1. Chapter 5 Loop Control Statements
The for Statement
The while Statement
The do-while Statement
Numerical Accuracy
Numerical Analysis
Copyright 1999, James M. Slack

2. Loops: Introduction Loop Three loop statements in Java
Group of statements the computer executes over and over, as long as some criterion holds
Three loop statements in Java
for
while
do-while
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3. Loops: Introduction Many real-world activities involve loops
Example: Library checkout
Clear up patron's overdue materials and outstanding fines, if any.
Scan or type patron's ID number. Update ID if not current and valid.
Scan material code for each item.
Stamp due date on each item.
Give materials and library card back to the patron.
Checkout librarian does these steps until library closes
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4. Loops: Kinds Two kinds of loops Counting loop Counting
Event-controlled
Counting loop
Computer knows, when it begins the loop, how many times to execute the body
Counting loop statement in Java: for
Computer stops the loop when a condition is no longer true
Event-controlled loop statements in Java: while, do-while
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5. Event-controlled loops
Loops: Kinds
Counting loops are subset of event-controlled
"Event" of counting loop: counting variable reaches the limit
Event-controlled loops
Counting loops
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6. The for Statement The counting loop statement in Java Example Output
for (int count = 1; count <= 5; count++) {
System.out.println(count); }
Output 1 2 3 4 5
Initialization
Condition
Increment
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7. The for Statement: Example
Sum the first 20 integers
int total = 0;
for (int number = 1; number <= 20; number++) {
total = total + number; }
System.out.println(" is " total);
Output
is 210
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8. The for Statement: Example
What does this display?
for (int count = 10; count <= 6; count++) {
System.out.println(count); }
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9. The for Statement: Syntax
Can leave out initialization, condition, or increment
int total = 0, number = 1;
for (; number <= 20;) {
total = total + number;
number++; }
System.out.println(" is " + total);
Don't need to use same variable throughout
int y = 10;
for (int x = 0; x < y; y--)
System.out.println(x + " " + y);
(Confusing!)
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10. The for Statement: Draw Circles
Example: drawing circles in turtle graphics
Can simulate circles with drawPolygon()
Too many sides makes drawing too slow
20 to 40 sides looks ok
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11. The for Statement: drawPolygon()
The drawPolygon() method (Chapter 2)
// drawPolygon: Draws a regular polygon with the given
// number of sides, and all sides are of
// length size
void drawPolygon(int numSides, int size)
throws TurtleException {
for (int side = 1; side <= numSides; side++)
this.move(size);
this.turnRight(360 / numSides); }
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12. The for Statement: drawPolygon()
Drawing circles with drawPolygon()
How to draw circle with specific radius?
Circumference of a circle
2 x  x radius
Distance around a polygon
sides x size
Set these equal to each other, solve for size
2 x  x radius = sides x size
size = (2 x  x radius) / sides
In Java
int size = (int) Math.round(2 * Math.PI * radius) / NUM_SIDES;
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13. The for Statement: drawCircle()
Drawing circles with drawPolygon()
First version of drawCircle()
// drawCircle: (First version) Draws a circle of the given
// radius, to the right of the turtle. The turtle
// finishes at the same position and direction as
// before. The pen must be down beforehand, and is
// down afterward.
static final int NUM_SIDES = 20; // Must divide into 360
public void drawCircle(int radius)
throws TurtleException {
int size = (int) Math.round(2 * Math.PI * radius)
/ NUM_SIDES;
this.drawPolygon(NUM_SIDES, size); }
Computes size of 20-sided polygon to achieve desired radius
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14. The for Statement: drawCircle()
Test drawCircle()
// This program draws a circle inside a square,
// to see how accurate the circle drawing method is
import turtlegraphics.*;
import SmartTurtle;
public class TestCircle {
static final int CIRCLE_SIZE = 300;
public static void main[] (String args)
throws TurtleException
SmartTurtle myTurtle = new SmartTurtle();
myTurtle.goLeft(200);
myTurtle.turnAround();
myTurtle.move(CIRCLE_SIZE);
myTurtle.drawSquare(CIRCLE_SIZE * 2);
myTurtle.drawCircle(CIRCLE_SIZE); }
Oops!
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15. The for Statement: drawCircle()
What's wrong with drawCircle()?
