Data Structures and Algorithoms 07slide - 1D Arrays.pptx

Liang, Introduction to Java Programming and Data Structures, Twelfth Edition, (c) 2020 Pearson
Education, Inc. All rights reserved. 1
Chapter 7 Single-Dimensional
Arrays

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

Objectives
 To describe why arrays are necessary in programming (§7.1).
 To declare array reference variables and create arrays (§§7.2.1–7.2.2).
 To obtain array size using arrayRefVar.length and know default values in an array (§7.2.3).
 To access array elements using indexes (§7.2.4).
 To declare, create, and initialize an array using an array initializer (§7.2.5).
 To program common array operations (displaying arrays, summing all elements, finding the
minimum and maximum elements, random shuffling, and shifting elements) (§7.2.6).
 To simplify programming using the foreach loops (§7.2.7).
 To apply arrays in application development (AnalyzeNumbers, DeckOfCards) (§§7.3–7.4).
 To copy contents from one array to another (§7.5).
 To develop and invoke methods with array arguments and return values (§§7.6–7.8).
 To define a method with a variable-length argument list (§7.9).
 To search elements using the linear (§7.10.1) or binary (§7.10.2) search algorithm.
 To sort an array using the selection sort approach (§7.11).
 To use the methods in the java.util.Arrays class (§7.12).
 To pass arguments to the main method from the command line (§7.13).

Introducing Arrays
Array is a data structure that represents a collection of the
same types of data.

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

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.

Declaring and Creating
in One Step
 datatype[] arrayRefVar = new
datatype[arraySize];
double[] myList = new double[10];
 datatype arrayRefVar[] = new
datatype[arraySize];
double myList[] = new double[10];

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

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.

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];

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];

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.

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:
double[] myList = new double[4];
myList[0] = 1.9;
myList[1] = 2.9;
myList[2] = 3.4;
myList[3] = 3.5;

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};

Trace Program with Arrays
public class Test {
public static void main(String[] args) {
int[] values = new int[5];
for (int i = 1; i < 5; i++) {
values[i] = i + values[i-1];
}
values[0] = values[1] + values[4];
}
}
Declare array variable values, create an
array, and assign its reference to values
After the array is created
0
1
2
3
4
0
0
0
0
0
animation

public class Test {
for (int i = 1; i < 5; i++) {
}
}
}
i becomes 1
0
1
2
3
4
0
0
0
0
0
animation

public class Test {
for (int i = 1; i < 5; i++) {
}
}
}
i (=1) is less than 5
0
1
2
3
4
0
0
0
0
0
animation

public class Test {
for (int i = 1; i < 5; i++) {
}
}
}
After this line is executed, value[1] is 1
After the first iteration
0
1
2
3
4
0
1
0
0
0
animation

public class Test {
for (int i = 1; i < 5; i++) {
}
}
}
After i++, i becomes 2
animation
0
1
2
3
4
0
1
0
0
0

public class Test {
public static void main(String[]
args) {
for (int i = 1; i < 5; i++) {
}
values[0] = values[1] +
values[4];
}
}
i (= 2) is less than 5
animation
0
1
2
3
4
0
1
0
0
0

public class Test {
for (int i = 1; i < 5; i++) {
}
}
}
After this line is executed,
values[2] is 3 (2 + 1)
After the second iteration
0
1
2
3
4
0
1
3
0
0
animation

public class Test {
for (int i = 1; i < 5; i++) {
}
}
}
After this, i becomes 3.
0
1
2
3
4
0
1
3
0
0
animation

public class Test {
for (int i = 1; i < 5; i++) {
}
}
}
i (=3) is still less than 5.
0
1
2
3
4
0
1
3
0
0
animation

public class Test {
for (int i = 1; i < 5; i++) {
}
}
}
After this line, values[3] becomes 6 (3 + 3)
After the third iteration
0
1
2
3
4
0
1
3
6
0
animation

public class Test {
for (int i = 1; i < 5; i++) {
}
}
}
After this, i becomes 4
0
1
2
3
4
0
1
3
6
0
animation

