Transcript Import java.awt. - Internet Database Lab.

Great Ideas of CS with Java
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Part 1 WWW & Computer programming in the language Java
Ch 1: The World Wide Web
Ch 2: Watch out: Here comes Java
Ch 3: Numerical computation & Function
Ch 4: Subroutines & Databases
Ch 5: Graphics
Ch 6: Simulation
Ch 7: Software engineering
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Part 2 Understanding what a computer is and how it works
Ch 8: Machine architecture
Ch 9: Language translation
Ch 10: Virtual Environment for Computing
Ch 11: Security, Privacy, and Wishful thinking
Ch 12: Computer Communication
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Part 3 Advanced topics
Ch 13: Program Execution Time
Ch 14: Parallel Computation
Ch 15: Noncomputability
Ch 16: Artificial intelligence
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IDB Lab.
Ch 3. Numerical Computation
and the Study of Functions
Copyright © SNU IDB Lab.
SNU
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IDB Lab.
Table of contents
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Let’s Calculate Some Numbers
Some Simple Calculations
Looping and a Study of Functions
Storing Information in Arrays
Simple Statistics Program Design
Putting Things on Array
Summary
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Number crunching example
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Many situations like below
 Yearly bank interest rate: 5% & Your asset: $10000
 You want to know how much you would earn after 20 years?
Two obvious solutions
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Do it yourself using a calculator 20 times
Write a program and let a machine find the answer.
Solving optimization problems
 Find the best value for a parameter in some situation
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Number crunching example
Figure 3.1
1,000 square cm of tin:
How to make a largest
possible cylindrical can?
Solving optimization problems:
Find the best value for a parameter in some situation
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Basic Java Facts: Variables and Data Types
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An object stores its state in variables (data member)
Definition: A variable is an item of data named by an identifier
Variable declaration  To give a variable a type and a name
type variable-name (ex. Int varx)
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The Java programming language has two categories of data types: primitive and
reference .
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A variable of primitive type
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contains a single value of the appropriate size and format for its type
a number, a character, or a boolean value.
For example
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an integer value is 32 bits of data in a format known as two's complement
the value of a character is 16 bits of data formatted as a Unicode character
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Primitive Data Types in Java
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Basic Java Fact: Primitive Data Types
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You can put a literal primitive value directly in your code.
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A series of digits with no decimal point is typed as an integer
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You can specify a long integer by putting an 'L' or 'l' after the number
'L' is preferred as it cannot be confused with the digit '1‘: (ex) 8864L
A series of digits with a decimal point is of type float
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For example int anInt = 4;
You can specify a float by putting an 'f' or 'F' after the number: (ex) 87.14F
A literal character value is any single Unicode character between single
quote marks (ex) ‘greeting’
The two boolean literals  true and false
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Basic Java Fact: Reference Data Types
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Arrays, classes, and interfaces are reference types
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The value of a reference type variable is a reference to the value or set of values represented by the
variable
A reference to the value == an address of the value
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A reference is called a pointer, or a memory address in other languages.
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The Java programming language does not support the explicit use of addresses like other
languages do
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So, there is no pointer in Java
Java use the variable's name instead.
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Int[] SampleArray;
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Basic Java Fact: “Final” Variables
