1. Chapter 8 Fall 2006 CS 101 Aaron Bloomfield
Arrays
Chapter 8
Fall 2006
CS 101
Aaron Bloomfield

2. Introduction to arrays

3. 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

4. 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 can only reference char arrays
v can only reference int arrays
value - c …

5. 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();
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();
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();
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();
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();
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();
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();
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();
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();
Suppose 3 is extracted
8 is displayed
int i = 7;
int j = 2;
int k = 4;
v[0] = 1; // element 0 of v given value 1
v[i] = 5; // element i of v given value 5
v[j] = v[i] + 3; // element j of v given value
// of element i of v plus 3
v[j+1] = v[i] + v[0]; // element j+1 of v given value
// of element i of v plus
// value of element 0 of v
v[v[j]] = 12; // element v[j] of v given
// value 12
System.out.println(v[2]); // element 2 of v is displayed
v[k] = stdin.nextInt();
// element k of v given next
// extracted value

6. Array variable definition styles
Without initialization
ElementType
[ ]
id;
Type of
values in
list
Brackets
indicate array
variable being
defined
Name of
list
int [] a;
int a[];

7. 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

8. 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)

9. 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

10. 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 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…
More robust than arrays in most programming languages

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
int[] b = new int[100]; // b has 100 elements: b[0], … b[99]
b[-1] = 0; // illegal: subscript too small
b[100] = 0; // illegal: subscript too large

13. Consider Point[] p = new Point[3]; p[0] = new Point(0, 0);
p[0].setX(1);
p[1].setY(p[2].getY());
Point vertex = new Point(4,4);
p[1] = p[0];
p[2] = vertex;
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];
p[2] = vertex;
Point: (1, 0) p
p[0]
p[1]
Point: (2, 2)
p[2]
vertex
Point: (4, 4)
Point: (1, 0) p
p[0]
p[1]
p[2]
vertex
Point: (4, 4)
Point: (1, 0) p
p[0]
p[1]
Point: (1, 2)
Point: (2, 2)
p[2]
vertex
Point: (4, 4)
Point: (1, 0) p
p[0]
p[1]
Point: (1, 1)
Point: (2, 2)
p[2]
Point: (1, 0) p
p[0]
p[1]
Point: (1, 2)
Point: (2, 2)
p[2] p
p[0]
p[1]
p[2]
null
Point: (0, 0) p
p[0]
p[1]
Point: (1, 1)
Point: (2, 2)
p[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
exp ,
exp ,
...
exp []
= { } ; 1 n -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);
Point[] u = { new Point(0, 0), new Point(1, 1)};
Point[] v = u.clone();
v[1] = new Point(4, 30);
Point: (0, 0) v
v[0]
v[1]
Point: (1, 1) u
u[0]
u[1]
Point: (4, 30)
Point: (0, 0) v
v[0]
v[1]
Point: (1, 1) u
u[0]
u[1]
Point: (0, 0)
Point: (1, 1) u
u[0]
u[1]

18. Array members Point[] u = { new Point(0, 0), new Point(1, 1)};
Point[] v = u.clone();
v[1].setX(10);
Member clone()
Produces a shallow copy
Point[] u = { new Point(0, 0), new Point(1, 1)};
Point[] v = u.clone();
v[1].setX(10);
Point: (0, 0) v
v[0]
v[1]
Point: (1, 1) u
u[0]
u[1]
Point: (0, 0) v
v[0]
v[1]
Point: (10, 1) u
u[0]
u[1]
Point: (0, 0)
Point: (1, 1) u
u[0]
u[1]

19. 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

21. Review of arrays Creating an array: int[] foo = new int[10];
Accessing an array:
foo[3] = 7;
System.out.print (foo[1]);
String[] bar = new String[10];
bar[3] = “qux”;
System.out.println (bar[1]);

22. How Java represents arrays
Consider
int[] a = { 1, 2, 3, 4, 5 };
+ …
Array
- length = 5
- data = 1 2 3 4 5 1 2 3 4 5 a

