Transcript Arrays

Arrays
Chapter 8
Fall 2006
CS 101
Aaron Bloomfield
1
Introduction to arrays
2
Background
 Programmer often need the ability to represent a group of
values as a list
 List may be one-dimensional or multidimensional
 Java provides arrays and the collection classes
 The Vector class is an example of a collection class
 Consider arrays first
3
Example
 Definitions
char[] c;
int[] value = new int[10];
 Causes
 Array object variable c is un-initialized
 Array object variable value references a new ten element
list of integers
 Each of the integers is default initialized to 0
c
value
0
0
0
0
…
0
4
An array example
int[] v = new int[10];
int i = 7;
int j = 2;
int k = 4;
v[0] = 1;
v[i] = 5;
v[j] = v[i] + 3;
v[j+1] = v[i] + v[0];
v[v[j]] = 12;
System.out.println(v[2]);
v[k] = stdin.nextInt();
v
8 is displayed
Suppose
3 is extracted
0
1
0
0
8
0
6
0
3
0
0
0
5
12
0
0
v[0]
v[1]
v[2]
v[3]
v[4]
v[5]
v[6]
v[7]
v[8]
v[9]
5
Array variable definition styles
 Without initialization
ElementType [ ] id;
Brackets
Name of
Type of
list
values in indicate array
variable being
list
defined
int [] a;
int a[];
6
Array variable definition styles
 With initialization
Nonnegative integer expression specifying the
number of elements in the array
ElementType [ ] id = new ElementType [n];
A new array of n
elements
7
Where we’ve seen arrays
 public static void main (String[] args)
 Thus, the main() method takes in a String array as the
parameter
 Note that you can also define it as:
 public static void main (String args[])
 or
 public static void main (String[] foobar)
8
Basic terminology
 List is composed of elements
 Elements in a list have a common name
 Example: a[3] = 5;
 The common name is ‘a’
 The list as a whole is referenced through the common name
 List elements are of the same type — the base type
 Elements of a list are referenced by subscripting (indexing) the
common name
9
Java array features
 Subscripts are denoted as expressions within brackets: [ ]
 Base (element) type can be any type
 Size of array can be specified at run time
 This is different that pure C! (for the most part, at least)
 Index type is integer and the index range must be 0 ... n-1
 Where n is the number of elements
 Just like Strings indexing!
 Automatic bounds checking
 Ensures any reference to an array element is valid
 Data field length specifies the number of elements in the list
 Array is an object
 Has features common to all other objects
 More on this later…
11
New 2005 demotivatiors!
12
Consider
 Segment
int[] b = new int[100];
b[-1] = 0;
b[100] = 0;
 Causes
 Array variable to reference a new list of 100 integers
 Each element is initialized to 0
 Two exceptions to be thrown
 -1 is not a valid index – too small
 100 is not a valid index – too large
 IndexOutOfBoundsException
13
Consider
Point[] p = new Point[3];
p[0] = new Point(0, 0);
p[1] = new Point(1, 1);
p[2] = new Point(2, 2);
p[0].setX(1);
p[1].setY(p[2].getY());
Point vertex = new Point(4,4);
p[1] = p[0];
vertex
p[2] = vertex;
p
p[0]
p[1]
p[2]
null
null
null
Point: (1,
(0, 0)
Point: (4, 4)
Point: (1, 2)
1)
Point: (2, 2)
14
Explicit initialization
 Syntax
id references an array of n elements. id[0] has
value exp0, id[1] has value exp1, and so on.
ElementType []
id = {
exp0 , exp1 , ... expn-1 } ;
Each expi is an expression that
evaluates to type ElementType
15
Explicit initialization
 Example
String[] puppy = { “pika”, “mila”, “arlo”,
“nikki” };
int[] unit = { 1 };
 Equivalent to
String[] puppy = new String[4];
puppy[0] = “pika";
puppy[1] = “mila";
puppy[2] = “arlo";
puppy[3] = “nikki";
int[] unit = new int[1];
unit[0] = 1;
16
Array members
 Member length
 Size of the array
for (int i = 0; i < puppy.length; ++i) {
System.out.println(puppy[i]);
}
 Note that length is a field, not a method!