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You can declare a variable in any scope to be final
The value of a final variable cannot change after it has been initialized
Such variables are similar to constants in other programming languages
To declare a final variable, use the final keyword in the variable declaration
before the type:
final int aFinalVar = 0;
You may defer initialization of a final local variable.
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Declare and initialize it later, like this:
final int blankfinalsample;
...
blankfinalsample = 0;
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A final local variable that has been declared but not yet initialized is called a
blank final.
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Java Fact on Floating Point Data Types
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Limitations of “int” data type
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32bit (two’s complement)
Minimum and maximum of int (-2,147,483,648 ~~ 2,147,483,647)
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Cannot take on fractional values like 3.14159265358979
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The solution is using real numbers.
Real numbers are specified with floating point (부동소수점) data type
In Java, there are two data types in this category (float and double)
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“long” data type extends the range
float is single-precision floating point (단정도 실수)
double is double-precision floating point (배정도 실수)
FP(Floating Point) data type represents numbers in two parts
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significant digits and an exponent
177 might be represented as 1.77 * 102 in float data type
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Roundoff error in floating point numbers
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Even if we are using “double” data type, the following things still can
happen!
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An infinite decimal expansion: 0.3333333333333333333333333333……
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will not fit in a computer register
Instead, 0.333333333333 will be stored
More than 17 digit decimal number: 100000000000000000100
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64 bit representation is not enough for some cases
is approximated by the computer to 100000000000000000000
There are some tricks for the above cases, but ,,,,,,,,,
import java.math.BigDecimal (or import.java.math.BigInteger)
BigDecimal bignum = new BigDecimal("100000000000000000000000000000")
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IDB Lab.
ErrorDemo program:
a program for reading
a number and printing the same number (1)
Import awb.*;
Import java.awt.*;
Import java.awt.event.*;
Public class ErrorDemo extends java.applet.Applet implements ActionListener
{ double data, extra;
DoubleField dataF, extraF;
Button b1;
Public void init ()
{ dataF = new DoubleField(20);
dataF.setLabel(“Data”);
extraF = new DoubleField(20);
extraF.setLabel(“Extra”);
b1 = new Button(“Compute”);
b1.addActionListener(this);
add(dataF);
add(extraF);
dataF.setDouble(0);
extraF.setDouble(0);
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ErrorDemo program:
a program for reading
a number and printing the same number (2)
Public void actionPerformed(ActionEvent event)
{
object cause = event.getSource();
if (cause = b1)
{
data = dataF.getDouble();
extra = extraF.getDouble();
data = data + extra;
data = data – extra;
dataF.setDouble(data);
}
}
}
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Result of the ErrorDemo program
(p. 93 - Table 3.1)
data(Input)
extra(Input)
data(Output)
100
100
100
100
1000
100
100
10000
100
.
.
.
.
.
.
100
10000000000000000
100
100
100000000000000000 96
100
100000000000000000 128
0
100
100000000000000000 0
00
.
.
.
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Table of contents
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Let’s Calculate Some Numbers
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Some Simple Calculations
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Looping and a Study of Functions
Storing Information in Arrays
Simple Statistics Program Design
Putting Things on Array
Summary
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Two Special Classes for easy-handling Numbers
only for this textbook (See appendix)
** These classes enable you to read and write int and double numbers easily in applets
without having to deal with additional Java syntax.
** Put these into awb directory under your public html directory and then use the import
awb.* command at the top of each program
public class IntField extends TextField
{
public IntField();
public IntField(int size);
public void setInt(int number);
public int getInt();
}
public class DoubleField extends TextField