23. More about how Java represents Arrays
int[] a;
int[] b = null;
int[] c = new int[5];
int[] d = { 1, 2, 3, 4, 5 };
a = c;
d = c;
Consider
int[] a;
int[] b = null;
int[] c = new int[5];
int[] d = { 1, 2, 3, 4, 5 };
a = c;
d = c; a
c can only reference char arrays
v can only reference int arrays - b
null c 1 2 3 4 5 d

24. How are we doing with arrays?
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

26. 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

27. 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) { ... }

28. 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);
Method sequentialSearch() has two formal parameters—the first parameter is an int[] array data and the second parameter is the search value key.
Method sequentialSearch() is similar in form to the code segment that searched an array for a key value in Section . However, sequentialSearch() does not display a message indicating whether it found the value. If sequentialSearch() finds the key value in the array, it returns the subscript of the first matching element. If the key value is not among the array element values, sequentialSearch() returns the number of elements in the array. Because the array elements occupy subscript positions 0 through data.length-1 in the array, the value -1 indicates that the key value is not in the array.

29. 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;

30. 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);
Method sequentialSearch() has two formal parameters—the first parameter is an int[] array data and the second parameter is the search value key.
Method sequentialSearch() is similar in form to the code segment that searched an array for a key value in Section . However, sequentialSearch() does not display a message indicating whether it found the value. If sequentialSearch() finds the key value in the array, it returns the subscript of the first matching element. If the key value is not among the array element values, sequentialSearch() returns the number of elements in the array. Because the array elements occupy subscript positions 0 through data.length-1 in the array, the value -1 indicates that the key value is not in the array.

31. 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 ("Your list");
ArrayTools.putList (numbers);
ArrayTools.reverse (numbers);
System.out.println ("Your list in reverse");
System.out.println (); }

33. ArrayTools demo…
ArrayDemo.java

34. How are we doing with ArrayTools?
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.

35. Today’s demotivators

36. … main (String args[])

37. 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] + "'"); }

38. Program Demo
MainParameters.java
Via JCreator
Via the command line

39. Basic array searching

40. Searching for a value i = 0
System.out.println("Enter search value (number): ");
int key = stdin.nextInt();
int i;
if (key == data[i]) {
break;
if (i != data.length) {
System.out.println(key + " is the " + i + "-th element"); }
++i
System.out.println("Enter search value (number): ");
int key = stdin.nextInt();
int i;
for (i = 0; i < data.length; ++i) {
if (key == data[i]) {
break; }
if (i != data.length) {
System.out.println(key + " is the " + i + "-th element");
else {
System.out.println(key + " is not in the list");
i < data.length

41. 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]; }
The key value search code segment is typical of array processing. There is initialization to prepare for the processing of the array, a loop to process each array element in turn, and a check to see how the list processing completed. For example, the next code segment finds the minimum value of a list sample where the list size of sample is at least 1.
int minimumSoFar = sample[0];
for (int i = 1; i < sample.length; ++i) {
if (sample[i] < minimumSoFar) {
minimumSoFar = sample[i]; }
To find the minimum value in an array requires examining each element in turn. If the code segment keeps track of the minimum array element value seen so far, the lesser of that value and the current element is the minimum value seen so far. If this processing is done for each array element, then after the last array element has been considered, the minimum value seen so far is in fact the minimum. Observe that our code segment for finding the minimum of an arbitrarily sized list is even smaller than the code segment presented at the start of this chapter for finding the minimum of five values!

42. 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; }
return -1;
Consider
int[] score = { 6, 9, 82, 11, 29, 85, 11, 28, 91 };
int i1 = sequentialSearch(score, 11);
int i2 = sequentialSearch(score, 30);
Method sequentialSearch() has two formal parameters—the first parameter is an int[] array data and the second parameter is the search value key.
Method sequentialSearch() is similar in form to the code segment that searched an array for a key value in Section . However, sequentialSearch() does not display a message indicating whether it found the value. If sequentialSearch() finds the key value in the array, it returns the subscript of the first matching element. If the key value is not among the array element values, sequentialSearch() returns the number of elements in the array. Because the array elements occupy subscript positions 0 through data.length-1 in the array, the value -1 indicates that the key value is not in the array.