public class Test {
for (int i = 1; i < 5; i++) {
}
}
}
i (=4) is still less than 5
0
1
2
3
4
0
1
3
6
0
animation

public class Test {
for (int i = 1; i < 5; i++) {
}
}
}
After this, values[4] becomes 10 (4 + 6)
After the fourth iteration
0
1
2
3
4
0
1
3
6
10
animation

public class Test {
for (int i = 1; i < 5; i++) {
}
}
}
After i++, i becomes 5
animation
0
1
2
3
4
0
1
3
6
10

public class Test {
for (int i = 1; i < 5; i++) {
}
}
}
i ( =5) < 5 is false. Exit the loop
animation
0
1
2
3
4
0
1
3
6
10

public class Test {
for (int i = 1; i < 5; i++) {
}
}
}
After this line, values[0] is 11 (1 + 10)
0
1
2
3
4
11
1
3
6
10
animation

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)

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();

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

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

Summing all elements
double total = 0;
total += myList[i];
}

Finding the largest element
double max = myList[0];
if (myList[i] > max) max = myList[i];
}

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

Shifting Elements

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.

Analyze Numbers
Read one hundred numbers, compute their
average, and find out how many numbers are
above the average.
AnalyzeNumbers

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

Problem: Deck of Cards, cont.

Problem: Deck of Cards, cont.
DeckOfCards

Problem: Deck of Cards
This problem builds a foundation for future more interesting and
realistic applications:
See Exercise 20.15.
https://liveexample.pearsoncmg.com/
dsanimation/24Point.html

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;

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];

The arraycopy Utility
arraycopy(sourceArray, src_pos,
targetArray, tar_pos, length);
Example:
System.arraycopy(sourceArray, 0,
targetArray, 0, sourceArray.length);

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

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.

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.

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]
}
}
Simple Example

Call Stack
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.

Call Stack
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.

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

Passing Arrays as Arguments
 Objective: Demonstrate differences of
passing primitive data type variables
and array variables.
TestPassArray

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

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

Trace the reverse Method
}
return result;
}
int[] list1 = {1, 2, 3, 4, 5, 6};
list
result
1 2 3 4 5 6
0 0 0 0 0 0
Declare result and create array
animation

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

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

}
return result;
}
int[] list1 = {1, 2, 3, 4, 5, 6};
list
result
1 2 3 4 5 6
0 0 0 0 0 1
i = 0 and j = 5
Assign list[0] to result[5]
animation

}
return result;
}
int[] list1 = {1, 2, 3, 4, 5, 6};
list
result
1 2 3 4 5 6
0 0 0 0 0 1
After this, i becomes 1 and j
becomes 4
animation

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

}
return result;
}
int[] list1 = {1, 2, 3, 4, 5, 6};
list
result
1 2 3 4 5 6
0 0 0 0 2 1
i = 1 and j = 4
Assign list[1] to result[4]
animation

}
return result;
}
int[] list1 = {1, 2, 3, 4, 5, 6};
list
result
1 2 3 4 5 6
0 0 0 0 2 1
After this, i becomes 2 and
j becomes 3
animation

}
return result;
}
int[] list1 = {1, 2, 3, 4, 5, 6};
list
result
1 2 3 4 5 6
0 0 0 0 2 1
animation

}
return result;
}
int[] list1 = {1, 2, 3, 4, 5, 6};
list
result
1 2 3 4 5 6
0 0 0 3 2 1
i = 2 and j = 3
Assign list[i] to result[j]
animation

}
return result;
}
int[] list1 = {1, 2, 3, 4, 5, 6};
list
result
1 2 3 4 5 6
0 0 0 3 2 1
j becomes 2
animation

}
return result;
}
int[] list1 = {1, 2, 3, 4, 5, 6};
list
result
1 2 3 4 5 6
0 0 0 3 2 1
animation

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

}
return result;
}
int[] list1 = {1, 2, 3, 4, 5, 6};
list
result
1 2 3 4 5 6
0 0 4 3 2 1
j becomes 1
animation

}
return result;
}
int[] list1 = {1, 2, 3, 4, 5, 6};
list
result
1 2 3 4 5 6
0 0 4 3 2 1
animation