{
public DoubleField();
public DoubleField(int size);
public void setDouble(double num);
public double getDouble();
}
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IDB Lab.
Calculating Cylinder Volume
• User puts values for radius and length of a cylinder
• Using DoubleField in example of calculating cylinder volume
CylVol.java
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import awb.*;
import java.awt.*;
import java.awt.event.*;
public class Numbers extends java.applet.Applet implements ActionListener
{
TextField
instruct, result, mRadius, mLength;
DoubleField gRadius, gLength;
Button bCompute;
double radius, length, cylVol, pi=3.14159265;
public void init ()
{
instruct = new TextField(72);
instruct.setText("Please enter radius and length below.");
mRadius = new TextField(9);
mRadius.setText("radius:");
}
public void actionPerformed(ActionEvent event)
{
Object cause = event.getSource();
if (cause == bCompute)
{
length = gLength.getDouble();
radius = gRadius.getDouble();
cylVol = pi * radius * radius * length;
result.setText("The volume of the cylinder is: " +
cylVol);
}
}
mLength = new TextField(9);
mLength.setText("length:");
gRadius = new DoubleField(10);
gLength = new DoubleField(10);
result = new TextField(72);
result.setText("The volume of the cylinder is: " + cylVol);
bCompute = new Button("Compute");
bCompute.addActionListener(this);
}
add(instruct) ;
add(mRadius) ;
add(gRadius) ;
add(mLength) ;
add(gLength) ;
add(bCompute) ;
add(result) ;
CylVol.java
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Installment-based Purchase Calculation
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Suppose you are going to buy a car on the installment plan
 You want to know monthly payments by clicking a button
 Variables: principal, rate, payment, balance
 ButCompound.java
Iteration by Button Pushing
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Often need to repeat a calculation with minor changes
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Sometimes refine previous solution
Sometimes calculate successive values in series
Can do this under control of a button
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import awb.*;
import java.awt.*;
import java.awt.event.*;
public void actionPerformed(ActionEvent event)
{
Object cause = event.getSource();
public class ButCompound extends java.applet.Applet
implements ActionListener
{
TextField mInstruct, mBalance;
DoubleField gRate, gPrinc, gPay;
IntField gMonths;
Button bStart, bNextInstallment;
double rate, princ, pay, balance;
int months;
if (cause == bStart)
{
princ = gPrinc.getDouble();
rate = gRate.getDouble()/12;
pay = gPay.getDouble();
months = 0;
balance = princ;
public void init()
{
mInstruct = new TextField(80);
mInstruct.setText("Enter principal, rate, payment, " +
"then press Start");
gPrinc = new DoubleField(10);
gRate = new DoubleField(10);
gPay = new DoubleField(10);
mBalance = new TextField(80);
bStart = new Button("Start");
bNextInstallment = new Button("Next Installment");
bStart.addActionListener(this);
bNextInstallment.addActionListener(this);
}
add(mInstruct);
add(gPrinc);
add(gRate);
add(gPay);
add(bStart);
add(bNextInstallment);
add(mBalance);
mInstruct.setText("Press Next Installment for next Balance");
mBalance.setText("After " + months + " months at " +
100*rate*12 + "% and payments of " +
pay + " the balance is " + balance);
}
if (cause == bNextInstallment)
{
months = months + 1;
balance = balance*(1.0 + rate) - pay;
}
}
}
mBalance.setText("After " + months + " months at " +
100*rate*12 + "% and payments of " +
pay + " the balance is " + balance);
ButCompound.java
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Table of contents
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Let’s calculate some numbers
Some Calculations
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Looping and a Study of Functions
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Storing Information in Arrays
Simple Statistics Program Design
Putting Things on Array
Summary
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IDB Lab.
Java Control Flow Statements
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The Looping statements
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You use a while or do-while or for statement to continually execute a block
of statements while a condition remains true.
The general syntax of the while statement is:
while (expression)
{
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}
statement(s)
Example:
int sum = 0;
int k = 0;
while (k < 100)
{
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}
k = k + 1;
sum = sum + k;
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The Looping Statements
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do
{
The general syntax of the do-while :
statement(s)
} while (expression);
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The for statement provides a compact way to iterate over a range of values.