 I.e., it is not puppy.length()
17
Array members
 Member clone()
 Produces a shallow copy
Point[] u = { new Point(0, 0), new Point(1, 1)};
Point[] v = u.clone();
v[1] = new Point(4, 30);
u[0]
u[1]
u
Point: (0, 0)
v
Point: (1, 1)
Point: (4, 30)
18
v[0]
v[1]
Array members
 Member clone()
 Produces a shallow copy
Point[] u = { new Point(0, 0), new Point(1, 1)};
Point[] v = u.clone();
v[1].setX(10);
u[0]
u[1]
u
Point: (0, 0)
(1, 1)1)
Point: (10,
v
19
v[0]
v[1]
Making a deep copy
 We want to copy the array and all the objects each element
of the array references
 This is called a deep copy
 Example
Point[] w = new Point[u.length];
for (int i = 0; i < u.length; ++i) {
w[i] = (Point) u[i].clone();
}
20
Making a deep copy
u[0]
u[1]
u[2]
u
Point: (0, 0)
w[0]
w[1]
Point: (2, 1)
Point: (2, 2)
Point: (2, 1)
Point: (2, 2)
w[2]
w
Point: (0, 0)
21
Review of arrays
 Creating an array:
int[] foo = new int[10];
 Accessing an array:
foo[3] = 7;
System.out.print (foo[1]);
 Creating an array:
String[] bar = new String[10];
 Accessing an array:
bar[3] = “qux”;
System.out.println (bar[1]);
22
How Java represents arrays
 Consider
int[] a = { 1, 2, 3, 4, 5 };
Array
- length = 5
a
- data =
1
1
2
2
3
4
3
5
4
5
+…
23
More about how Java represents Arrays
 Consider
int[] a;
int[] b = null;
int[] c = new int[5];
int[] d = { 1, 2, 3, 4, 5 };
a = c;
d = c;
a
-
b
null
c
0
0
0
0
0
d
1
2
3
4
5
24
How are we
doing with arrays?
a)
b)
c)
d)
e)
Very well! This stuff is so easy.
With a little review, I’ll be good.
Not very well at all.
I’m so lost. What’s an array again?
I’d rather not answer this question, thanks.
25
ArrayTools
27
ArrayTools.java
 We want to create a series of general utility methods to be
used for arrays
 We will put these into an ArrayTools class
28
ArrayTools.java – outline
public class ArrayTools {
// class constant
private static final int MAX_LIST_SIZE = 1000;
// sequentialSearch(): examine unsorted list for key
public static int sequentialSearch(int[] data, int key) { ...
// putList (): prints list to screen
public static void putList(int[] data) { ...
// getList(): extract and return up to MAX_LIST_SIZE values
public static int[] getList() { ...
// reverse(): reverses the order of the element values
public static void reverse(int[] list) { ...
// binarySearch(): examine sorted list for a key
public static int binarySearch(char[] data, char key) { ...
}
29
ArrayTools.java method putList()
 To print the array:
public static void putList(int[] data) {
for (int i = 0; i < data.length; ++i) {
System.out.println(data[i]);
}
}
 Consider
int[] score = { 6, 9, 82, 11, 29, 85, 11, 28, 91 };
putList(score);
30
ArrayTools.java method getList()
public static int[] getList() {
Scanner stdin = new Scanner (System.in);
int[] buffer = new int[MAX_LIST_SIZE];
int listSize = 0;
for (int i = 0; (i < MAX_LIST_SIZE) &&
stdin.hasNext(); ++i) {
buffer[i] = stdin.nextInt();
++listSize;
}
int[] data = new int[listSize];
for (int i = 0; i < listSize; ++i) {
data[i] = buffer[i];
}
return data;
}
31
ArrayTools.java method reverse()
public static void reverse(int[] data) {
int[] clone = data.clone();
for ( int i = 0; i < clone.length; ++i ) {
data[i] = clone[clone.length-1-i];
}
}
 Consider
int[] foo = { 1, 2, 3, 4, 5 };
reverse (foo);
putList (foo);
32
ArrayDemo.java
public class ArrayDemo {
// main(): application entry point
public static void main(String[] args) {
System.out.println ("");
System.out.println ("Enter list of integers:");
int[] numbers = ArrayTools.getList ();
System.out.println ("");
System.out.println ("Your list");
ArrayTools.putList (numbers);
ArrayTools.reverse
System.out.println
System.out.println
ArrayTools.putList
System.out.println
(numbers);
("");
("Your list in reverse");
(numbers);
();
}
}
33
ArrayTools demo…

