JavaYDL6

Chapter 6 Arrays

Liang, Introduction to Java Programming, Ninth Edition, (c) 2013 Pearson Education, Inc. All
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1

Opening Problem
Read one hundred numbers, compute their
average, and find out how many numbers are
above the average.

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Solution

AnalyzeNumbers Run

Run with prepared input

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3

Objectives
 To describe why arrays are necessary in programming (§6.1).
 To declare array reference variables and create arrays (§§6.2.1–6.2.2).
 To initialize obtain array size using arrayRefVar.length and know default the values
in an array (§6.2.3).
 To access array elements using indexed variables (§6.2.4).
 To declare, create, and initialize an array using an array initializer (§6.2.5).
 To program common array operations (displaying arrays, summing all elements,
finding the minimum and maximum elements, random shuffling, and shifting elements)
(§6.2.6).
 To simplify programming using the for-eachfor-each loops (§6.2.7).
 To apply arrays in the application development (LottoNumbers, DeckOfCards)
(§§6.3–6.4).
 To copy contents from one array to another (§6.5).
 To develop and invoke methods with array arguments and return values (§§6.6–6.78).
 To define a method with a variable-length argument list (§6.89).
 To search elements using the linear (§6.910.1) or binary (§6.910.2) search algorithm.
 To sort an array using the selection sort approach (§6.1011.1).
 To sort an array using the insertion sort approach (§6.1011.2).
 To use the methods in the java.util.Arrays class (§6.1112).

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Introducing Arrays
Array is a data structure that represents a collection of the
same types of data.
double[] myList = new double[10];

myList reference
myList[0] 5.6
myList[1] 4.5

Array reference myList[2] 3.3
variable
myList[3] 13.2

myList[4] 4
Array element at
myList[5] 34.33 Element value
index 5
myList[6] 34

myList[7] 45.45

myList[8] 99.993

myList[9] 11123

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5

Declaring Array Variables
 datatype[] arrayRefVar;

Example:
double[] myList;

 datatype arrayRefVar[]; // This style is
allowed, but not preferred
Example:
double myList[];

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Creating Arrays
arrayRefVar = new datatype[arraySize];

Example:
myList = new double[10];

myList[0] references the first element in the array.
myList[9] references the last element in the array.

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Declaring and Creating
in One Step
 datatype[] arrayRefVar = new
datatype[arraySize];

 datatype arrayRefVar[] = new
datatype[arraySize];
double myList[] = new double[10];

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The Length of an Array
Once an array is created, its size is fixed. It cannot be
changed. You can find its size using

arrayRefVar.length

For example,

myList.length returns 10

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Default Values
When an array is created, its elements are
assigned the default value of

0 for the numeric primitive data types,
'u0000' for char types, and
false for boolean types.

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10

Indexed Variables
The array elements are accessed through the index. The
array indices are 0-based, i.e., it starts from 0 to
arrayRefVar.length-1. In the example in Figure 6.1,
myList holds ten double values and the indices are
from 0 to 9.

Each element in the array is represented using the
following syntax, known as an indexed variable:

arrayRefVar[index];

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Using Indexed Variables
After an array is created, an indexed variable can
be used in the same way as a regular variable.
For example, the following code adds the value
in myList[0] and myList[1] to myList[2].

myList[2] = myList[0] + myList[1];

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Array Initializers
 Declaring, creating, initializing in one step:
double[] myList = {1.9, 2.9, 3.4, 3.5};

This shorthand syntax must be in one
statement.

