8.1: Declaring + Initializing 2D Arrays; Determining their
Review: Arrays are a collection (list) of elements (primitive or object reference type data)
So, a 2-Dimensional array is an array where the elements within that array are other arrays
2D arrays can be better at storing certain types of information
- Especially if the data represents a space, with rows and columns
Seating chart:
| . | Column 1 | Column 2 | Column 3 | |
|---|---|---|---|---|
| Row 1 | Abby | Ben | Clara | Principalida |
| Row 2 | Ethan | Frank | Flanklin | |
| Row 3 | Isabelle | John | Kim | Leo |
Note that this is a non-rectangular 2D array
- Or if the data needs to be classified under categories
| . | Month 1 | Month 2 | Month 3 |
|---|---|---|---|
| Winter | December | January | February |
| Spring | March | April | May |
| Summer | June | July | August |
| Fall | Summer | October | November |
This is a rectangular 2D array. Non-rectangular 2D arrays are not a part of the CSA course
Declaring a 2D array
2D Arrays can be declared like this:
dataType[][] nameOfArray;
Initializing a 2D array
new dataType[r][c];
r: number of rows (number of arrays)
c: number of columns (length of each array)
public class Seasons {
private String[][] Seasons = new String[2][3];
// Or, if you already know what the elements should be:
private String[][] Seasons2 = {
{"December", "January", "February"},
{"March", "April", "May"},
{"June", "July", "August"},
{"September", "October", "November"}
};
}
Size of 2D Arrays
The size of the 2D array is classified by number of rows by number of columns
Number of rows can be found like this:
r = trimesterCourses.length
This would give the number of arrays within the 2D array, since each array is an element
For number of columns:
c = trimesterCourses[0].length
This finds the number of elements of the first array within the 2D array.
Accessing the Elements of a 2D Array
The elements of a 2D array can be accessed using index
Seasons[0][2]
Output: February
the value in the first bracket is the index of the rows, or which array we are accessing. In this case, the 0th index means we are accessing the first array
The value in the second bracket is the index within the array. So we are looking for the 2nd value within the first array.
To update the element of a 2D array, all you need to do is reference its location and change the value.
public class Seasons {
private String[][] seasons = new String[2][3];
private static String[][] seasons2 = {
{"December", "January", "February"},
{"March", "April", "May"},
{"June", "July", "August"},
{"September", "October", "November"}
};
public static void main(String[] args) {
System.out.println(seasons2[0][2]);
seasons2[0][2] = "Changed Value";
System.out.println(seasons2[0][2]);
}
}
Seasons.main(null);
Notes on Common Mistakes
Here are some notes on common mistakes made in the context of the 2D arrays question. People around the country will definitely make all of these mistakes many times over, so let’s hope that none of those people are people at our school.
Array Errors
We just had a lesson on common Arrays errors, so rather than rephrase their work, give these mistakes another look.
There are some Array errors that are especially relevant to 2D arrays problems, however. For example…
- Off-By-One Errors
When working with a 2D array, you are working with an array full of arrays. In this structure, there is a set number of rows and columns when the structure is initialized. The length of each row and the number of rows are often different, so both must be identified properly before iterating using index-based loops.
Out of bounds errors will always lose you at least one point on the scoring guidelines, according to our research.
- For-Each loop modification
If values are intended to be modified during an iterative process, do not use a for-each loop. The elements accessed using this strategy are copies; accessing the array indexes directly to make modifications is the only way for them to be retained. See the example below:
import java.util.Arrays;
int[][] modifyArray = {
{1, 4, 3},
{3, 8, 9}
};
System.out.println("Prior to modification: " + Arrays.deepToString(modifyArray));
for (int[] row : modifyArray) {
for (int col : row) {
if (col == 3) {
col = 0;
}
}
}
System.out.println("After to modification: " + Arrays.deepToString(modifyArray));
Prior to modification: [[1, 4, 3], [3, 8, 9]]
After to modification: [[1, 4, 3], [3, 8, 9]]
Instead, when modifying, you can use a traditional for loop (which also comes with the added benefit of having direct access to the relevant indexes):
import java.util.Arrays;
int[][] actualModifyArray = {
{1, 4, 3},
{3, 8, 9}
};
System.out.println("Prior to modification: " + Arrays.deepToString(actualModifyArray));
for (int r = 0; r < actualModifyArray.length; r++) {
for (int c = 0; c < actualModifyArray[r].length; c++) {
if (actualModifyArray[r][c] == 3) {
actualModifyArray[r][c] = 0;
}
}
}
System.out.println("After to modification: " + Arrays.deepToString(actualModifyArray));
Prior to modification: [[1, 4, 3], [3, 8, 9]]
After to modification: [[1, 4, 0], [0, 8, 9]]
FRQ Scoring Guidelines Mistakes
To succeed on the AP test, it’s important to be able to identify which elements of a correct answer earn points.