ArrayDemo.java
35
How are we
doing with ArrayTools?
a)
b)
c)
d)
e)
Very well! This stuff is so easy.
With a little review, I’ll be good.
Not very well at all.
I’m so lost. What’s an array again?
I’d rather not answer this question, thanks.
36
Today’s demotivators
37
… main (String args[])
38
Consider that main() method again
 public static void main (String args[])
 How does one pass in a parameter to the main method?
public class MainParameters {
public static void main (String args[]) {
System.out.println ("Number of paramters to “ +
"main(): " + args.length);
if ( args.length > 0 ) {
for ( int i = 0; i < args.length; i++ )
System.out.println ("parameter " +
i + ": '" + args[i] + "'");
}
}
39
}
Program Demo

MainParameters.java


Via JCreator
Via the command line
40
Basic array searching
41
Searching for a value
System.out.println("Enter search value (number): ");
int key = stdin.nextInt();
int i;
for (i
i = 0
0; i < data.length
data.length; ++i
++i) {
if (key == data[i]) {
break;
}
}
0
1
2
data
4
9
5
key
5
i
0
1
2
if (i != data.length) {
System.out.println(key + " is the " + i
+ "-th element");
}
else {
System.out.println(key + " is not in the list");42
}
Searching for the minimum value
 Segment
int minimumSoFar = sample[0];
for (int i = 1; i < sample.length; ++i) {
if (sample[i] < minimumSoFar) {
minimumSoFar = sample[i];
}
}
43
ArrayTools.java method sequentialSearch()
public static int sequentialSearch(int[] data, int key) {
for (int i = 0; i < data.length; ++i) {
if (data[i] == key) {
return i;
}
}
key
11
return -1;
}
data
0
1
2
3
4
5
6
7
8
6
9
82
11
29
85
11
29
91
 Consider
int[] score = { 6, 9, 82, 11, 29, 85, 11, 28, 91 };
int i1 = sequentialSearch(score, 11);
44
int i2 = sequentialSearch(score, 30);
How are we
doing with searching?
a)
b)
c)
d)
e)
Very well! This stuff is so easy.
With a little review, I’ll be good.
Not very well at all.
I’m so lost. What’s a search again?
I’d rather not answer this question, thanks.
45
A solution to commenting your
code

The commentator:
http://www.cenqua.com/commentator/
46
Sorting
47
Sorting
 Problem
 Arranging elements so that they are ordered according to
some desired scheme
 Standard is non-decreasing order
 Why don't we say increasing order?
 Major tasks
 Comparisons of elements
 Updates or element movement
48
Selection sorting
 Algorithm basis
 On iteration i, a selection sorting method:
 Finds the element containing the ith smallest value of
its list v and exchanges that element with v[i]
 Example – iteration 0
 Swaps smallest element with v[0]
 This results in smallest element being in the correct place
for a sorted result
v
0
1
2
3
4
5
6
‘Q'
'E'
'W'
‘E'
'Q'
'R'
'T'
'Y'
'U'
7
'I'
8
9
'O'
'P'
49
Selection sorting
 Algorithm basis
 On iteration i, a selection sorting method:
 Finds the element containing the ith smallest value of
its list v and exchanges that element with v[i]
 Example – iteration 1
 Swaps second smallest element with v[1]
 This results in second smallest element being in the
correct place for a sorted result
v
0
1
2
3
4
5
6
7
8
9
'E'
'W'
'I'
'Q'
'R'
'T'
'Y'
'U'
'I'
'W'
'O'
'P'
50
Selection sorting
 Algorithm basis
 On iteration i, a selection sorting method:
 Finds the element containing the ith smallest value of
its list v and exchanges that element with v[i]
 Example – iteration 2
 Swaps third smallest element with v[2]
 This results in third smallest element being in the correct
place for a sorted result
0
v
'E'
1
'I'
2
3
4
5
6
7
8
9
'Q'
‘O'
'R'
'T'
'Y'
'U'
'W'
'O'
‘Q'
'P'
51
Selection sorting
 Algorithm basis
 On iteration i, a selection sorting method:
 Finds the element containing the ith smallest value of
its list v and exchanges that element with v[i]
 Example – iteration 3
 Swaps fourth smallest element with v[3]
 This results in fourth smallest element being in the correct
place for a sorted result
0
v
'E'
1
'I'
2
3
4
5
6
7
8
9
‘O'
'R'
‘P'
'T'
'Y'
'U'
'W'
‘Q'
'P'
‘R'
52
Selection sorting
 Algorithm basis
 On iteration i, a selection sorting method:
 Finds the element containing the ith smallest value of
its list v and exchanges that element with v[i]
 Example – iteration 4
 Swaps fifth smallest element with v[4]
 This results in fifth smallest element being in the correct
place for a sorted result
0
v
'E'
1
'I'
2
3
4
5
6
7
8
9
‘O'
‘P'
'T'
‘Q'
'Y'
'U'
'W'
‘Q'
‘T'
‘R'
53
ArrayTools.java selection sorting
public static void selectionSort(int[] v) {
for (int i = 0; i < v.length-1; ++i) {
// find the location of the ith smallest element
int spot = i;
for (int j = i+1; j < v.length; ++j) {
if (v[j] < v[spot]) { // is current location ok?
// update spot to index of smaller element
spot = j;
}
}
// spot is now correct, so swap elements
int rmbr = v[i];
v[i] = v[spot];
v[spot] = rmbr;
}
}
54
Iteration i
// find the location of the ith smallest element
int spot = i;
for (int j = i+1; j < v.length; ++j) {
if (v[j] < v[spot]) // is spot ok?
// update spot with index of smaller element
spot = j;
}
// spot is now correct, swap elements v[spot] and v[i]
55
How are we
doing with sorting?
a)
b)
c)
d)
e)
Very well! This stuff is so easy.
With a little review, I’ll be good.
Not very well at all.
I’m so lost. What’s a sort again?
I’d rather not answer this question, thanks.
56
Very unofficial demotivators
57
Binary search
58
Binary search
 Given a list, find a specific element in the list
 List MUST be sorted!
 Each time it iterates through, it cuts the search
space in half
 A binary search is MUCH faster than a sequential
search
59
Binary search use
The ‘BS’ in BSDemo is for Binary Search, mind you