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Declaring, creating, initializing
Using the Shorthand Notation
double[] myList = {1.9, 2.9, 3.4, 3.5};

This shorthand notation is equivalent to the
following statements:
myList[0] = 1.9;
myList[1] = 2.9;
myList[2] = 3.4;
myList[3] = 3.5;

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CAUTION
Using the shorthand notation, you
have to declare, create, and initialize
the array all in one statement.
Splitting it would cause a syntax
error. For example, the following is
wrong:
double[] myList;

myList = {1.9, 2.9, 3.4, 3.5};
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animation
Trace Program with Arrays
Declare array variable values, create an
array, and assign its reference to values

public class Test {
public static void main(String[] args) { After the array is created

int[] values = new int[5]; 0 0
for (int i = 1; i < 5; i++) { 1 0
values[i] = i + values[i-1]; 2 0

} 3 0

values[0] = values[1] + values[4]; 4 0

}
}

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animation
i becomes 1

public class Test {
public static void main(String[] args) {
After the array is created
int[] values = new int[5];
for (int i = 1; i < 5; i++) { 0 0


0
} 2

3 0
values[0] = values[1] + values[4]; 0
4
}
}

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animation
i (=1) is less than 5

public class Test {
After the array is created
for (int i = 1; i < 5; i++) { 0 0

} 2 0


4 0
}
}

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animation
After this line is executed, value[1] is 1

public class Test {
public static void main(String[] args) { After the first iteration

for (int i = 1; i < 5; i++) { 1 1


} 3 0


}
}

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animation

After i++, i becomes 2

public class Test {
int[] values = new int[5]; After the first iteration

for (int i = 1; i < 5; i++) {
0 0

} 2 0

3 0

}
}

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animation
i (= 2) is less than 5
public class Test {
public static void main(String[]
args) {
int[] values = new int[5]; After the first iteration

for (int i = 1; i < 5; i++) { 0 0

} 2 0

3 0
values[0] = values[1] + 4 0
values[4];
}
}

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animation
After this line is executed,
values[2] is 3 (2 + 1)

public class Test {
public static void main(String[] args) { After the second iteration

for (int i = 1; i < 5; i++) { 1 1


} 3 0


}
}

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animation
After this, i becomes 3.

public class Test {

for (int i = 1; i < 5; i++) { 1 1

} 3 0


}
}

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animation
i (=3) is still less than 5.

public class Test {

for (int i = 1; i < 5; i++) { 1 1

} 3 0


}
}

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animation
After this line, values[3] becomes 6 (3 + 3)

public class Test {
public static void main(String[] args) { After the third iteration

for (int i = 1; i < 5; i++) { 1 1


} 3 6


}
}

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animation
After this, i becomes 4

public class Test {

for (int i = 1; i < 5; i++) { 1 1


} 3 6


}
}

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animation
i (=4) is still less than 5

public class Test {

for (int i = 1; i < 5; i++) { 1 1


} 3 6


}
}

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animation
After this, values[4] becomes 10 (4 + 6)

public class Test {
public static void main(String[] args) { After the fourth iteration

for (int i = 1; i < 5; i++) { 1 1


} 3 6


}
}

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animation
After i++, i becomes 5

public class Test {
public static void main(String[] args)
{
for (int i = 1; i < 5; i++) {
After the fourth iteration
values[i] = i + values[i-1];
}
0 0
values[0] = values[1] + values[4]; 1
1
}
2 3
}
3 6

4 10

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animation

i ( =5) < 5 is false. Exit the loop

public class Test {
for (int i = 1; i < 5; i++) { After the fourth iteration
values[i] = i + values[i-1];
0
} 0

1 1

} 3 6

} 4 10

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animation
After this line, values[0] is 11 (1 + 10)

public class Test {
for (int i = 1; i < 5; i++) { 0 11


} 2 3


} 4 10

}

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31

Processing Arrays
See the examples in the text.
1. (Initializing arrays with input values)
2. (Initializing arrays with random values)
3. (Printing arrays)
4. (Summing all elements)
5. (Finding the largest element)
6. (Finding the smallest index of the largest element)
7. (Random shuffling)
8. (Shifting elements)

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Initializing arrays with input values
java.util.Scanner input = new java.util.Scanner(System.in);
System.out.print("Enter " + myList.length + " values: ");
for (int i = 0; i < myList.length; i++)
myList[i] = input.nextDouble();

