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 }