- Most often, if you create a method in a previous part used to interact with a 2D array, it is intended that you use that method again in future methods.
Means of traversing and interacting with 2D arrays are relatively specific in the context of one College Board problem (i.e., iterate through to determine a condition about a row, find a value in a row, search columns by condition, etc.), so make sure to analyze the context to determine if a certain method may be used again to abstract what would otherwise be a more complex task in a future method. With practice, this connection should be obvious.
If there is no possible relevance between two methods, this may not necessarily be the case.
Make sure that you use the proper parameters when calling your own method! Scoring guidelines are sometimes lenient about this, but don’t tempt fate. Just format your call properly.
- If a “helper” method is provided to you in a question, make sure to note it and use it.
If one is provided, it is most certainly present to make the process of writing the code less complex. Scoring guidelines will always include utilizing past student-created methods and “helper” methods.
You can also use the helper method’s functionality to aid your thinking about a question. If you are confused by its content and aren’t sure how to tackle the problem instinctively, you can be sure that a provided “helper” method will be a part of the solution.
Once again, make sure that you’re using the proper parameters!
- Know how to use column-major order. (Many go into the test having only used row-major order.)
It’s very possible that a question will prompt you to access a 2D array by its columns. (We found two in research for this lesson.) If you know you haven’t practiced column-major order, give the code below a look. It might be a good idea to create your own code cell with a unique 2D array to practice with.
int[][] array = {
{3, 5, 1},
{9, 9, 7}
};
// you should always be able to use array[0].length for the number of columns
// since each row is the same length
int colNum = 1;
for (int col = 0; col < array[0].length; col++) {
System.out.print("Column " + colNum + ":\t");
for (int row = 0; row < array.length; row++) {
System.out.print(array[row][col] + "\t");
}
System.out.println();
colNum++;
}
Column 1: 3 9
Column 2: 5 9
Column 3: 1 7
Popcorn Hack:
public class TrimesterGrades {
private static void printArray(int[][] a) {
for (int i = 0; i < a.length; ++i) {
for (int j = 0; a[i] != null && j < a[i].length; ++j) {
System.out.print(a[i][j] + " ");
}
System.out.println();
}
}
private int[][] trimesterGrades = {
{85, 90, 78, 92, 99}, // tri 1
{92, 88, 91, 97, 80}, // tri 2
{79, 85, 83, 95, 67} // tri 3
};
public static void main(String[] args) {
TrimesterGrades gradesCalculator = new TrimesterGrades();
printArray(gradesCalculator.trimesterGrades);
}
}
TrimesterGrades.main(null);
85 90 78 92 99
92 88 91 97 80
79 85 83 95 67
The 2D array keeps track of a students grade, grouped by each trimester. The student, currently in Trimester 3, retook a test in their 3rd period, which raised that grade to 90.
