1. Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 1 Chapter 7 Multidimensional Arrays

2. Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 2 Motivations 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. Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 3 Objectives F To give examples of representing data using two-dimensional arrays (§7.1). F To declare variables for two-dimensional arrays, create arrays, and access array elements in a two-dimensional array using row and column indexes (§7.2). F To program common operations for two-dimensional arrays (displaying arrays, summing all elements, finding min and max elements, and random shuffling) (§7.3). F To pass two-dimensional arrays to methods (§7.4). F To write a program for grading multiple-choice questions using two- dimensional arrays (§7.5). F To solve the closest-pair problem using two-dimensional arrays (§7.6). F To check a Sudoku solution using two-dimensional arrays (§7.7). F To use multidimensional arrays (§7.8).

4. Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 4 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];

5. Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 5 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;

6. Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 6 Two-dimensional Array Illustration array.length? 4 array[0].length? 3 matrix.length? 5 matrix[0].length? 5

7. Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 7 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; array[1][0] = 4; array[1][1] = 5; array[1][2] = 6; array[2][0] = 7; array[2][1] = 8; array[2][2] = 9; array[3][0] = 10; array[3][1] = 11; array[3][2] = 12; int[][] array = { {1, 2, 3}, {4, 5, 6}, {7, 8, 9}, {10, 11, 12} }; Same as

8. Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 8 Lengths of Two-dimensional Arrays int[][] x = new int[3][4];

9. Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 9 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

10. Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 10 Ragged Arrays 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 matrix[1].length is 4 matrix[2].length is 3 matrix[3].length is 2 matrix[4].length is 1

11. Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 11 Ragged Arrays, cont.

12. Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 12 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)

13. Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 13 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(); }

14. Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 14 Initializing arrays with random values for (int row = 0; row < matrix.length; row++) { for (int column = 0; column < matrix[row].length; column++) { matrix[row][column] = (int)(Math.random() * 100); }

15. Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 15 Printing 2-D arrays for (int row = 0; row < matrix.length; row++) { for (int column = 0; column < matrix[row].length; column++) { System.out.print(matrix[row][column] + " "); } System.out.println(); } To print a two-dimensional array, you have to print each element in the array using a loop like the following:

16. Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 16 Summing all elements int total = 0; for (int row = 0; row < matrix.length; row++) { for (int column = 0; column < matrix[row].length; column++) { total += matrix[row][column]; } Use a variable named total to store the sum. Initially total is 0. Add each element in the array to total using a loop like this:

17. Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 17 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); } For each column, use a variable named total to store its sum. Add each element in the column to total using a loop like this:

18. Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 Finding the Row with the Largest Sum F Video Link Video Link F Multidimensional Array – Find the Row with Largest Sum Multidimensional Array – Find the Row with Largest Sum 18 Which row has the largest sum? Use variables maxRow and indexOfRow to track the largest sum and index of the row, for each row, compute its sum and update maxRow and indexOfMaxRow if the new sum is greater. See the video below

19. Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 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. Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 20 Passing Tow-Dimensional Arrays to Methods Run import java.util.Scanner; public class PassTwoDimensionalArray { public static void main(String[] args) { // Create a Scanner Scanner input = new Scanner(System.in); // Enter array values int[][] m = new int[3][4]; System.out.println("Enter " + m.length + " rows and " + m[0].length + " columns: "); for (int i = 0; i < m.length; i++) for (int j = 0; j < m[i].length; j++) m[i][j] = input.nextInt(); // Display result System.out.println("\nSum of all elements is " + sum(m)); } public static int sum(int[][] m) { int total = 0; for (int row = 0; row < m.length; row++) { for (int column = 0; column < m[row].length; column++) { total += m[row][column]; } } return total; } }

21. Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 21 Problem: Grading Multiple- Choice Test F Objective: write a program that grades multiple-choice test. GradeExamRun

22. Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 Problem Grading a Multiple-Choice test F Video Link –Grade multiple-choice textGrade multiple-choice text 22 The problem is to write a program that grades multiple-choice tests. Suppose there are eight students and ten questions, and the answers are stored in a two-dimensional array. Each row records a students’ answers to the questions, as show on

23. Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 23 Problem: Finding Two Points Nearest to Each Other FindNearestPoints Run

24. Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 24 What is Sudoku? Video Link Chapter 7.3 – Sudoku What is Sudoku? Sudoku is an easy to learn logic-based number placement puzzle. The word Sudoku is short for Su-ji wa dokushin ni kagiru which means "the numbers must be single". Rules & Terms A Sudoku puzzle consists of 81 cells which are divided into nine columns, rows and regions. The task is now to place the numbers from 1 to 9 into the empty cells in such a way that in every row, column and 3×3 region each number appears only once. A Sudoku has at least 17 given numbers but normally there are 22 to 30. Sudoku

25. Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 25 Every row contains the numbers 1 to 9

26. Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 26 Every column contains the numbers 1 to 9 5 34 6 78 9 1 2 67 2 1 9 5 3 4 8 1 9 83 4 2 5 67 85 9 7 6 1 4 2 3 42 6 85 37 9 1 71 3 9 24 8 5 6 9 61 5 3 7 2 8 4 2 8 7 4 1 9 6 3 5 3 4 5 2 86 1 7 9

27. Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 27 Every 3×3 box contains the numbers 1 to 9 5 34 6 78 9 1 2 67 2 1 9 5 3 4 8 1 9 83 4 2 5 67 85 9 7 6 1 4 2 3 42 6 85 37 9 1 71 3 9 24 8 5 6 9 61 5 3 7 2 8 4 2 8 7 4 1 9 6 3 5 3 4 5 2 86 1 7 9

28. Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 28 Checking Whether a Solution Is Correct RunCheckSudokuSolution

29. Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 29 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. For example, the following syntax declares a three-dimensional array variable scores, creates an array, and assigns its reference to scores. double[][][] scores = new double[10][5][2];

30. Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 30 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}}};

31. Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 Matrix Transposition (Formally Multiply two Matrices 31 http://media.pearsoncmg.com/ph/esm/ecs_liang_vnijp_8/Li angCh07Ex6.html

32. Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 JVA JDK 32 The Java Development Kit (JDK) is an implementation of either one of the Java SE, Java EE or Java ME platforms [1] released by Oracle Corporation in the form of a binary product aimed at Java developers on Solaris, Linux, Mac OS X or Windows. [2] Since the introduction of Java platform, it has been by far the most widely used Software Development Kit (SDK). [citation needed] On 17 November 2006, Sun announced that it would be released under the GNU General Public License (GPL), thus making it free software. This happened in large part on 8 May 2007, when Sun contributed the source code to the OpenJDK. [3]Java SEJava EEJava ME [1] Oracle CorporationJavaSolarisLinuxMac OS XWindows [2]JavaSDKcitation needed GNU General Public Licensefree softwareOpenJDK [3] JDK contents The JDK has as its primary components a collection of programming tools, including: appletviewerappletviewer – this tool can be used to run and debug Java applets without a web browser