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Initializing arrays with random values

for (int i = 0; i < myList.length; i++) {
myList[i] = Math.random() * 100;
}

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Printing arrays

System.out.print(myList[i] + " ");
}

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Summing all elements

double total = 0;
total += myList[i];
}

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Finding the largest element

double max = myList[0];
if (myList[i] > max) max = myList[i];
}

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Random shuffling
for (int i = 0; i < myList.length; i++) { myList
// Generate an index j randomly i [0]
int index = (int)(Math.random() [1]
* myList.length);
. swap
// Swap myList[i] with myList[index] .
double temp = myList[i]; .
myList[i] = myList[index]; [index]
myList[index] = temp;
A random index
}

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Shifting Elements
double temp = myList[0]; // Retain the first element

// Shift elements left myList
myList[i - 1] = myList[i];
}

// Move the first element to fill in the last position
myList[myList.length - 1] = temp;

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39

Enhanced for Loop (for-each loop)
JDK 1.5 introduced a new for loop that enables you to traverse the complete array
sequentially without using an index variable. For example, the following code
displays all elements in the array myList:

for (double value: myList)
System.out.println(value);

In general, the syntax is

for (elementType value: arrayRefVar) {
// Process the value
}

You still have to use an index variable if you wish to traverse the array in a
different order or change the elements in the array.

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40

Problem: Lotto Numbers
Suppose you play the Pick-10 lotto. Each ticket has
10 unique numbers ranging from 1 to 99. You buy
a lot of tickets. You like to have your tickets to
cover all numbers from 1 to 99. Write a program
that reads the ticket numbers from a file and checks
whether all numbers are covered. Assume the last
number in the file is 0.

Lotto Numbers Sample Data LottoNumbers Run

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Problem: Lotto Numbers
isCovered isCovered isCovered isCovered isCovered

false [0] true [0] true [0] true [0] true
[0]
[1] false [1] false [1] true [1] true [1] true

[2] false [2] false [2] false [2] true [2] true

[3] false [3] false [3] false [3] false [3] false

. . . . .

. . . . .

. . . . .

[97] [97] false [97] false [97] false [97] false
false
[98] [98] false [98] false [98] false [98] true
false

(a) (b) (c) (d) (e)

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42

Problem: Deck of Cards
The problem is to write a program that picks four cards
randomly from a deck of 52 cards. All the cards can be
represented using an array named deck, filled with initial
values 0 to 51, as follows:

int[] deck = new int[52];
// Initialize cards
for (int i = 0; i < deck.length; i++)
deck[i] = i;

DeckOfCards Run
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Problem: Deck of Cards, cont.
deck deck
0 [0] 0 [0] 6 Card number 6 is the
. . .
. 13 Spades (♠) . .
[1] 48 7 (6 % 13 = 6) of
[2] 11 Spades (7 / 13 is 0)
. . . [3] 24
12 [12] 12 Card number 48 is the
[4] .
13 [13] 13 10 (48 % 13 = 9) of
[5] .
. . . Clubs (48 / 13 is 3)
.
13 Hearts (♥)
. .
. . . .
. . . Card number 11 is the
Random shuffle . .
25 [25] 25 Queen (11 % 13 = 11) of
[25] .
26 [26] 26 Spades (11 / 13 is 0)
[26] .
. . .
13 Diamonds (♦)
. .
. . . Card number 24 is the
. .
. . . Queen (24 % 13 = 11) of
. .
38 [38] 38 Hearts (24 / 13 is 1)
[38] .
39 [39] 39 [39] .
. . . . .
. 13 Clubs (♣) . . . .
. . . . .
51 [51] 51 [51] .

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Problem: Deck of Cards, cont.
0 Ace
0 Spades 1 2
1 Hearts .
cardNumber / 13 =
2 Diamonds
cardNumber % 13 = .
3 Clubs
10 Jack

11 Queen

12 King

GUI Demo (picking four cards) DeckOfCards Run
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Problem: Deck of Cards
This problem builds a foundation for future more interesting and
realistic applications:

See Exercise 22.15.