The general form of the for statement:
for (initialization; termination; increment)
{
}
statement(s)
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IDB Lab.
Searching the best value:
CylinderVolumeMax
1,000 square cm of tin:
How to make a largest
possible cylindrical can?
Find such radius
Find such volume
Figure 3.1
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Searching the best value:
CylinderVolumeMax
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Volume V = Pi * r * r * h
Area
A = 2 * Pi * r * r + 2 * Pi * r * h = 1000
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If we remove h from V
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V = 500 * r - Pi * r * r * r
Start with r =1 cm
Keep going by increasing r by 1 until V becomes maximum
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Figure 3.4
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Figure 3.5
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Figure 3.6
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CylinderVolumeMax Algorithm
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Set r at some starting value.
Decide how much r should be increased each cycle
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Mostly given by the user
Algorithm
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Initialize previous V at zero.
Find V.
Repeat the following:
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(1)
(2)
(3)
(4)
if V < previousV, stop loop
increase r by some amount
save V in a place called “previousV”.
find V
After looping, Previous V is supposed to have Max Volume
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IDB Lab.
CylinderVolumeMax.Java
import awb.*;
import java.awt.*;
import java.awt.event.*;
public class CylinderVolumeMax extends java.applet.Applet implements ActionListener
{
double
r, previousV, increase, V;
DoubleField rF, increaseF, VF;
Button
b1;
public void init ()
{
rf = new DoubleField(20);
rf.setLabel(“Radius”);
increaseF = new DoubleField(20);
increaseF.setLabel(“increase”);
b1 = new Button(“Compute”);
b1.addActionListener(20);
add(rF) ;
add(increaseF) ;
add(b1) ;
add(VF) ;
}
rF.setDouble(1.0);
increaseF.setDouble(0.01);
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IDB Lab.
CylinderVolumeMax.Java
Pubic void actionPerformed(ActionEvent event)
{ Object cause = event.getSource();
if (cause == b1)
{r
= rF.getDouble();
increase = increaseF.getDouble();
previousV = 0;
V = 500 * r – 3.14159 * r * r * r;
while(V >= previousV)
{
r += increase;
previousV = V;
V = 500 * r – 3.14159 * r * r * r;
}
VF.setDouble(previousV);
}
}
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One last thing to consider
in searching the best value!
Local-Maxima Loophole
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Another Looping examples
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Computing Interests
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CompInterest.java
Wild Card Bonus (WCB-1)!
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Submit 5 page report explaining the following code
Diamond.java
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IDB Lab.
import awb.*;
import java.awt.*;
import java.awt.event.*;
public void actionPerformed(ActionEvent event)
{
Object cause = event.getSource();
public class CompInterest extends java.applet.Applet
implements ActionListener
{
TextField mInstruct, mBalance;
DoubleField gRate, gPrinc, gPay;
Button bCompute;
IntField gMonths;
double rate, princ, pay, balance;
int months, k;
public void init()
{
mInstruct = new TextField(80);
mInstruct.setText("Enter principal, rate, payment, " +
"#months; then press 'Compute'");
gPrinc = new DoubleField(10);
gRate = new DoubleField(10);
gPay = new DoubleField(10);
gMonths = new IntField(10);
bCompute = new Button("Compute");
mBalance = new TextField(80);
bCompute.addActionListener(this);
add(mInstruct);
add(gPrinc);
add(gRate);
add(gPay);
add(gMonths);
add(bCompute);
add(mBalance);
}
}
}
if (cause == bCompute)
{
princ = gPrinc.getDouble();
rate = gRate.getDouble()/12;
pay = gPay.getDouble();
months = gMonths.getInt();
balance = princ;
k = 0;
while (k < months)
{
balance = balance*(1.0 + rate) - pay;
k = k + 1;
}
mBalance.setText("After " + months + " months at " +
100*rate*12 + "% and payments of " +
pay + " the balance is " + balance);
}
CompInterest.java
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IDB Lab.
import java.awt.*;
import java.awt.event.*;
public void actionPerformed(ActionEvent event)
{
Object cause = event.getSource();
public class Diamond extends java.applet.Applet
implements ActionListener
{
TextField tf;
TextArea ta;
Button bDraw;
String stars = "*******************";
String spaces = "
";
int k;
public void init()
{
tf = new TextField("Hello ");
ta = new TextArea(22, 20);
ta.setFont(new Font("Monospaced", Font.BOLD, 12));
bDraw = new Button("Draw");