public class BSDemo {
public static void main(String[] args) {
int[] numbers = { 9, 3, 1, 8, 4, 6, 10, 2 };
System.out.println ("The original list of numbers:");
ArrayTools.putList(numbers);
System.out.println();
ArrayTools.selectionSort(numbers);
System.out.println ("The sorted list of numbers:");
ArrayTools.putList(numbers);
System.out.println();
System.out.println
System.out.println
System.out.println
System.out.println
System.out.println
System.out.println
System.out.println
("Searching
("Searching
("Searching
("Searching
("Searching
("Searching
("Searching
for
for
for
for
for
for
for
0: " + ArrayTools.binarySearch(numbers, 0));
1: " + ArrayTools.binarySearch(numbers, 1));
4: " + ArrayTools.binarySearch(numbers, 4));
5: " + ArrayTools.binarySearch(numbers, 5));
6: " + ArrayTools.binarySearch(numbers, 6));
10: " + ArrayTools.binarySearch(numbers, 10));
11: " + ArrayTools.binarySearch(numbers, 11));
}
}
60
Binary search use demo…

BSDemo.java
61
Binary search
public static int binarySearch (int[] data, int key) {
int i = 0;
// left endpoint of search interval
int j = data.length-1; // right endpoint of search interval
while ( i < j ) {
int m = (i+j)/2;
if ( key > data[m] ) {
i = m+1;
} else {
j = m;
}
}
if ( key == data[i] ) {
return i;
} else {
return -1;
}
62
}
Binary search, take 1
public static int binarySearch (int[] data, int key) {
int i = 0;
int j = data.length-1;
data
i
while ( i < j ) {
int m = (i+j)/2;
if ( key > data[m] ) {
i = m+1;
} else {
j = m;
}
}
if ( key == data[i] ) {
return i;
} else {
return -1;
}
key
returns:
a0
a1
a2
a3
a4
a5
a6
a7
a8
a9
2
4
6
8
10
12
14
16
18
20
0
5
6
m
4
7
6
5
j
9
7
6
14
6
63
Binary search
 But what if the element is not in the list?
64
Binary search, take 2
public static int binarySearch (int[] data, int key) {
int i = 0;
int j = data.length-1;
data
i
while ( i < j ) {
int m = (i+j)/2;
if ( key > data[m] ) {
i = m+1;
} else {
j = m;
}
}
if ( key == data[i] ) {
return i;
} else {
return -1;
}
key
returns:
a0
a1
a2
a3
a4
a5
a6
a7
a8
a9
2
4
6
8
10
12
14
16
18
20
0
5
7
m
4
7
6
j
9
7
15
-1
65
How are we
doing with binary search?
a)
b)
c)
d)
e)
Very well! This stuff is so easy.
With a little review, I’ll be good.
Not very well at all.
I’m so lost. What’s a search again?
I’d rather not answer this question, thanks.
66
Binary search
 A somewhat alternative view of what a binary search does…
67
How long does a binary search take?
 Given a array of 64 elements
 1st iteration cuts the array to 32
 2nd iteration cuts the array to 16
 3rd to 8
 4th to 4
 5th to 2
 6th to 1
 Given a array of 1024 elements
 1st iteration cuts the array to 512
 ...
 10th iteration cuts the list to 1 element
 Thus, the binary search takes log2 n iterations!
 Where n is the size of the array
68
Binary search vs. sequential search
 Assume the array has n elements
 Sequential search takes n iterations to find the element
 Binary search takes log2 n iterations to find the element
 Consider a list of 1 million elements
 Binary search takes about 20 iterations
 Sequential search takes 1,000,000 iterations
 Consider a list of 1 trillion elements
 Binary search takes about 40 iterations