Run 24 Point Game
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Copying Arrays
Often, in a program, you need to duplicate an array or a part of an
array. In such cases you could attempt to use the assignment statement
(=), as follows:

list2 = list1;
Before the assignment After the assignment
list2 = list1; list2 = list1;

list1 list1
Contents Contents
of list1 of list1

list2 list2
Contents Contents
of list2 of list2
Garbage

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Copying Arrays
Using a loop:
int[] sourceArray = {2, 3, 1, 5, 10};
int[] targetArray = new
int[sourceArray.length];

for (int i = 0; i < sourceArrays.length; i++)
targetArray[i] = sourceArray[i];

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The arraycopy Utility
arraycopy(sourceArray, src_pos,
targetArray, tar_pos, length);

Example:
System.arraycopy(sourceArray, 0,
targetArray, 0, sourceArray.length);

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Passing Arrays to Methods
public static void printArray(int[] array) {
for (int i = 0; i < array.length; i++) {
System.out.print(array[i] + " ");
}
}

Invoke the method

int[] list = {3, 1, 2, 6, 4, 2};
printArray(list);

Invoke the method
printArray(new int[]{3, 1, 2, 6, 4, 2});

Anonymous array

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Anonymous Array
The statement
printArray(new int[]{3, 1, 2, 6, 4, 2});

creates an array using the following syntax:
new dataType[]{literal0, literal1, ..., literalk};

There is no explicit reference variable for the array.
Such array is called an anonymous array.

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Pass By Value
Java uses pass by value to pass arguments to a method. There
are important differences between passing a value of variables
of primitive data types and passing arrays.

 For a parameter of a primitive type value, the actual value is
passed. Changing the value of the local parameter inside the
method does not affect the value of the variable outside the
method.

 For a parameter of an array type, the value of the parameter
contains a reference to an array; this reference is passed to the
method. Any changes to the array that occur inside the method
body will affect the original array that was passed as the
argument.
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Simple Example
public class Test {
int x = 1; // x represents an int value
int[] y = new int[10]; // y represents an array of int values

m(x, y); // Invoke m with arguments x and y

System.out.println("x is " + x);
System.out.println("y[0] is " + y[0]);
}

public static void m(int number, int[] numbers) {
number = 1001; // Assign a new value to number
numbers[0] = 5555; // Assign a new value to numbers[0]
}
}
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Call Stack
Stack Heap
Space required for
method m
int[] numbers:reference
The arrays are
int number: 1 0 stored in a
0 heap.
Space required for the
main method
int[] y: reference Array of
int x: 1 0 ten int
values is

When invoking m(x, y), the values of x and y are
passed to number and numbers. Since y contains the
reference value to the array, numbers now contains
the same reference value to the same array.

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Call Stack
Stack Heap
Space required for
method m
int[] numbers:reference
The arrays are
int number: 1001 5555 stored in a
0 heap.
main method
int[] y: reference Array of ten int
int x: 1 values is stored here
0

When invoking m(x, y), the values of x and y are
passed to number and numbers. Since y contains the
reference value to the array, numbers now contains
the same reference value to the same array.

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Heap
Heap

The arrays are
5555 stored in a
0 heap.
main method
int[] y: reference
int x: 1 0

The JVM stores the array in an area of memory,
called heap, which is used for dynamic memory
allocation where blocks of memory are allocated and
freed in an arbitrary order.
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Passing Arrays as Arguments

 Objective:Demonstrate differences of
passing primitive data type variables
and array variables.

TestPassArray Run

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Example, cont.
Stack Heap Stack
Space required for the swapFirstTwoInArray
swap method method
n2: 2 int[] array reference
n1: 1

Space required for the Space required for the
main method main method
int[] a reference int[] a reference
a[1]: 2
a[0]: 1
Invoke swap(int n1, int n2). Invoke swapFirstTwoInArray(int[] array).
The primitive type values in The arrays are The reference value in a is passed to the
a[0] and a[1] are passed to the stored in a swapFirstTwoInArray method.
swap method. heap.

