1. Arrays
Continued

2. Considered int[] v = new int[10]; int i = 7; int j = 2; int k = 4;
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 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

3. Considered Array members length
clone()
Deep versus shallow
Point[] u = { new Point(0, 0), new Point(1, 1)};

4. Considered Array members length clone()
Deep versus shallow
Point[] v = (Point[]) u.clone();

5. Considered Array members length Point[] v = new Point[u.length];;
clone()
Deep versus shallow
Point[] v = new Point[u.length];;
for (int i = 0; i < u.length; ++i) {
w[i] = (Point) u[i].clone(); }

6. Searching for a value
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");

7. Searching for a value
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");

8. Searching for a value
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");

9. Searching for a value
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");

10. Searching for a value
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");

11. Searching for a value
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");

12. Searching for a value
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");

13. Searching for a value
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");

14. Searching for a value
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");

15. Searching for a value
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");

16. Searching for a value
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");

17. Searching for a value
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");

18. Searching for a value
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");

19. 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!

20. 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.

21. ArrayTools.java method putList()
public static void putList(int[] data) {
for (int i = 0; i < data.length; ++i) {
System.out.print(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.

22. 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; ++i) {
if (stdin.hasNext()) {
buffer[i] = stdin.nextInt();
++listSize; }
else {
break;
int[] data = new int[listSize];
for (int i = 0; i < listSize; ++i) {
data[i] = buffer[i];
return data;
ArrayTools.java method getList()

23. ArrayTools.java – outline
In java.util
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(): produces a string representation
public static void putList(int[] data) { ...
// getList(): extract and return up to MAX_LIST_SIZE values
public static int[] getList() throws IOException { ...
// 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) { ... }

24. Demo.java import java.io.*; public class Demo {
// main(): application entry point
public static void main(String[] args) throws IOException {
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(); }

26. 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].

27. 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

28. 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

29. 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

30. 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

31. ArrayTools.java selection sorting
public static void selectionSort(char[] 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
char 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.

32. 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[0]
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.

33. 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.

34. When an array is created, each value is initialized!
Example
Consider
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!

35. Example
Alternative
int[][] m = new int[3][4];
Produces

36. Multidimensional array visualization
A multi-dimensional array declaration (either one):
int[][] m = new int[3][4];
Has two views or

37. Example Consider 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(); }

38. Example Consider String[][] s = new String[4][]; s[0] = new String[2];
Produces

39. Multidimensional array ragged arrays
Consider
int[][] s = new int[4][];
s[0] = new int[2];
s[1] = new int[2];
s[2] = new int[2];
s[3] = new int[2];
Produces or

40. Example Consider int c[][] = {{1, 2}, {3, 4}, {5, 6}, {7, 8, 9}};
Produces

41. 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

42. 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

43. 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;