 Sequential search takes 1,000,000,000,000 iterations
69
How are we
doing with binary search?
a)
b)
c)
d)
e)
Very well! This stuff is so easy.
With a little review, I’ll be good.
Not very well at all.
I’m so lost. What’s a search again?
I’d rather not answer this question, thanks.
70
Multi-dimensional arrays
72
Multidimensional arrays
 Many problems require information be organized as a twodimensional or multidimensional list
 Examples
 Matrices
 Graphical animation
 Economic forecast models
 Map representation
 Time studies of population change
 Microprocessor design
73
Example
 Segment
int[][] m = new int[3][];
m[0] = new int[4];
m[1] = new int[4];
m[2] = new int[4];
 Produces
m[0]
m
m[1]
m[2]
m[2][0]
m
0
m[0][0]
0
m[0][1]
When an array is
created, each
value is initialized!
0
m[0][2]
0
m[0][3]
m[2][1]
m[2][2]
m[2][3]
0
0
0
0
0
0
0
0
m[1][0]
m[1][1]
m[1][2]
m[1][3]
74
Example
 Alternative
int[][] m = new int[3][4];
 Produces
m[0]
m[1]
m[2]
m[2][0]
m
0
m[0][0]
0
m[0][1]
0
m[0][2]
0
m[0][3]
m[2][1]
m[2][2]
m[2][3]
0
0
0
0
0
0
0
0
m[1][0]
m[1][1]
m[1][2]
m[1][3]
75
Multidimensional array visualization
 A multi-dimensional array declaration (either one):
int[][] m = new int[3][4];
 How we visualize it:
0
0
0
0
0
0
0
0
0
0
0
0
or
0
0
0
0
0
0
0
0
0
0
0
0
76
Example
 Segment
for (int c = 0; c < m.length; ++c) {
for (int r = 0; r < m[c].length; ++r) {
System.out.print("Enter a value: ");
m[c][r] = stdin.nextInt();
}
}
0
0
0
0
0
0
0
0
0
0
0
0
77
Rows by columns or columns by rows?
 Consider int[][] m = new int[3][4];
 Is that 3 rows by 4 columns or 3 columns by 4 rows?
0
0
0
0
0
0
0
0
0
0
0
0
or
0
0
0
0
0
0
0
0
0
0
0
0
 The answer is that it can be either
 As long as you are consistent with your column/row
78
placement
Rows by columns or columns by rows?
 This makes it 3 columns by 4 rows:
for (int c = 0; c < m.length; ++c)
for (int r = 0; r < m[c].length; ++r) {
System.out.print("Enter a value: ");
m[c][r] = stdin.nextInt();
}
 This makes it 3 rows by 4 columns:
for (int r = 0; r < m.length; ++r)
for (int c = 0; c < m[r].length; ++c) {
System.out.print("Enter a value: ");
m[r][c] = stdin.nextInt();
}
79
Today’s demotivators
80
Example
 Segment
String[][]
s[0] = new
s[1] = new
s[2] = new
s[3] = new
 Produces
s[0]
s = new String[4][];
String[2];
String[2];
String[4];
String[3];
s[1]
s[2]
s[3]
null
null null
s[3][0] s[3][1] s[3][2]
s
null
null null
null
s[2][0] s[2][1] s[2][2] s[2][3]
null null
s[0][0] s[0][1]
null
null
81
s[1][0] s[1][1]
Multidimensional array visualization
 Segment
String[][]
s[0] = new
s[1] = new
s[2] = new
s[3] = new
 Produces
s = new String[4][];
String[2];
String[2];
String[4];
String[3];
0
0
0
0
0
0
0
0
0
0
or
0
0
0
0
0
0
0
0
0
0
0
 Called a “ragged”
array
0
82
Explicit Initialization
 Segment
int c[][] = {{1, 2}, {3, 4}, {5, 6}, {7, 8, 9}};
 Produces
c[0]
c[1]
c[2]
7
c[3]
8
9
c[3][0] c[3][1] c[3][2]
c
5
6
c[2][0] c[2][1]
1
2
c[0][0] c[0][1]
3
4
c[1][0] c[1][1]
83
Matrices
 A two-dimensional array is sometimes known as a matrix
because it resembles that mathematical concept
 A matrix a with m rows and n columns is represented
mathematically in the following manner
a1  1 a 1 2  a 1 n
a2  1 a 2 2  a 2 n