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Returning an Array from a Method
public static int[] reverse(int[] list) {
int[] result = new int[list.length];

for (int i = 0, j = result.length - 1;
i < list.length; i++, j--) {
result[j] = list[i];
}
list
return result;
} result

int[] list1 = {1, 2, 3, 4, 5, 6};
int[] list2 = reverse(list1);

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animation

Trace the reverse Method
int[] list1 = {1, 2, 3, 4, 5, 6};
Declare result and create array

}

return result;
}

list 1 2 3 4 5 6

result 0 0 0 0 0 0

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animation

Trace the reverse Method, cont.
int[] list1 = {1, 2, 3, 4, 5, 6};
i = 0 and j = 5

}

return result;
}

list 1 2 3 4 5 6

result 0 0 0 0 0 0

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animation

int[] list1 = {1, 2, 3, 4, 5, 6};
i (= 0) is less than 6

}

return result;
}

list 1 2 3 4 5 6

result 0 0 0 0 0 0

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animation

int[] list1 = {1, 2, 3, 4, 5, 6};
i = 0 and j = 5
public static int[] reverse(int[] list) { Assign list[0] to result[5]

}

return result;
}

list 1 2 3 4 5 6

result 0 0 0 0 0 1

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animation

int[] list1 = {1, 2, 3, 4, 5, 6};

After this, i becomes 1 and j
public static int[] reverse(int[] list) { becomes 4

}

return result;
}

list 1 2 3 4 5 6

result 0 0 0 0 0 1

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animation

int[] list1 = {1, 2, 3, 4, 5, 6};

i (=1) is less than 6

}

return result;
}

list 1 2 3 4 5 6

result 0 0 0 0 0 1

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animation

int[] list1 = {1, 2, 3, 4, 5, 6};
i = 1 and j = 4
public static int[] reverse(int[] list) { Assign list[1] to result[4]

}

return result;
}

list 1 2 3 4 5 6

result 0 0 0 0 2 1

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animation

int[] list1 = {1, 2, 3, 4, 5, 6};
After this, i becomes 2 and
public static int[] reverse(int[] list) { j becomes 3

}

return result;
}

list 1 2 3 4 5 6

result 0 0 0 0 2 1

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animation

int[] list1 = {1, 2, 3, 4, 5, 6};

}

return result;
}

list 1 2 3 4 5 6

result 0 0 0 0 2 1

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animation

int[] list1 = {1, 2, 3, 4, 5, 6};
i = 2 and j = 3
public static int[] reverse(int[] list) { Assign list[i] to result[j]

}

return result;
}

list 1 2 3 4 5 6

result 0 0 0 3 2 1

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animation

int[] list1 = {1, 2, 3, 4, 5, 6};

}

return result;
}

list 1 2 3 4 5 6

result 0 0 0 3 2 1

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animation

int[] list1 = {1, 2, 3, 4, 5, 6};

}

return result;
}

list 1 2 3 4 5 6

result 0 0 0 3 2 1

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animation

int[] list1 = {1, 2, 3, 4, 5, 6};
i = 3 and j = 2

}

return result;
}

list 1 2 3 4 5 6

result 0 0 4 3 2 1

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animation

int[] list1 = {1, 2, 3, 4, 5, 6};

}

return result;
}

list 1 2 3 4 5 6

result 0 0 4 3 2 1

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animation

int[] list1 = {1, 2, 3, 4, 5, 6};

}

return result;
}

list 1 2 3 4 5 6

result 0 0 4 3 2 1

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animation

int[] list1 = {1, 2, 3, 4, 5, 6};
i = 4 and j = 1

}

return result;
}

list 1 2 3 4 5 6

result 0 5 4 3 2 1

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animation

int[] list1 = {1, 2, 3, 4, 5, 6};