Turtle draws first side of polygon straight up
Turtle draws last side of polygon at an angle
Need to balance these two angles
At beginning
this.turnRight(360 / NUM_SIDES / 2);
At end
this.turnLeft(360 / NUM_SIDES / 2);
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16. The for Statement: drawCircle()
Final version of drawCircle()
// drawCircle: (Final version) Draws a circle of the given
// radius, to the right of the turtle. The turtle
// finishes at the same position and direction as
// before. The pen must be down beforehand, and is
// down afterward.
static final int NUM_SIDES = 20; // must divide into 360
// with an even quotient
public void drawCircle(int radius)
throws TurtleException {
this.turnRight(360 / NUM_SIDES / 2);
int size = (int) Math.round(2 * Math.PI * radius)
/ NUM_SIDES;
this.drawPolygon(NUM_SIDES, size);
this.turnLeft(360 / NUM_SIDES / 2); }
New restriction: number of sides must divide into 360 with even quotient
(So can divide this by 2 for start and end angles)
Ah...
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17. The while Statement while One of two event-controlled loop statements
Body keeps executing as long as condition is true
Example
int i = 0;
while (i < 3) {
System.out.println(i);
i++; }
Output 1 2
while
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18. The while Statement while similar to if statement while statement
while (i < 3) {
System.out.println(i);
i++; }
if statement
if (i < 3)
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19. The while Statement: Sentinels
Sentinel loop
Sentinel: not data, but marks the end of data
Sentinel loop: reads data values until sentinel
Example
Sum series of numbers terminated by zero
10, 20, 30, 0
Data values
Sentinel
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20. The while Statement: Sentinels
Sentinel loop example
int sum = 0, number;
number = Keyboard.readInt("Enter first number: ");
while (number != 0) {
sum = sum + number;
number = Keyboard.readInt("Enter next number: "); }
System.out.println("The sum is " + sum);
Trace
Enter first number: 10
Enter next number: 20
Enter next number: 30
Enter next number: 0
The sum is 60
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21. The while Statement: Infinite Loop
Loop that doesn't stop
Easy to write accidentally with while statement
Infinite loop example 1
while (x < 3) {
y++; }
Infinite loop example 2
sum = 0;
count = 0;
while (count < 100)
sum = sum + count;
System.out.println("Sum of numbers from 1 to 100 is " + sum);
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22. The while Statement: Infinite Loop
Infinite loop example 3
answer = Keyboard.readChar("Say hi? (y/n)");
while (answer == 'y')
System.out.println("Hi!");
System.out.println("Bye!");
int x = 0;
while (x < 10); {
System.out.println(x);
x++; }
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23. The while Statement: Infinite Loop
Why doesn't compiler catch infinite loops?
Halting problem: Impossible for a computer program to detect all possible infinite loops in another program
Up to the programmer to avoid infinite loops
When you write a while statement
Make sure some statement in the while-body makes the condition false
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24. The while Statement: Menus
Example: Writing menu-based programs
Menu: List of selections that user can pick from
Writing a text-based menu system with while
Present menu
Get selection from user
As long as not quit
Do the selection
Present the menu
Get next selection
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25. The while Statement: Menus
Skeleton for text-based menu
// Present the menu the first time
// Get first selection from user
while (selection != quitOption) {
// Do selection
// Present the menu again
// Get next selection from user }
Example: Compute bank balance
--- Bank Balance Menu ---
0. Quit
1. Enter beginning balance
2. Enter interest rate
3. Compute ending balance
Enter selection (0, 1, 2, or 3): _
Menu
0. Quit
1. Enter beginning balance
2. Enter interest rate
3. Compute ending balance
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26. The while Statement: Menus
Bank Balance Program
Present menu
Get selection from user
As long as not quit
Do the selection
Present the menu
Get next selection
int selection;
double balance = 0.00;
double rate = 0.00;
// Display program title
System.out.println("--- Compute End-of-Year Bank Balance ---");
System.out.println();
// Display menu, get first selection
System.out.println("--- Bank Balance Menu ---");
System.out.println("0. Quit");
System.out.println("1. Enter beginning balance");
System.out.println("2. Enter interest rate");
System.out.println("3. Compute ending balance");
selection = Keyboard.readInt("Enter selection (0, 1, 2, or 3): ", 0, 3);
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27. The while Statement: Menus
// Handle the first selection; keep handling selections until
// user picks the quit selection (0)
while (selection != 0) {
switch (selection)
case 1:
balance = Keyboard.readDouble("Enter beginning balance: ");
break;
case 2:
rate = Keyboard.readDouble("Enter interest rate: ");
case 3:
System.out.println("Ending balance is " + (balance + balance * rate));
default:
System.out.println("Problem with switch statement"); }
// Display menu, get next selection
System.out.println();
System.out.println("--- Bank Balance Menu ---");
