 1 + generator. next. Int(6);

File 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. next. Int(sides); 26 }

27 28 29 private Random generator; 30 private int sides; 31 }

File Die. Test. java 1 /** 2 This program simulates casting a die ten times. 3 */ 4 public class Die. Test 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

File Needle. java 1 import java. util. Random; 2 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 } 16

17 /** 18 Drops the needle on the grid of lines and 19 remembers whether the needle hit a line. 20 */ 21 public void drop() 22 { 23 double ylow = 2 * generator. next. Double(); 24 double angle = 180 * generator. next. Double(); 25

26 // compute high point of needle 27 28 double yhigh = ylow + Math. sin(Math. to. Radians(angle)); 29 if (yhigh >= 2) hits++; 30 tries++; 31 } 32 33 /** 34 Gets the number of times the needle hit a line. 35 @return the hit count 36 */

37 public int get. Hits() 38 { 39 return hits; 40 } 41 42 /** 43 Gets the total number of times the needle was dropped. 44 @return the try count 45 */

46 public int get. Tries() 47 { 48 return tries; 49 } 50 51 private Random generator; 52 private int hits; 53 private int tries; 54 }

File Needle. Test. java 1 /** 2 This program simulates the Buffon needle experiment 3 and prints the resulting approximations of pi. 4 */ 5 public class Needle. Test 6{ 7 public static void main(String[] args) 8{

9 Needle n = new Needle(); 10 final int TRIES 1 = 10000; 11 final int TRIES 2 = 100000; 12 13 for (int i = 1; i <= TRIES 1; i++) 14 n. drop(); 15 System. out. println("Tries / Hits = " 16 + (double)n. get. Tries() / n. get. Hits()); 17

18 for (int i = TRIES 1 + 1; i <= TRIES 2; i++) 19 n. drop(); 20 System. out. println("Tries / Hits = " 21 + (double)n. get. Tries() / n. get. Hits()); 22 } 23 }