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

}
return result;
}
int[] list1 = {1, 2, 3, 4, 5, 6};
list
result
1 2 3 4 5 6
0 5 4 3 2 1
j becomes 0
animation

}
return result;
}
int[] list1 = {1, 2, 3, 4, 5, 6};
list
result
1 2 3 4 5 6
0 5 4 3 2 1
animation

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

}
return result;
}
int[] list1 = {1, 2, 3, 4, 5, 6};
list
result
1 2 3 4 5 6
6 5 4 3 2 1
j becomes -1
animation

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

}
return result;
}
int[] list1 = {1, 2, 3, 4, 5, 6};
list
result
1 2 3 4 5 6
6 5 4 3 2 1
Return result
list2
animation

Problem: Counting Occurrence of Each
Letter
 Generate 100 lowercase letters randomly and assign to an array of
characters.
 Count the occurrence of each letter in the array.
CountLettersInArray

Variable-Length Arguments
You can pass a variable number of arguments of the same
type to a method.
VarArgsDemo

Searching Arrays
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])
return i;
return -1;
}
}
list
key Compare key with list[i] for i = 0, 1, …
[0] [1] [2] …
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.

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.

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

https://liveexample.pearsoncmg.com/dsanimation/
LinearSearcheBook.html
Linear Search Animation
animation

From Idea to Solution
/** 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])
return i;
return -1;
}
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
Trace the method

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.

Binary Search, cont.
 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.
Consider the following three cases:

Binary Search
1 2 3 4 6 7 8 9
1 2 3 4 6 7 8 9
1 2 3 4 6 7 8 9
8
8
8
Key List
animation

BinarySearcheBook.html
Binary Search Animation
animation

[0] [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12]
2 4 7 10 11 45 50 59 60 66 69 70 79
key is 54
key > 50
list
mid
[0] [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12]
key < 66
key < 59
high
low
mid high
low
list
[7] [8]
mid high
low
list
59 60 66 69 70 79
59 60
[6] [7] [8]
high
low
59 60

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.

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;
}

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));
char[] chars = {'a', 'c', 'g', 'x', 'y', 'z'};
System.out.println("Index is " +
java.util.Arrays.binarySearch(chars, 't'));
For the binarySearch method to work, the array must be pre-sorted in increasing
order.
Return is 4
Return is –4 (insertion point
is 3, so return is -3-1)

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

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.

SelectionSortNew.html
Selection Sort Animation
animation

From Idea to Solution
for (int i = 0; i < list.length; i++) {
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+1..listSize-1]
}
list[0] list[1] list[2] list[3] ... list[10]
...

Expand
for (int i = 0; i < listSize; i++) {
// The next iteration apply on list[i..listSize-1]
}
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;
}
}

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

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

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)

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);
Java 8 now provides Arrays.parallelSort(list) that utilizes the multicore
for fast sorting.

The Arrays.toString(list) Method
The Arrays.toString(list) method can be used to return a string
representation for the list.

Pass Arguments to Invoke the Main
Method

Main Method Is Just a Regular Method
public class A {
String[] strings = {"New York",
"Boston", "Atlanta"};
B.main(strings);
}
}
class B {
for (int i = 0; i < args.length; i++)
System.out.println(args[i]);
}
}
You can call a regular method by passing actual
parameters. Can you pass arguments to main? Of
course, yes. For example, the main method in class
B is invoked by a method in A, as shown below:

Command-Line Parameters
class TestMain {
...
}
}
java TestMain arg0 arg1 arg2 ... argn

Processing
Command-Line Parameters
In the main method, get the arguments from
args[0], args[1], ..., args[n], which
corresponds to arg0, arg1, ..., argn in
the command line.

Problem: Calculator
 Objective: Write a program that will perform
binary operations on integers. The program
receives three parameters: an operator and two
integers.
java Calculator 2 + 3
java Calculator 2 - 3
java Calculator 2 / 3
java Calculator 2 . 3
Calculator

Data Structures and Algorithoms 07slide - 1D Arrays.pptx

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