43. How are we doing with searching?
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.

44. A solution to commenting your code
The commentator:

45. Sorting

46. 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
Chapter introduced the notion of sorting in SortTwo.java and SortThree.java, which respectively displayed two and three input values in nondecreasing order. We used the term nondecreasing rather than increasing to allow for duplicate values. Here we consider the general sorting problem of arranging the values in a list of arbitrary size into nondecreasing order.
A sort is often an iterative process such that each iteration rearranges some of the values in the list v to be sorted. For example, on iteration i the method known as selectionSort() finds the element containing the ith smallest value of its list v and exchanges that element with v[i]. As another example, on iteration i the method known as insertionSort() correctly places the value of v[i] with respect to the values stored in elements v[0] through v[i-1].

47. 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
'Q'
'E'
'W'
'Y'
'R'
'T'
'I'
'U'
'P'
'O' 2 1 5 3 4 7 6 9 8 v
‘E'
‘Q'
'W'
'Y'
'R'
'T'
'I'
'U'
'P'
'O' 2 1 5 3 4 7 6 9 8 v
‘E'
‘Q'
'W'
'Y'
'R'
'T'
'I'
'U'
'P'
'O' 2 1 5 3 4 7 6 9 8

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 1
Swaps second smallest element with v[1]
This results in second smallest element being in the correct place for a sorted result v
'Q'
'E'
'I'
'Y'
'R'
'T'
'W'
'U'
'P'
'O' 2 1 5 3 4 7 6 9 8 v
'Q'
'E'
'W'
'Y'
'R'
'T'
'I'
'U'
'P'
'O' 2 1 5 3 4 7 6 9 8

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 2
Swaps third smallest element with v[2]
This results in third smallest element being in the correct place for a sorted result v
‘O'
'E'
'I'
'Y'
'R'
'T'
'W'
'U'
'P'
‘Q' 2 1 5 3 4 7 6 9 8 v
'Q'
'E'
'I'
'Y'
'R'
'T'
'W'
'U'
'P'
'O' 2 1 5 3 4 7 6 9 8

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 3
Swaps fourth smallest element with v[3]
This results in fourth smallest element being in the correct place for a sorted result v
‘O'
'E'
'I'
'Y'
‘P'
'T'
'W'
'U'
‘R'
‘Q' 2 1 5 3 4 7 6 9 8 v
‘O'
'E'
'I'
'Y'
'R'
'T'
'W'
'U'
'P'
‘Q' 2 1 5 3 4 7 6 9 8

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 4
Swaps fifth smallest element with v[4]
This results in fifth smallest element being in the correct place for a sorted result v
‘O'
'E'
'I'
'Y'
‘P'
‘Q'
'W'
'U'
‘R'
‘T' 2 1 5 3 4 7 6 9 8 v
‘O'
'E'
'I'
'Y'
‘P'
'T'
'W'
'U'
‘R'
‘Q' 2 1 5 3 4 7 6 9 8

52. 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;
In analyzing a sorting algorithm, software developers are concerned normally with the total number of element comparisons and the total number of element copies/assignments performed by the sort. When i is 0 for selectionSort(), there are n – 1 element comparisons and 3 element copies/assignments, where n is the number of elements in array v. When i is 1, there are n – 2 element comparisons and 3 element copies/assignments. When i is 2, there are n – 3 element comparisons and 3 element copies/assignments. In general, on iteration i, there are n – (i + 1) element comparisons and 3 element copies/ assignments.
The total number of element comparisons is therefore n – 1 + n – 2 + … , which is proportional to n2. The total number of element copies/assignments is at most … + 3, which is proportional to n. Because the number of element comparisons is proportional to the square of the number of elements, we say that method selectionSort() has quadratic performance with respect to element comparisons. Because the number of element copies/assignments is proportional to the number of elements, we say that the algorithm has linear performance with respect to element copies/assignments. Because n2 > n, we say that overall algorithm performs a quadratic number of element operations.

