AP Computer Science A Unit 8 2D Arrays

Unit 8: 2D Arrays 2D Arrays: A 2D Array or Matrix is A two-dimensional array is a one-dimensional array of one-dimensional arrays. A matrix has rows and columns. Ex: A spreadsheet is a matrix. What does this matrix look like? Shown below! int[][] rayORays = new int[3][3]; (Index positions are green and also go vertically ) 0 1 2 0 0 0 0 0 0 0 0 0 What does this matrix look like? Shown below! int[][] mat = {{6, 9, 2}, {5, 3, 4, 6}}; 6 9 2 5 3 4 6 More Examples: String[][] words = new String[4][4]; //words is filled with 16 nulls double[][] dMat = new double[3][3]; //dMat is filled with 9 0.0s Reminder: To create a 2D Array jut extend the notation for a 1D array. For example, in the array below type is the type of value being stored, rows is the number of rows, and cols is the number of columns. type[][] name = new type[rows][cols]; A 2D array can be initialized with items that are each initializer lists for a 1D array: int[][] values = new int[][] {{1, 2, 3}, {4, 5, 6}}; If arr is a 2D array, the expression arr[r] refers to the element at position r in arr. But this element is itself a 1D array, so it can be further indexed with the expression arr[r][c]. The two subscripts should be thought of as the row and column positions in the rectangular array. The row and column indices both start at 0. The following example creates the matrix shown below: 1 2 3 4 5 6 Example of Printing Matrice values: int[][] mat = {{5,7,9,2,1,9}, {5,3,4}, {3,7,0,8,9}}; out.println(mat[7/4][0]); out.println(mat[1*2][2]); out.println(mat.length); out.println(mat[0].length); The Output: 5 0 3 6 You can also set Matrix Values: int[][] mat = new int[3][3]; mat[0][1]=2; This makes the following matrix: 0 2 0 0 0 0 0 0 0 Traversing 2D Arrays: Nested Loops are usually used to traverse 2D Arrays. In a row-major traversal, the outer loop iterates through each row, while the inner loop iterates through each column in the row. In a column-major traversal, the order of the loops is reversed. The number of rows in the 2D array arr is arr.length. The number columns can be accessed using arr[x].length, where x is any valid row index. All the standard 1D array algorithms can be applied to 2D arrays public static double average(int[][] values) { double total = 0; int count = 0; for (int r = 0; r < values.length; r++) { for (int c = 0; c < values[r].length; c++) { total += values[r][c]; count++; } } } Bonus Matrix algorithm: int[][] mat = {{5,7},{5,3,4,6},{0,8,9}}; int count = 0; for( int r = 0; r < mat.length; r++ ) { for( int c = 0; c < mat[r].length; c++) { if( mat[r][c] == 5 ) count++; } } System.out.println("5 count = " + count); The Output: 5 count = 2 Example question: Consider the following code segment, which contains line numbers. The loop is intended to return the sum of both diagonals in a 2d array. A precondition is that the number of rows and columns in the 2d array are equal. However, the program does not produce correct output. /** Preconditions: * array.length > 0 * array.length == array[0].length */ public int sumDiagonals(int[][] array) { int sum = 0; for (int i = 1; i < array.length; i++) {for (int j = 1; j < array[0].length; j++) { if (i == j || j == array[0].length-1-i) { sum += array[i][j]; } }} return sum; } Which of the below solutions will fix the program? A. Change the name of the parameter throughout the method to ary. B. In lines 4 and 6, initialize the variables i and j to 0 instead of 1. C. In lines 4 and 6, change the test of each loop to array[0].length and array.length, respectively. D. In line 8, change the first Boolean expression to i != j. E. Before the method returns, add a second nested for loop to account for the diagonal that spans from the top-right to the bottom-left corner. The correct answer is B. Both for loops should be initialized at 0, so that the iteration also includes the first row and first column. Choice A is incorrect because the identifier array is legal in Java. Changing the name would not affect the output of the program. Choice C is incorrect because the change would have no effect on the output of the program. Choice D is incorrect because the current Boolean expression i == j is correctly testing whether an element lies on the diagonal that spans from the top-left to the bottom-right. Choice E is incorrect because no second loop is necessary. The disjunction of Boolean expressions on Line 8 tests whether an element lies on either diagonal.