System.out.println("0. Quit");
System.out.println("1. Enter beginning balance");
System.out.println("2. Enter interest rate");
System.out.println("3. Compute ending balance");
selection = Keyboard.readInt("Enter selection (0, 1, 2, or 3): ", 0, 3);
System.out.println("Bye!");
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28. The while Statement: Counting
Writing counting loops with while
Can convert for statement to while
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29. Kinds of Loops
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30. Kinds of Loops Condition at the top Condition at the bottom
Condition tested before the body
Java statements: for and while
Condition at the bottom
Condition tested after the body
Java statements: do-while
Condition in the middle
Condition tested inside the body
No built-in Java statement
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31. The do-while Statement
The "other" event-controlled loop statement
Body keeps executing as long as condition is true
Example
int i = 0; do {
System.out.println(i);
i++;
} while (i < 3);
Output 1 2
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32. The do-while Statement
Difference from while statement
do-while executes body at least once
while statement may not execute body at all
Example
while do-while
int i = 10; int i = 10;
while (i < 3) do
{ {
System.out.println(i); System.out.println(i);
i++; i++;
} } while (i < 3);
Output
(nothing) 10
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33. The do-while Statement: Format
Poor style Preferred style
do do
{ {
do-while-body do-while-body
} } while (condition);
while (condition);
The brace before while distinguishes it as part of a do-while
Looks like the beginning of a while statement
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34. The do-while Statement: Example
Program to help children learn multiplication
int guessNum = 0, response;
System.out.println("What is " + operand1 + " times "
+ operand2 + "?"); do {
guessNum++;
response
= Keyboard.readInt("Enter guess number " + guessNum + ": ");
} while (response != operand1 * operand2);
System.out.println("Correct!");
Equivalent while statement requires two copies of body
One before loop starts
One inside the loop
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35. Numerical Accuracy // Add up 0.10 until the sum is 1.0 (Wrong)
public class AddTo1 {
public static void main(String[] args)
double total = 0.0;
while (total != 1.0)
total = total ;
System.out.println("Total so far: " + total); }
System.out.println("Done");
Total so far: 0.1
Total so far: 0.2
Total so far:
Total so far: 0.4
Total so far: 0.5
Total so far: 0.6
Total so far: 0.7
Total so far:
Total so far:
Total so far:
Total so far:
Total so far: 1.2
Total so far: 1.3
Total so far:
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36. Numerical Accuracy: Round-off
 1.0?
Round-off error
Can happen only with floating-point arithmetic
Computer stores numbers in binary, not base 10
Representable number: can store in finite number of digits
Unrepresentable in base 10: 1/3 =
Representable in base 10: 1/4 = 0.25
Some representable numbers in base 10 are unrepresentable in binary
0.10 (decimal) = (binary)
Can only store approximation of 0.10
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37. Numerical Accuracy: Round-off
Round-off error can happen with representable numbers
Example:
(decimal) = (binary)
Suppose computer can only store 8 binary digits
Computer's version of number is an approximation
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38. Numerical Accuracy: Comparisons
Don’t compare floating-point numbers with == or !=
double total = 0.0;
while (total != 1.0) // Avoid
Instead:
Use integers
int total = 0;
while (total != 10) // Use 1 for 1/10
Use <=, >=, <, or >
while (total <= 1.0) // Good approach
Check if numbers are very close
// Can set exact tolerance
while (Math.abs(total - 1.0) > ) ...
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39. Numerical Accuracy: Arithmetic
Avoid arithmetic on floating-point numbers that are very different in size
Simulate space probe from earth to Proxima Centauri
double centimetersToProximaCentauri = ;
while (centimetersToProximaCentauri > 0.0) {
// Simulate action of space probe here ...
centimetersToProximaCentauri = centimetersToProximaCentauri - 1.0; }
This loop is infinite: computer stores as
- 1.0
One solution: use kilometers instead
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40. Condition-in-the-Middle Loops
Hypothetical condition-in-the-middle loop (not Java)
loop {
number = Keyboard.readInt("Number (0 to stop): ");
until (number == 0);
sum = sum + number; }
Can use as while or do-while
Move until up for while, down for do-while
Equivalent while loop
number = Keyboard.readInt("Enter first number (0 to stop): ");
while (number != 0)
number = Keyboard.readInt("Enter next number (0 to stop): ");
Must duplicate part of body before loop starts
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41. Condition-in-the-Middle Loops
Can use break statement to stop loop early
Put "if (condition) break" in infinite loop
while (true) {
number = Keyboard.readInt("Number (0 to stop): ");
if (number == 0) break;
sum = sum + number; }
System.out.println("Sum is " + sum);
Doesn't work if break is inside switch
Must label the loop statement
loop:
switch (...)
case xx: break loop;
...
