Data Structures and Algorithoms 08slide - 2D Arrays.ppt

Liang, Introduction to Java Programming and Data Structures, Twelfth Edition, (c) 2020
Pearson Education, Inc. All rights reserved.
1
Chapter 8 Multidimensional Arrays

2
Motivations
Chicago
Boston
New York
Atlanta
Miami
Dallas
Houston
Distance Table (in miles)
Chicago Boston New York Atlanta Miami Dallas Houston
0 983 787 714 1375 967 1087
983 0 214 1102 1763 1723 1842
787 214 0 888 1549 1548 1627
714 1102 888 0 661 781 810
1375 1763 1549 661 0 1426 1187
967 1723 1548 781 1426 0 239
1087 1842 1627 810 1187 239 0
1723 1548 781 1426 0 239
Thus far, you have used one-dimensional arrays to model linear
collections of elements. You can use a two-dimensional array to
represent a matrix or a table. For example, the following table that
describes the distances between the cities can be represented using
a two-dimensional array.

3
Motivations

4
Objectives
 To give examples of representing data using two-dimensional arrays
(§8.1).
 To declare variables for two-dimensional arrays, create arrays, and
access array elements in a two-dimensional array using row and column
indexes (§8.2).
 To program common operations for two-dimensional arrays (displaying
arrays, summing all elements, finding the minimum and maximum
elements, and random shuffling) (§8.3).
 To pass two-dimensional arrays to methods (§8.4).
 To write a program for grading multiple-choice questions using two-
dimensional arrays (§8.5).
 To solve the closest-pair problem using two-dimensional arrays (§8.6).
 To check a Sudoku solution using two-dimensional arrays (§8.7).
 To use multidimensional arrays (§8.8).

5
Declare/Create Two-dimensional Arrays
// Declare array ref var
dataType[][] refVar;
// Create array and assign its reference to variable
refVar = new dataType[10][10];
// Combine declaration and creation in one statement
dataType[][] refVar = new dataType[10][10];
// Alternative syntax
dataType refVar[][] = new dataType[10][10];

6
Declaring Variables of Two-
dimensional Arrays and Creating
Two-dimensional Arrays
int[][] matrix = new int[10][10];
or
int matrix[][] = new int[10][10];
matrix[0][0] = 3;
for (int i = 0; i < matrix.length; i++)
for (int j = 0; j < matrix[i].length; j++)
matrix[i][j] = (int)(Math.random() * 1000);
double[][] x;

7
Two-dimensional Array Illustration
array.length? 4
array[0].length? 3
matrix.length? 5
matrix[0].length? 5

8
Declaring, Creating, and Initializing Using
Shorthand Notations
You can also use an array initializer to declare, create and
initialize a two-dimensional array. For example,
int[][] array = new int[4][3];
array[0][0] = 1; array[0][1] = 2; array[0][2] = 3;
int[][] array = {
{1, 2, 3},
{4, 5, 6},
{7, 8, 9},
{10, 11, 12}
};
Same as

9
Lengths of Two-dimensional
Arrays
int[][] x = new int[3][4];

10
Lengths of Two-dimensional
Arrays, cont.
int[][] array = {
{1, 2, 3},
{4, 5, 6},
{7, 8, 9},
{10, 11, 12}
};
array.length
array[0].length
array[1].length
array[2].length
array[3].length
array[4].length ArrayIndexOutOfBoundsException

11
Each row in a two-dimensional array is itself an array. So,
the rows can have different lengths. Such an array is
known as a ragged array. For example,
int[][] matrix = {
{1, 2, 3, 4, 5},
{2, 3, 4, 5},
{3, 4, 5},
{4, 5},
{5}
};
matrix.length is 5
matrix[0].length is 5

12
Ragged Arrays, cont.

13
Processing Two-Dimensional Arrays
See the examples in the text.
1. (Initializing arrays with input values)
2. (Printing arrays)
3. (Summing all elements)
4. (Summing all elements by column)
5. (Which row has the largest sum)
6. (Finding the smallest index of the largest element)
7. (Random shuffling)

14
Initializing arrays with input values
java.util.Scanner input = new Scanner(System.in);
System.out.println("Enter " + matrix.length + " rows and " +
matrix[0].length + " columns: ");
for (int row = 0; row < matrix.length; row++) {
for (int column = 0; column < matrix[row].length; column++) {
matrix[row][column] = input.nextInt();
}
}

15
Initializing arrays with random values
matrix[row][column] = (int)(Math.random() * 100);
}
}

16
Printing arrays
System.out.print(matrix[row][column] + " ");
}
System.out.println();
}

17
Summing all elements
int total = 0;
total += matrix[row][column];
}
}

18
Summing elements by column
for (int column = 0; column < matrix[0].length; column++) {
int total = 0;
for (int row = 0; row < matrix.length; row++)
total += matrix[row][column];
System.out.println("Sum for column " + column + " is "
+ total);
}

19
Random shuffling
for (int i = 0; i < matrix.length; i++) {
for (int j = 0; j < matrix[i].length; j++) {
int i1 = (int)(Math.random() * matrix.length);
int j1 = (int)(Math.random() * matrix[i].length);
// Swap matrix[i][j] with matrix[i1][j1]
int temp = matrix[i][j];
matrix[i][j] = matrix[i1][j1];
matrix[i1][j1] = temp;
}
}