}

return result;
}

list 1 2 3 4 5 6

result 0 5 4 3 2 1

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animation

int[] list1 = {1, 2, 3, 4, 5, 6};

}

return result;
}

list 1 2 3 4 5 6

result 0 5 4 3 2 1

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animation

int[] list1 = {1, 2, 3, 4, 5, 6};
i = 5 and j = 0

}

return result;
}

list 1 2 3 4 5 6

result 6 5 4 3 2 1

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animation

int[] list1 = {1, 2, 3, 4, 5, 6};
public static int[] reverse(int[] list) { j becomes -1

}

return result;
}

list 1 2 3 4 5 6

result 6 5 4 3 2 1

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animation

int[] list1 = {1, 2, 3, 4, 5, 6};
i (=6) < 6 is false. So exit
public static int[] reverse(int[] list) { the loop.

}

return result;
}

list 1 2 3 4 5 6

result 6 5 4 3 2 1

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animation

int[] list1 = {1, 2, 3, 4, 5, 6};
Return result

}

return result;
}

list 1 2 3 4 5 6

list2
result 6 5 4 3 2 1

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Problem: Counting Occurrence of Each
Letter

 Generate 100 lowercase (a) Executing
createArray in Line 6
(b) After exiting
createArray in Line 6

letters randomly and assign Stack Heap Stack Heap

to an array of characters. Space required for the
createArray method
Array of 100 Array of 100
characters characters
char[] chars: ref

 Count the occurrence of each Space required for the
main method
main method

letter in the array. char[] chars: ref char[] chars: ref

CountLettersInArray Run
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Searching Arrays
Searching is the process of looking for a specific element in
an array; for example, discovering whether a certain score is
included in a list of scores. Searching is a common task in
computer programming. There are many algorithms and
data structures devoted to searching. In this section, two
commonly used approaches are discussed, linear search and
binary search.
public class LinearSearch {
/** The method for finding a key in the list */
public static int linearSearch(int[] list, int key) {
for (int i = 0; i < list.length; i++)
if (key == list[i]) [0] [1] [2] …
return i; list
return -1;
} key Compare key with list[i] for i = 0, 1, …
}

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Linear Search
The linear search approach compares the key
element, key, sequentially with each element in
the array list. The method continues to do so
until the key matches an element in the list or
the list is exhausted without a match being
found. If a match is made, the linear search
returns the index of the element in the array
that matches the key. If no match is found, the
search returns -1.

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animation

Linear Search Animation
Key List
3 6 4 1 9 7 3 2 8
3 6 4 1 9 7 3 2 8

3 6 4 1 9 7 3 2 8

3 6 4 1 9 7 3 2 8

3 6 4 1 9 7 3 2 8

3 6 4 1 9 7 3 2 8
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animation
Linear Search Animation
http://www.cs.armstrong.edu/liang/animation/LinearSearc
hAnimation.html

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From Idea to Solution
/** The method for finding a key in the list */
public static int linearSearch(int[] list, int key) {
if (key == list[i])
return i;
return -1;
}

Trace the method
int[] list = {1, 4, 4, 2, 5, -3, 6, 2};
int i = linearSearch(list, 4); // returns 1
int j = linearSearch(list, -4); // returns -1
int k = linearSearch(list, -3); // returns 5
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Binary Search
For binary search to work, the elements in the
array must already be ordered. Without loss of
generality, assume that the array is in
ascending order.
e.g., 2 4 7 10 11 45 50 59 60 66 69 70 79
The binary search first compares the key with
the element in the middle of the array.