53. 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]
The code is similar to our other array processing code. In particular, the code is most similar to the code that searches an array. The code segment begins defining int index variable guess. Variable guess represents where we believe the ith smallest element can be found. The definition initializes guess to i. The code segment then determines whether the value of guess is correct. The for loop body repeatedly tests whether v[j] < v[guess], with j iteratively taking on the values i + 1 through v.length - 1.
If it is determined that v[j] < v[guess], then our value for guess is wrong and it is updated with the value of j. At this point, guess is the index of the smallest value among elements v[i] through v[j]. Thus, completing the for loop assures that guess is the index of the ith smallest element.

54. How are we doing with sorting?
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.

55. Very unofficial demotivators

56. Binary search

57. 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

58. 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:");
System.out.println ("Searching for 0: " + ArrayTools.binarySearch(numbers, 0));
System.out.println ("Searching for 1: " + ArrayTools.binarySearch(numbers, 1));
System.out.println ("Searching for 4: " + ArrayTools.binarySearch(numbers, 4));
System.out.println ("Searching for 5: " + ArrayTools.binarySearch(numbers, 5));
System.out.println ("Searching for 6: " + ArrayTools.binarySearch(numbers, 6));
System.out.println ("Searching for 10: " + ArrayTools.binarySearch(numbers, 10));
System.out.println ("Searching for 11: " + ArrayTools.binarySearch(numbers, 11)); }

59. Binary search use demo…
BSDemo.java

60. 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;
return -1;

61. Binary search, take 1
public static int binarySearch (int[] data, int key) {
int i = 0;
int j = data.length-1;
int i = 0;
int j = data.length-1;
while ( i < j ) {
int m = (i+j)/2;
if ( key > data[m] ) {
i = m+1;
} else {
j = m; }
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; }
if ( key == data[i] ) {
return i;
} else {
return -1; }
key 14
returns: 6 a0 a1 a2 a3 a4 a5 a6 a7 a8 a9 2 4 6 8 10 12 14 16 18 20
data i 6 5 m 4 6 5 7 j 6 7 9

62. Binary search
But what if the element is not in the list?

63. Binary search, take 2
public static int binarySearch (int[] data, int key) {
int i = 0;
int j = data.length-1;
int i = 0;
int j = data.length-1;
while ( i < j ) {
int m = (i+j)/2;
if ( key > data[m] ) {
i = m+1;
} else {
j = m; }
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; }
if ( key == data[i] ) {
return i;
} else {
return -1; }
key 15
returns: -1 a0 a1 a2 a3 a4 a5 a6 a7 a8 a9 2 4 6 8 10 12 14 16 18 20
data i 7 5 m 4 7 6 j 9 7

64. How are we doing with binary search?
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.

65. Binary search
A somewhat alternative view of what a binary search does…

66. 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

67. 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

68. How are we doing with binary search?
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.

69. Multi-dimensional arrays

70. Multidimensional arrays
Many problems require information be organized as a two-dimensional or multidimensional list
Examples
Matrices
Graphical animation
Economic forecast models
Map representation
Time studies of population change
Microprocessor design
In addition to defining one-dimensional arrays, it is also possible to define multidimensional arrays. There are a great many problems whose solutions can be determined through the manipulation of multidimensional arrays. The application domains include matrices, graphical animation, economic forecast models, map representation, time studies of population change, and microprocessor design to name just a few.