am  1 a m 2  a m n
84
Matrix addition
 Definition C = A + B
 cij = aij + bij
 cij is sum of the elements in the same row and column of
A and B
85
Matrix addition
public static double[][] add(double[][] a, double[][] b) {
// determine number of rows in solution
int m = a.length;
// determine number of columns in solution
int n = a[0].length;
// create the array to hold the sum
double[][] c = new double[m][n];
// compute the matrix sum row by row
for (int i = 0; i < m; ++i) {
// produce the current row
for (int j = 0; j < n; ++j) {
c[i][j] = a[i][j] + b[i][j];
}
}
return c;
}
86
Homework J9
 You will be creating a Board class
 The Board class contains a 2-D array
 In each spot will be a Ship object
 (from a previous HW)
 Lab 11 is going to be a MapPrinter class
 Will print out the 2-D Board via text
87
How are we
doing with 2-D arrays?
a)
b)
c)
d)
e)
Very well! This stuff is so easy.
With a little review, I’ll be good.
Not very well at all.
I’m so lost. What’s an array again?
I’d rather not answer this question, thanks.
88
DeCSS: The program
#include<stdlib.h> typedef unsigned int uint; char
ctb[512]="33733b2663236b763e7e362b6e2e667bd393db0643034b96de9ed60b4e0e4\
69b57175f82c787cf125a1a528fca8ac21fd999d10049094190d898d001480840913d7d35246\
d2d65743c7c34256c2c6475dd9dd5044d0d4594dc9cd4054c0c449559195180c989c11058185\
081c888c011d797df0247074f92da9ad20f4a0a429f53135b86c383cb165e1e568bce8ec61bb\
3f3bba6e3a3ebf6befeb6abeeaee6fb37773f2267276f723a7a322f6a2a627fb9f9b1a0e9a9e\
1f0b8f8b0a1e8a8e0f15d1d5584cd8dc5145c1c5485cc8cc415bdfdb5a4edade5f4bcfcb4a5e\
cace4f539793120692961703878302168286071b7f7bfa2e7a7eff2bafab2afeaaae2ff"; typedef
unsigned char uchar;uint tb0[11]={5,0,1,2,3,4,0,1,2,3,4};uchar* F=NULL; uint lf0,lf1,out;void
ReadKey(uchar* key){int i;char hst[3]; hst[2]=0;if(F==\
NULL){F=malloc(256);for(i=0;i<256;i++){hst[0]=ctb[2*i];hst[1]=ctb[2*i+1];F[i]=\
strtol(hst,NULL,16);}}out=0;lf0=(key[1]<<9)|key[0]|0x100;lf1=(key[4]<<16)|(key\
[3]<<8)|key[2];lf1=((lf1&0xfffff8)<<1)|(lf1&0x7)|0x8;}uchar Cipher(int sw1,\ int sw2){int
i,a,b,x=0,y=0;for(i=0;i<8;i++){a=((lf0>>2)^(lf0>>16))&1;b=((lf1\
>>12)^(lf1>>20)^(lf1>>21)^(lf1>>24))&1;lf0=(lf0<<1)|a;lf1=(lf1<<1)|b;x=(x>>1)\
|(a<<7);y=(y>>1)|(b<<7);}x^=sw1;y^=sw2;return out=(out>>8)+x+y;} void \
CSSdescramble(uchar *sec,uchar *key){uint i;uchar *end=sec+0x800;uchar KEY[5];
for(i=0;i<5;i++)KEY[i]=key[i]^sec[0x54+i];ReadKey(KEY);sec+=0x80;while(sec!=\
end)*sec++=F[*sec]^Cipher(255,0);}void CSStitlekey1(uchar *key,uchar *im) {uchar k[5];int i;
ReadKey(im);for(i=0;i<5;i++)k[i]=Cipher(0,0);for(i=9;i>=0;\ i-)key[tb0[i+1]]=k[tb0[i+1]]^F[key[tb0[i+1]]]^key[tb0[i]];}void CSStitlekey2\ (uchar *key,uchar
*im){uchar k[5];int i;ReadKey(im);for(i=0;i<5;i++)k[i]=\ Cipher(0,255);for(i=9;i>=0;i-)key[tb0[i+1]]=k[tb0[i+1]]^F[key[tb0[i+1]]]^key\ [tb0[i]];}void CSSdecrypttitlekey(uchar
*tkey,uchar *dkey){int i;uchar im1[6]; uchar
im2[6]={0x51,0x67,0x67,0xc5,0xe0,0x00};for(i=0;i<6;i++)im1[i]=dkey[i];
CSStitlekey1(im1,im2);CSStitlekey2(tkey,im1);}
89
DeCSS: The shirt (and tie!)
90
DeCSS: The poem
How to decrypt a
DVD: in haiku form.
(Thanks, Prof. D. S. T.)
------------------------
Table Zero is:
Five, zero, one, two, three, four,
oh, one, two, three, four.
(I abandon my
exclusive rights to make or
perform copies of
Table One is long:
two to the eighth power bytes.
Ready? Here they are:
this work, U. S. Code
Title Seventeen, section
One Hundred and Six.)
Muse! When we learned to
count, little did we know all
the things we could do
some day by shuffling
those numbers: Pythagoras
said "All is number"
long before he saw
computers and their effects,
or what they could do
Fifty one; then one
hundred fifteen; fifty nine;
thirty eight; ninety
nine; thirty five; one
hundred seven; one hundred
eighteen; sixty two;
one hundred twenty
six; fifty four; forty three;
one hundred ten; then
91
DeCSS: The number