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Binary Search, cont.
Consider the following three cases:
 If the key is less than the middle element,
you only need to search the key in the first
half of the array.
 If the key is equal to the middle element,
the search ends with a match.
 If the key is greater than the middle
element, you only need to search the key in
the second half of the array.
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animation

Binary Search

Key List

8 1 2 3 4 6 7 8 9
8 1 2 3 4 6 7 8 9

8 1 2 3 4 6 7 8 9

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animation
Binary Search Animation
http://www.cs.armstrong.edu/liang/animation/BinarySearc
hAnimation.html

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91

key is 11 low mid high

key < 50 [0] [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12]
list 2 4 7 10 11 45 50 59 60 66 69 70 79
low mid high

[0] [1] [2] [3] [4] [5]
key > 7 list 2 4 7 10 11 45

low mid high

[3] [4] [5]
key == 11 list 10 11 45

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key is 54 Binary Search, cont.
low mid high

key > 50 [0] [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12]
list 2 4 7 10 11 45 50 59 60 66 69 70 79
low mid high

[0] [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12]
key < 66 list 59 60 66 69 70 79

low mid high

[7] [8]
key < 59 list 59 60

low high

[6] [7] [8]
59 60
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93

The binarySearch method returns the index of the
element in the list that matches the search key if it
is contained in the list. Otherwise, it returns

-insertion point - 1.

The insertion point is the point at which the key
would be inserted into the list.

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94

From Idea to Soluton
/** Use binary search to find the key in the list */
public static int binarySearch(int[] list, int key) {
int low = 0;
int high = list.length - 1;

while (high >= low) {
int mid = (low + high) / 2;
if (key < list[mid])
high = mid - 1;
else if (key == list[mid])
return mid;
else
low = mid + 1;
}

return -1 - low;
}

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95

The Arrays.binarySearch Method
Since binary search is frequently used in programming, Java provides several
overloaded binarySearch methods for searching a key in an array of int, double,
char, short, long, and float in the java.util.Arrays class. For example, the
following code searches the keys in an array of numbers and an array of
characters.

int[] list = {2, 4, 7, 10, 11, 45, 50, 59, 60, 66, 69, 70, 79};
System.out.println("Index is " +
java.util.Arrays.binarySearch(list, 11)); Return is 4

char[] chars = {'a', 'c', 'g', 'x', 'y', 'z'};
System.out.println("Index is " +
java.util.Arrays.binarySearch(chars, 't'));
Return is –4 (insertion point is
3, so return is -3-1)

For the binarySearch method to work, the array must be pre-sorted in increasing
order.

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96

Sorting Arrays
Sorting, like searching, is also a common task in
computer programming. Many different algorithms
have been developed for sorting. This section
introduces two simple, intuitive sorting algorithms:
selection sort and insertion sort.

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Selection Sort
Selection sort finds the smallest number in the list and places it first. It then finds
the smallest number remaining and places it second, and so on until the list
contains only a single number.
swap

Select 1 (the smallest) and swap it 2 9 5 4 8 1 6
with 2 (the first) in the list
swap
The number 1 is now in the
Select 2 (the smallest) and swap it 1 9 5 4 8 2 6 correct position and thus no
with 9 (the first) in the remaining longer needs to be considered.
list swap

list
5 is the smallest and in the right 1 2 4 5 8 9 6 correct position and thus no
position. No swap is necessary longer needs to be considered.
swap

list swap

list

Since there is only one element 1 2 4 5 6 8 9 correct position and thus no
remaining in the list, sort is longer needs to be considered.
completed

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animation
Selection Sort Animation
http://www.cs.armstrong.edu/liang/animation/SelectionSo
rtAnimation.html

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{
select the smallest element in list[i..listSize-1];
swap the smallest with list[i], if necessary;
// list[i] is in its correct position.
// The next iteration apply on list[i..listSize-1]
}

list[0] list[1] list[2] list[3] ... list[10]





...