bDraw.addActionListener(this);
add(tf);
add(bDraw);
add(ta);
}
}
}
if (cause == bDraw)
{
tf.setText("Goodbye");
k = 0;
while (k < 10)
{
ta.append(spaces.substring(0,10-k) +
stars.substring(0,2*k+1)+"\n");
k = k + 1;
}
k = 1;
while (k < 10)
{
ta.append(spaces.substring(0,1+k) +
stars.substring(0,19-2*k)+"\n");
k = k + 1;
}
}
Diamond.java
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IDB Lab.
Table of contents
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Let’s calculate some numbers
Some Calculations
Looping and a Study of Functions
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Storing Information in Arrays
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Simple Statistics Program Design
Putting Things on Array
Summary
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IDB Lab.
Concept of Array
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Holds multiple values of the same type
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Aggregate Data Types: set, bag, list
Deal with items of same type
The length of an array is established when the array is created
(at runtime)
After creation, an array is a fixed-length structure
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IDB Lab.
Motivations of Arrays
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Analogies
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mailboxes in Post Office
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CD rack with slots
Advantages
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Simplifies naming of similar objects
Allows use of loops
Useful for statistical problems and numerical problems
The most fundament data structure in computer science for constructing
other advanced data structures
Many other kinds of data structures are built by “Array”
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List
Matrix
Stack
Queue
Binary Tree
And so on
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IDB Lab.
Declaring an Array in Java
int anArray[];
anArray = new int[10];
int[] anArray;
anArray = new int[10];
=
=
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int anArray[10];
SNU
IDB Lab.
Creating and using an Array
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To get the size of an array, you write
arrayname.length
This is a member-variable. Not a function (not length() ) !
int[] anArray;
// declare an array of integers
anArray = new int[10]; // create an array of integers
// assign a value to each array element
for (int i = 0; i < anArray.length; i++) {
anArray[i] = i;
}
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IDB Lab.
Some more on Array
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shortcut syntax for creating and initializing an array.
boolean[] answers = { true, false, true, true, false };
int[] primeNumsBelowTen = { 2, 3, 5, 7 };
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Setting up an array
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Declaration: double weights[ ];
Definition:
weights = new double[50];
Or Combined:
double weights[ ] = new double[50];
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IDB Lab.
Array Creation and Use
int k = 2;
while(k<6)
{ num[k] = k*k;
k = k+1;
}
int num[ ] = new int[6];
?
0
?
1
?
2
?
3
?
4
?
5
?
num[1] = 21; num[5] = 13;
?
21
?
0
1
2
?
3
?
4
13
0
21
1
4
9
16
25
2
3
4
5
5
** Real Array Example
Hotel.java: A hotel has room[500] which are all “0” in the
beginning. If a guest registers a particular room P, the value of
room[p] is changed to the number of guests. Whenever a new
guest registers a room, the message about the room occupancy
comes up.
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IDB Lab.
import awb.*;
import java.awt.*;
import java.awt.event.*;
public void actionPerformed(ActionEvent event)
{
Object cause = event.getSource();
public class Hotel extends java.applet.Applet
implements ActionListener
{
TextField mInstruct, mHotelCensus;
IntField gRoomNo, gNoGuests;
Button bRegister;
int k=0, totGuests = 0, noOccupied = 0, roomNo, noGuests;
int room[];
public void init()
{
room = new int[500];
k = 0;
while (k < 500)
{
room[k] = 0;
k = k + 1;
}
mInstruct = new TextField(60);
mInstruct.setText("Enter room number, number of guests, "+
"then press Register");
gRoomNo = new IntField(6);
gNoGuests = new IntField(6);
bRegister = new Button("Register");
mHotelCensus = new TextField(60);
bRegister.addActionListener(this);
add(mInstruct);
add(gRoomNo);
add(gNoGuests);
add(bRegister);
add(mHotelCensus);
}
}
}
if (cause == bRegister)
{
roomNo = gRoomNo.getInt();
noGuests = gNoGuests.getInt();
if (room[roomNo] != 0)
{
mHotelCensus.setText("That room is occupied!");
}
else
{
room[roomNo] = noGuests;
totGuests = totGuests + noGuests;
noOccupied = noOccupied + 1;
mHotelCensus.setText("There are " + totGuests +
" occupying " + noOccupied + " rooms.");
}
}
Hotel.java
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IDB Lab.
Table of contents