The world’s first illegal prime number:
4856507896573978293098418946942861377074420873513579240196520736686985134010472
3744696879743992611751097377770102744752804905883138403754970998790965395522701
1712157025974666993240226834596619606034851742497735846851885567457025712547499
9648219418465571008411908625971694797079915200486670997592359606132072597379799
3618860631691447358830024533697278181391479795551339994939488289984691783610018
2597890103160196183503434489568705384520853804584241565482488933380474758711283
3959896852232544608408971119771276941207958624405471613210050064598201769617718
0947811362200272344827224932325954723468800292777649790614812984042834572014634
8968547169082354737835661972186224969431622716663939055430241564732924855248991
2257394665486271404821171381243882177176029841255244647445055834628144883356319
0272531959043928387376407391689125792405501562088978716337599910788708490815909
7548019285768451988596305323823490558092032999603234471140776019847163531161713
0785760848622363702835701049612595681846785965333100770179916146744725492728334
8691600064758591746278121269007351830924153010630289329566584366200080047677896
7984382090797619859493646309380586336721469695975027968771205724996666980561453
3820741203159337703099491527469183565937621022200681267982734457609380203044791
2277498091795593838712100058876668925844870047077255249706044465212713040432118
2610103591186476662963858495087448497373476861420880529443
92
DeCSS: The images
93
DeCSS: The recordings

All this info from
http://www-2.cs.cmu.edu/~dst/DeCSS/Gallery/

Or do a Google search for “decss gallery”
94
DeCSS: The movie
95
Vector class
This is also the review
for the third midterm
96
Limitations of arrays
 You can’t change their size once created
 This can be a big problem!
 So



we will create a new class that will operate like an array:
We can store and get elements by index number
It will automatically increase in size as needed
And other fancy features…
 Let’s call the class Vector
 As we are basically writing the java.util.Vector class
97
Properties of our Vector class
 It needs to have an array to hold the values
 As our internal array will often be bigger than the number of
elements in the Vector, we need a size as well
 More on what this means in a slide or two…
 Not much else…
98
Methods in our Vector class




Insert and remove elements into the Vector
Get an element from the Vector
Find the length
Print it out to the screen
 What happens when the array field is full, and we want to add
an element?
 We will need to increase the size of the array
 So we need a method to do that as well
99
Our first take on our Vector class
public class Vector {
private Object array[];
private int size = 0;
Vector() {
array = new Object[100];
}
Vector(int length) {
array = new Object[length];
}
}

What does this mean?
 We’ll see that a bit later…
 But briefly, it means the array can store any object
100
Adding an element to our Vector
public void add (Object o) {
array[size++] = o;
}
 Pretty easy!
 But what if the array is full?
 We need a way to increase the capacity of the array
101
Increasing the Vector’s array’s capacity
private void increaseCapacity() {
int oldSize = array.length;
Object newArray[] = new Object[2*oldSize];
for ( int i = 0; i < oldSize; i++ )
newArray[i] = array[i];
array = newArray;
}