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for (int i = 0; i < listSize; i++)
{
}
Expand
double currentMin = list[i];
int currentMinIndex = i;
for (int j = i+1; j < list.length; j++) {
if (currentMin > list[j]) {
currentMin = list[j];
currentMinIndex = j;
}
}

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{
}
Expand
for (int j = i; j < list.length; j++) {
}
}

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{
}
Expand
if (currentMinIndex != i) {
list[currentMinIndex] = list[i];
list[i] = currentMin;
}

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Wrap it in a Method
/** The method for sorting the numbers */
public static void selectionSort(double[] list) {
for (int i = 0; i < list.length; i++) {
// Find the minimum in the list[i..list.length-1]
for (int j = i + 1; j < list.length; j++) {
}
}

// Swap list[i] with list[currentMinIndex] if necessary;
if (currentMinIndex != i) {
list[currentMinIndex] = list[i];
list[i] = currentMin;
Invoke it
}
} selectionSort(yourList)
}

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104

Insertion Sort
int[] myList = {2, 9, 5, 4, 8, 1, 6}; // Unsorted
The insertion sort
Step 1: Initially, the sorted sublist contains the 2 9 5 4 8 1 6
algorithm sorts a list first element in the list. Insert 9 into the sublist.
of values by
repeatedly inserting Step2: The sorted sublist is {2, 9}. Insert 5 into 2 9 5 4 8 1 6
the sublist.
an unsorted element
into a sorted sublist Step 3: The sorted sublist is {2, 5, 9}. Insert 4 2 5 9 4 8 1 6
until the whole list into the sublist.

is sorted. Step 4: The sorted sublist is {2, 4, 5, 9}. Insert 8 2 4 5 9 8 1 6
into the sublist.

Step 5: The sorted sublist is {2, 4, 5, 8, 9}. Insert 2 4 5 8 9 1 6
1 into the sublist.

Step 6: The sorted sublist is {1, 2, 4, 5, 8, 9}. 1 2 4 5 8 9 6
Insert 6 into the sublist.

Step 7: The entire list is now sorted. 1 2 4 5 6 8 9

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animation
Insertion Sort Animation
http://www.cs.armstrong.edu/liang/animation/InsertionSor
tAnimation.html

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animation

Insertion Sort
int[] myList = {2, 9, 5, 4, 8, 1, 6}; // Unsorted

2 9 5 4 8 1 6
2 9 5 4 8 1 6
2 5 9 4 8 1 6
2 4 5 9 8 1 6
2 4 5 8 9 1 6
1 2 4 5 8 9 6
1 2 4 5 6 8 9

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How to Insert?

The insertion sort [0] [1] [2] [3] [4] [5] [6]
algorithm sorts a list list 2 5 9 4 Step 1: Save 4 to a temporary variable currentElement

of values by [0] [1] [2] [3] [4] [5] [6]
repeatedly inserting list 2 5 9 Step 2: Move list[2] to list[3]
an unsorted element [0] [1] [2] [3] [4] [5] [6]
into a sorted sublist list 2 5 9 Step 3: Move list[1] to list[2]
until the whole list
[0] [1] [2] [3] [4] [5] [6]
is sorted. list 2 4 5 9 Step 4: Assign currentElement to list[1]

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108

insert list[i] into a sorted sublist list[0..i-1] so that
list[0..i] is sorted
}

list[0]

list[0] list[1]

list[0] list[1] list[2]

list[0] list[1] list[2] list[3]

list[0] list[1] list[2] list[3] ...

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109

insert list[i] into a sorted sublist list[0..i-1] so that
list[0..i] is sorted
}

Expand
double currentElement = list[i];
int k;
for (k = i - 1; k >= 0 && list[k] > currentElement; k--) {
list[k + 1] = list[k];
}
// Insert the current element into list[k + 1]
list[k + 1] = currentElement;

InsertSort
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110

The Arrays.sort Method
Since sorting is frequently used in programming, Java provides several
overloaded sort methods for sorting an array of int, double, char, short,
long, and float in the java.util.Arrays class. For example, the following
code sorts an array of numbers and an array of characters.

double[] numbers = {6.0, 4.4, 1.9, 2.9, 3.4, 3.5};
java.util.Arrays.sort(numbers);

char[] chars = {'a', 'A', '4', 'F', 'D', 'P'};
java.util.Arrays.sort(chars);

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