20
Passing Tow-Dimensional Arrays to
Methods
PassTwoDimensionalArray

21
Problem: Grading Multiple-
Choice Test
Objective: write a
program that grades
multiple-choice test.
Students’ answer

22
Problem: Finding Two Points
Nearest to Each Other
https://liveexample.pearsoncmg.com/
dsanimation/ClosestPaireBook.html

23
What is Sudoku?
5 3 7
6 1 9 5
9 8 6
8 6 3
4 8 3 1
7 2 6
6
4 1 9 5
8 7 9
https://liveexample.pearsoncmg.com/
dsanimation/Sudoku.html

24
Every row contains the numbers 1 to 9
5 3 7
6 1 9 5
9 8 6
8 6 3
4 8 3 1
7 2 6
6
4 1 9 5
8 7 9
5 3 4 6 7 8 9 1 2
6 7 2 1 9 5 3 4 8
1 9 8 3 4 2 5 6 7
8 5 9 7 6 1 4 2 3
4 2 6 8 5 3 7 9 1
7 1 3 9 2 4 8 5 6
9 6 1 5 3 7 2 8 4
2 8 7 4 1 9 6 3 5
3 4 5 2 8 6 1 7 9

25
Every column contains the numbers 1 to 9
5 3 7
6 1 9 5
9 8 6
8 6 3
4 8 3 1
7 2 6
6
4 1 9 5
8 7 9
5 3 4 6 7 8 9 1 2
6 7 2 1 9 5 3 4 8
1 9 8 3 4 2 5 6 7
8 5 9 7 6 1 4 2 3
4 2 6 8 5 3 7 9 1
7 1 3 9 2 4 8 5 6
9 6 1 5 3 7 2 8 4
2 8 7 4 1 9 6 3 5
3 4 5 2 8 6 1 7 9

26
Every 3×3 box contains the numbers 1 to 9
5 3 7
6 1 9 5
9 8 6
8 6 3
4 8 3 1
7 2 6
6
4 1 9 5
8 7 9
5 3 4 6 7 8 9 1 2
6 7 2 1 9 5 3 4 8
1 9 8 3 4 2 5 6 7
8 5 9 7 6 1 4 2 3
4 2 6 8 5 3 7 9 1
7 1 3 9 2 4 8 5 6
9 6 1 5 3 7 2 8 4
2 8 7 4 1 9 6 3 5
3 4 5 2 8 6 1 7 9

27
Checking Whether a Solution Is Correct
5 3 7
6 1 9 5
9 8 6
8 6 3
4 8 3 1
7 2 6
6
4 1 9 5
8 7 9
5 3 4 6 7 8 9 1 2
6 7 2 1 9 5 3 4 8
1 9 8 3 4 2 5 6 7
8 5 9 7 6 1 4 2 3
4 2 6 8 5 3 7 9 1
7 1 3 9 2 4 8 5 6
9 6 1 5 3 7 2 8 4
2 8 7 4 1 9 6 3 5
3 4 5 2 8 6 1 7 9
CheckSudokuSolution

28
Multidimensional Arrays
Occasionally, you will need to represent n-
dimensional data structures. In Java, you can create
n-dimensional arrays for any integer n.
The way to declare two-dimensional array
variables and create two-dimensional arrays can be
generalized to declare n-dimensional array
variables and create n-dimensional arrays for n >=
3.

29
Multidimensional Arrays
double[][][] scores = {
{{7.5, 20.5}, {9.0, 22.5}, {15, 33.5}, {13, 21.5}, {15, 2.5}},
{{4.5, 21.5}, {9.0, 22.5}, {15, 34.5}, {12, 20.5}, {14, 9.5}},
{{6.5, 30.5}, {9.4, 10.5}, {11, 33.5}, {11, 23.5}, {10, 2.5}},
{{6.5, 23.5}, {9.4, 32.5}, {13, 34.5}, {11, 20.5}, {16, 7.5}},
{{8.5, 26.5}, {9.4, 52.5}, {13, 36.5}, {13, 24.5}, {16, 2.5}},
{{9.5, 20.5}, {9.4, 42.5}, {13, 31.5}, {12, 20.5}, {16, 6.5}}
};
scores[ i ] [ j ] [ k ]
Which student Which exam Multiple-choice or essay

30
Problem: Calculating Total Scores
Objective: write a program that calculates the total score for students
in a class. Suppose the scores are stored in a three-dimensional array
named scores. The first index in scores refers to a student, the second
refers to an exam, and the third refers to the part of the exam.
Suppose there are 7 students, 5 exams, and each exam has two parts--
the multiple-choice part and the programming part. So, scores[i][j][0]
represents the score on the multiple-choice part for the i’s student on
the j’s exam. Your program displays the total score for each student.
TotalScore

31
Problem: Weather Information
Suppose a meteorology station records the temperature and
humidity at each hour of every day and stores the data for
the past ten days in a text file named weather.txt. Each line
of the file consists of four numbers that indicate the day,
hour, temperature, and humidity. Your task is to write a
program that calculates the average daily temperature and
humidity for the 10 days.
1 1 76.4 0.92
1 2 77.7 0.93
...
10 23 97.7 0.71
10 24 98.7 0.74
(a)
10 24 98.7 0.74
1 2 77.7 0.93
...
10 23 97.7 0.71
1 1 76.4 0.92
(b)
Weather

32
Problem: Guessing Birthday
Listing 4.3, GuessBirthday.java, gives a
program that guesses a birthday. The program
can be simplified by storing the numbers in five
sets in a three-dimensional array, and it prompts
the user for the answers using a loop.
GuessBirthdayUsingArray

Data Structures and Algorithoms 08slide - 2D Arrays.ppt

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