Show how they would write code that changes the grade for the 3rd period class
public class TrimesterGrades {
private static void printArray(int[][] a) {
for (int i = 0; i < a.length; ++i) {
for (int j = 0; a[i] != null && j < a[i].length; ++j) {
System.out.print(a[i][j] + " ");
}
System.out.println();
}
}
private int[][] trimesterGrades = {
{85, 90, 78, 92, 99}, // tri 1
{92, 88, 91, 97, 80}, // tri 2
{79, 85, 83, 95, 67} // tri 3
};
public static void main(String[] args) {
TrimesterGrades gradesCalculator = new TrimesterGrades();
printArray(gradesCalculator.trimesterGrades);
gradesCalculator.trimesterGrades[2][2] = 90;
System.out.println("------After------");
printArray(gradesCalculator.trimesterGrades);
}
}
TrimesterGrades.main(null);
85 90 78 92 99
92 88 91 97 80
79 85 83 95 67
------After------
85 90 78 92 99
92 88 91 97 80
79 85 90 95 67
Hacks: Finish FRQ from Friday, 2019 Q3
(b) Write a static method rowSums that calculates the sums of each of the rows in a given twodimensional array and returns these sums in a one-dimensional array. The method has one parameter, a twodimensional array arr2D of int values. The array is in row-major order: arr2D[r][c] is the entry at row r and column c. The method returns a one-dimensional array with one entry for each row of arr2D such that each entry is the sum of the corresponding row in arr2D. As a reminder, each row of a two-dimensional array is a one-dimensional array. For example, if mat1 is the array represented by the following table, the call rowSums(mat1) returns the array {16, 32, 28, 20}. Assume that arraySum works as specified, regardless of what you wrote in part (a). You must use arraySum appropriately to receive full credit. Complete method rowSums below.
/** Returns a one-dimensional array in which the entry at index k is the sum of * the entries of row k of the two-dimensional array arr2D. */
public class SumOf2Darray {
public static int arraySum (int [ ] arr) { // used in Part A
int sum = 0;
for (int i = 0; i < arr.length; i++) {
sum += arr[i];
}
return sum;
}
public static int [ ] rowSums(int [ ] [ ] arr2D) {
int[] sums = new int[arr2D.length]; // create array to return at the end
int sum = 0; // initialize sum as 0
for (int i=0; i < arr2D.length; i++) {
sum = arraySum(arr2D[i]); // put arr2D[i] which will be int[] in arraySum()
sums[i] = sum; // put the sum into the array created at beginning
sum = 0; // reset the sum
}
return sums;
}
public static void main(String[] args) {
int[][] mat1 = {
{1, 3, 2, 7, 3},
{10,10,4,6,2},
{5,3,5,9,6},
{7,6,4,2,1}
};
int[] sums = SumOf2Darray.rowSums(mat1); // make int[] sums
System.out.print("Sum: ");
for (int i = 0; i < sums.length; i++) {
System.out.print(sums[i] + " "); // print the int[] sums
}
}
}
SumOf2Darray.main(null);
Sum: 16 32 28 20
(c) A two-dimensional array is diverse if no two of its rows have entries that sum to the same value. In the following examples, the array mat1 is diverse because each row sum is different, but the array mat2 is not diverse because the first and last rows have the same sum.Assume that arraySum and rowSums work as specified, regardless of what you wrote in parts (a) and (b). You must use rowSums appropriately to receive full credit. Complete method isDiverse below.
/** Returns true if all rows in arr2D have different row sums; * false otherwise. */
public class check {
public static int arraySum (int [ ] arr) { // answer for part A
int sum = 0;
for (int i = 0; i < arr.length; i++) {
sum += arr[i];
}
return sum;
}
public static int [ ] rowSums(int [ ] [ ] arr2D) { // answer for part B
int[] sums = new int[arr2D.length];
int sum = 0;
for (int i=0; i < arr2D.length; i++) {
sum = arraySum(arr2D[i]);
sums[i] = sum;
sum = 0;
}
return sums;
}
public static boolean isDiverse(int[][] arr2D) {
int[] sums = rowSums(arr2D); // get the row sums
for (int i = 0; i < sums.length; i++) { // using for loop
for (int j = i + 1; j < sums.length; j++) {
if (sums[i] == sums[j]) { // compare each elements
return false;
}
}
}
return true;
}
public static void main(String[] args) {
int[][] mat1 = {
{1, 3, 2, 7, 3},
{10, 10, 4, 6, 2},
{5, 3, 5, 9, 6},
{7, 6, 4, 2, 1}
};
System.out.println(isDiverse(mat1));
int[][] mat2 = {
{1, 1, 5, 3, 4},
{12, 7, 6, 1, 9},
{8, 11, 10, 2, 5},
{3, 2, 3, 0, 6}
};
System.out.println(isDiverse(mat2));
}
}
check.main(null);
true
false