And our new add() method:
public void add (Object o) {
if ( size == array.length )
increaseCapacity();
array[size++] = o;
}
102
Methods can be private as well
 Notice that the increaseCapacity() method is called only by
the add() method when necessary
 It’s not ever going to be called by whomever is using our
Vector
 Thus, we will make it private
 That means that only other Vector methods can call it
103
Removing an element from a Vector
public Object remove (int which) {
Object ret = array[which];
for ( int i = which; i < array.length-1; i++ )
array[i] = array[i+1];
array[array.length-1] = null;
size--;
return ret;
}
104
Miscellaneous other methods
public int size() {
return size;
}
public Object get (int which) {
return array[which];
}
105
Today’s demotivators
106
Our toString() method
public String toString() {
String ret = "[";
for ( int i = 0; i < size; i++ ) {
ret += array[i];
if ( i != size-1 )
ret += ", ";
}
ret += "]";
return ret;
}
107
Using our Vector

This code is in a separate class called VectorUsage
public static void main (String[] args) {
Vector v = new Vector();
for ( int i = 12; i < 30; i++ ) {
v.add (String.valueOf(i));
}
System.out.println (v);
System.out.println (v.size());
String s = (String) v.get(5);
System.out.println (s);
v.remove (5);
System.out.println (v);
v.remove (5);
System.out.println (v);
}
108
Program Demo

VectorUsage.java
109
The “real” Vector class
 Java provides a Vector class
 In java.util
 It contains all of the methods shown
110
Program Demo

VectorUsage.java

But using java.util.Vector
111
What about those errors?
 When compiled with java.util.Vector, we see:
 Note: C:\...\VectorUsage.java uses unchecked or
unsafe operations.
 Note:
Recompile
with
-Xlint:unchecked
for
details.
 You can ignore these
 They deal with generics (aka templates), which you will
see in future courses
 The program was still compiled
112
More on using the Vector class
 To add a String object s to the end of a Vector v
 v.add(s);
 To get the String object at the end of the Vector v
 String s = (String) v.get(v.size()-1);
 To remove a String object from the end of a Vector v
 String s = (String) v.remove(v.size()-1);
 This both removes the object from the Vector and stores
the removed value into s
113
How are we
doing with Vectors?
a)
b)
c)
d)
e)
Very well! This stuff is so easy.
With a little review, I’ll be good.
Not very well at all.
I’m so lost. What’s an array again?
I’d rather not answer this question, thanks.
114
Wrapper classes
116
But what about adding variables?
 The add method takes an Object as a parameter
 public void add (Object o) {
 Although we haven’t seen it yet, this means you can add
any object you want to the vector
 Primitive types (i.e. variables) are not objects
 How can they be added?
 The solution: wrapper classes!
117
The Integer wrapper class
 This is how you add an int variable to a Vector:
int x = 5;
Integer i = new Integer(x);
vector.add (i);
//…
Integer j = (Integer) v.get(0);
int y = j.intValue();
 Pretty annoying syntax – we’ll see how to get around it in a
bit…
118
More on wrapper classes
 All the primitive types have wrapper classes
 Usually, the names are just the capitalized version of the
type
 I.e. Double for double, Byte for byte, etc.
 Two exceptions: int and char
 int has Integer
 char has Character
119
More on wrapper classes
 Consider this code:
int x = 5;
vector.add (x);
//…
int y = vector.get(0);
 Does this code work?
 It shouldn’t
 As we are adding a variable (not an object) to a vector
 But it does work!
 Why?
120
Auto-boxing
 Java 1.5 will automatically “wrap” a primitive value into it’s
wrapper class when needed
 And automatically “unwrap” a wrapper object into the
primitive value
 So Java translates the previous code into the following:
int x = 5;
vector.add (new Integer(x));
//…
int y = ((Integer)vector.get(0)).intValue();
 This is called autoboxing
 And auto-unboxing (unauto-boxing?)
 This does not work in Java 1.4 or before
121
More on auto-boxing
 Consider the following code:
Double d = 7.5;
Double e = 6.5;
Double f = d + e;
System.println (f);
 This is doing a lot of auto-boxing (and auto-unboxing):
Double d = new Double(7.5);
Double e = new Double(6.5);
Double f = newDouble(d.doubleValue() +
e.doubleValue());
System.println (f);
122
How are we
doing with Wrapper classes?
a)
b)
c)
d)
e)
Very well! This stuff is so easy.
With a little review, I’ll be good.
Not very well at all.
I’m so lost. What’s Java again?
I’d rather not answer this question, thanks.
123
Star Wars Episode 3 Trailer
124
Star Wars Episode 3 Trailer

That was a edited version
– I changed the PG-rated trailer to a G-rated
trailer

The original one can be found at
http://www.sequentialpictures.com/
– Or Google for “star wars parody”
125