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42. The continue Statement
Syntax
continue; or
continue label;
Example
for (i = 0; i < 100; i++) {
if (i % 2 == 0) // Ignore even numbers }
System.out.println(i);
Action
Control skips rest of loop iteration; starts next iteration
for loop: computer executes the increment part before starting next iteration
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43. Numerical Analysis Study of use of arithmetic in computer programs
Some issues in numerical analysis
Minimize round-off errors
Solve problems that don't have exact solution (or exact solution is difficult to find)
Finding roots of mathematical functions
Root of function: Value of x that makes function 0
Often difficult to find roots algebraically
Example: find all roots of f(x) = x5 - 5x + 1
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44. Numerical Analysis: Roots
Find roots of f(x) = x5 - 5x + 1
Plot the function
Three roots: one is between -1 and -2
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45. Numerical Analysis: Bisection
Use bisection to find root of f(x) = x5 - 5x + 1
Plot shows a root between -1 and -2
Pick 2 values of x, one on either side of root
Use -1.5 as approximation of root, plug into function
> 0, so it replaces old "above 0" value
-1.5
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46. Numerical Analysis: Bisection
Use bisection to find root of f(x) = x5 - 5x + 1
Next evaluate f(x) at (halfway between -1.5 and -2)
f(-1.75) is
< 0, so it replaces old "below 0" value
-1.75
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47. Numerical Analysis: Bisection
Keep using bisection to get as close to 0 as desired
Each iteration cuts range by half
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48. Numerical Analysis: Bisection
Bisection advantages
Simple and effective
Little or no round-off error
Bisection disadvantages
Slow
Only finds one root at a time
Can't tell if function has other roots
Appropriate for continuous intervals only
Noncontinuous function
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49. Numerical Analysis: Bisection
Bisection Program
// Find zero of a function by bisection.
// Displays bound1, bound2, midpoint between bound1 and
// bound2, and f(midpoint). If f(midpoint) is not within
// +/- ERROR, cuts area in half and repeats.
// NOte: Required that f(bound2) < 0 < f(bound1), and there
// exists f(x) such that f(x) == 0, x is between
// bound1 and bound2, and f() is continuous between
// f(bound1) and f(bound2)
import Keyboard;
import Format;
public class Bisection {
static final double ERROR = 0.001; // Maximum difference between
// generated solution and zero
static final int WIDTH = 14; // Width of output numbers
static final int DECIMALS = 5; // Decimals of output numbers
// evaluateFunction: Returns f(x) (Put your function here)
static double evaluateFunction(double x)
return Math.pow(x, 5) - (5 * x) + 1; }
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50. Numerical Analysis: Bisection
public static void main(String[] args)
throws java.io.IOException {
double bound1, bound2;
System.out.println("--- Find Zeros of a Function "
+ "by Bisection ---");
System.out.println();
// Get initial bounds for the value of x from the user
System.out.println("Enter two values that surround the value");
System.out.println("of x that makes the function 0.");
bound1 = Keyboard.readDouble("Value of x that gives "
+ "positive value "
+ "from function: ");
bound2 = Keyboard.readDouble("Value of x that gives "
+ "negative value "
double midpoint;
System.out.println(Format.padRight("Bound1", WIDTH)
+ Format.padRight("Bound2", WIDTH)
+ Format.padRight("Midpoint", WIDTH)
+ Format.padRight("f(Midpoint)", WIDTH));
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51. Numerical Analysis: Bisection
// Do first cut before the loop
midpoint = (bound1 + bound2) / 2;
System.out.println(Format.pad(bound1, WIDTH, DECIMALS)
+ Format.pad(bound2, WIDTH, DECIMALS)
+ Format.pad(midpoint, WIDTH, DECIMALS)
+ Format.pad(evaluateFunction(midpoint), WIDTH, DECIMALS));
// Keep reducing the area between the bounds until the
// f(midpoint) is within ERROR tolerance of 0.0
while (Math.abs(evaluateFunction(midpoint)) > ERROR) {
if (evaluateFunction(midpoint) > 0.0)
bound1 = midpoint;
else
bound2 = midpoint; }
Program uses Format.pad() (from Chapter 7)
Format.pad(floating-point-number, width, decimals)
Format.pad(string, width)
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52. Num. Analysis: Bisection
Bisection program run on f(x) = x5 - 5x + 1
--- Find Zeros of a Function by Bisection ---
Enter two values that surround the value
of x that makes the function 0.
Value of x that gives positive value from function: -1
Value of x that gives negative value from function: -2
Bound Bound Midpoint f(Midpoint)
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53. Num. Analysis: Bisection
Bisection program run on f(x) = (6x3 + 4x2 + 1) / 25x
--- Find Zeros of a Function by Bisection ---
Enter two values that surround the value
of x that makes the function 0.
Value of x that gives positive value from function: 1.0
Value of x that gives negative value from function: -0.4
Bound Bound Midpoint f(Midpoint)
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