71. When an array is created, each value is initialized!
Example
Segment
int[][] m = new int[3][];
m[0] = new int[4];
m[1] = new int[4];
m[2] = new int[4];
Produces
When an array is created, each value is initialized!
m[0]
m[1]
m[2]
m[2][0]
m[2][1]
m[2][2]
m[2][3]
m[0][0]
m[0][1]
m[0][2]
m[0][3]
m[1][0]
m[1][1]
m[1][2]
m[1][3] m m

72. Example Alternative int[][] m = new int[3][4]; Produces m m[0] m[1]
m[2][0]
m[2][1]
m[2][2]
m[2][3]
m[0][0]
m[0][1]
m[0][2]
m[0][3]
m[1][0]
m[1][1]
m[1][2]
m[1][3]

73. Multidimensional array visualization
A multi-dimensional array declaration (either one):
int[][] m = new int[3][4];
How we visualize it: or

74. 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(); }

75. 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?
The answer is that it can be either
As long as you are consistent with your column/row placement or

76. 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) {
m[r][c] = stdin.nextInt();

77. Today’s demotivators

78. Example Segment String[][] s = new String[4][]; s[0] = new String[2];
Produces

79. Multidimensional array visualization
Segment
String[][] s = new String[4][];
s[0] = new String[2];
s[1] = new String[2];
s[2] = new String[4];
s[3] = new String[3];
Produces
Called a “ragged” array or

80. Explicit Initialization
Segment
int c[][] = {{1, 2}, {3, 4}, {5, 6}, {7, 8, 9}};
Produces

81. 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

82. Matrix addition cij = aij + bij
Definition C = A + B
cij = aij + bij
cij is sum of the elements in the same row and column of A and B

83. 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;

84. 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

85. How are we doing with 2-D arrays?
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.

86. DeCSS: The program
#include<stdlib.h> typedef unsigned int uint; char ctb[512]="33733b b763e7e362b6e2e667bd393db b96de9ed60b4e0e4\ 69b57175f82c787cf125a1a528fca8ac21fd999d d898d d7d35246\ d2d65743c7c34256c2c6475dd9dd5044d0d4594dc9cd4054c0c c989c \ 081c888c011d797df f92da9ad20f4a0a429f53135b86c383cb165e1e568bce8ec61bb\ 3f3bba6e3a3ebf6befeb6abeeaee6fb37773f f723a7a322f6a2a627fb9f9b1a0e9a9e\ 1f0b8f8b0a1e8a8e0f15d1d5584cd8dc5145c1c5485cc8cc415bdfdb5a4edade5f4bcfcb4a5e\ cace4f b7f7bfa2e7a7eff2bafab2afeaaae2ff"; 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);}

87. DeCSS: The shirt (and tie!)

88. DeCSS: The poem How to decrypt a DVD: in haiku form.
(Thanks, Prof. D. S. T.)
(I abandon my
exclusive rights to make or
perform copies of
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
Table Zero is:
Five, zero, one, two, three, four,
oh, one, two, three, four.
Table One is long:
two to the eighth power bytes.
Ready? Here they are:
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

89. DeCSS: The number The world’s first illegal prime number:

90. DeCSS: The images

91. DeCSS: The recordings
All this info from
Or do a Google search for “decss gallery”

92. DeCSS: The movie

93. This is also the review for the third midterm
Vector class
This is also the review
for the third midterm

94. 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

95. 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…

96. 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

97. 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

98. 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

99. 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;

100. 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

101. 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; }

102. Miscellaneous other methods
public int size() {
return size; }
public Object get (int which) {
return array[which];

103. Today’s demotivators

104. 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;

105. 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);

106. Program Demo
VectorUsage.java

107. The “real” Vector class
Java provides a Vector class
In java.util
It contains all of the methods shown

108. Program Demo
VectorUsage.java
But using java.util.Vector

109. 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

110. 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

111. How are we doing with Vectors?
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.

112. Wrapper classes

113. 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!

114. 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…

115. 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

116. 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?

117. 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

118. 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());

119. How are we doing with Wrapper classes?
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.

120. Star Wars Episode 3 Trailer

121. 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
Or Google for “star wars parody”