Let’s calculate some numbers
Some Calculations
Looping and a Study of Functions
Storing Information in Arrays

Simple Statistics Program Design





Putting Things on Array
Summary
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IDB Lab.
Simple Statistics Program Design
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Algorithms for Maximum, Minimum, and Mean in the
context of array
Array Statistics Example
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ArrayStats.java
Wild Card Bonus (WCB-2)

Submit a 5 page report explaining ArrayStats.Java
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IDB Lab.
import awb.*;
import java.awt.*;
import java.awt.event.*;
public class ArrayStats extends java.applet.Applet
implements ActionListener
{
TextField mInstruct, mAnswer;
IntField iCount;
double list[];
Button bStore, bShow, bExtremes, bMean, bClear;
int count, nextFree, nextUse;
double mean(double[] list, int size) {
int k = 0;
double sum = 0.0;
while (k < size) {
sum = sum + list[k];
k = k + 1;
}
return sum/size;
}
double max(double[] list, int size) {
int k = 1;
double largest = list[0];
while (k < size) {
if (list[k] > largest) {
largest = list[k];
}
k = k + 1;
}
return largest;
}
double min(double[] list, int size) {
int k = 1;
double smallest = list[0];
while (k < size) {
if (list[k] < smallest) {
smallest = list[k];
}
k = k + 1;
}
return smallest;
}
public void init()
{
list = new double[100];
mInstruct = new TextField(70);
mAnswer = new TextField(70);
mInstruct.setText("Enter Value, then press Store button");
iCount = new IntField(10);
bStore = new Button("Store");
bShow = new Button("Show");
bExtremes = new Button("Extremes");
bMean = new Button("Mean");
bClear = new Button("Clear");
nextFree = 0;
nextUse = 0;
bStore.addActionListener(this);
bShow.addActionListener(this);
bExtremes.addActionListener(this);
bMean.addActionListener(this);
bClear.addActionListener(this);
add(mInstruct);
add(iCount);
add(bStore);
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}
add(bShow);
add(bExtremes);
add(bMean);
add(bClear);
add(mAnswer);
public void actionPerformed(ActionEvent event)
{
int value, total;;
Object cause = event.getSource();
if (cause == bStore)
{
value = iCount.getInt();
list[nextFree] = value;
nextFree = nextFree + 1;
iCount.setInt(); // clear IntField
}
if (cause == bShow)
{
}
mAnswer.setText("The value in element "+nextUse+" is "+
}
list[nextUse]);
nextUse = (nextUse + 1)% nextFree;
}
if (cause == bExtremes)
{
mAnswer.setText("The largest data item is " +
max(list, nextFree) +
" and the smallest data item is " +
min(list, nextFree));
}
if (cause == bMean)
{
mAnswer.setText("The average is " + mean(list, nextFree)
}
if (cause == bClear)
{
nextUse = 0;
nextFree = 0;
mAnswer.setText("The old data has been cleared out");
}
ArrayStats.java (cont’d)
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Table of contents

Let’s calculate some numbers
Some Calculations
Looping and a Study of Functions
Storing Information in Arrays
Simple Statistics Program Design

Putting Things on Array

Summary




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Advanced discussion:
Putting things in an Array

An unending chain of bins than extends off into infinity
?
?
?
?
?


The question of whether there are enough bins to hold all the elements of a set of objects
If we can succeed with a set, the set is countable
If countable  computable  solvable  decidable

What about the set of positive numbers


1

2
3
4
5

What about the set of positive and negative integers
-1
1
-2
2
-3

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Advanced discussion:
Uncomputability




Let’s consider: the functions that input a positive integer and yields a
positive integer cannot be put in a row
No matter how one tries to squeeze them all into bins, there will
always be huge numbers more that will not fit
The notion of uncountable set
This is an important property with great implications for computer
science  uncomputability
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Figure 3.9
• Let’s call the function that accept positive numbers as input and yield
positive integers as output PIPO type function
• Let’s assume the set of PIPO type functions is countable
• If the assumption is true, all PIPO type functions would be put into bins
successfully
• That means no left-overs.
But …..
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Figure 3.10
** However, Consider the new function constructed as in Figure 3.10
** The new function is definitely different from existing functions
and definitely PIPO type function
** But it was not in the bin!
** The set of PIPO type functions is uncountable!
** The notion of uncountable set leads to uncomputability! (chap 15)SNU
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IDB Lab.
Table of contents







Let’s Calculate some Numbers
Some Calculations
Looping and a Study of Functions
Storing Information in Arrays
Simple Statistics Program Design
Putting Things on Array
Summary
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Summary



This chapter has discussed many aspects of numerical computation
We covered many Java constructs through sample programs
“Integers” are not adequate for general numerical computation




Even “Double” data type has round-off errors
Looping programs are frequent
Arrays were useful
Putting things into an array is simple job

but can lead to a discussion of uncomputability
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

Ch3: Mumerical Computation & Function
Textbook Review Time
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