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Questions and Answers
In Java, how are multi-dimensional arrays implemented?
In Java, how are multi-dimensional arrays implemented?
- As an array of arrays. (correct)
- As a hashmap with array-like keys.
- As a single block of memory with complex indexing.
- As a linked list of arrays.
Given a 2D array timesTable representing a multiplication table, what does timesTable[2][3] represent?
Given a 2D array timesTable representing a multiplication table, what does timesTable[2][3] represent?
- The element at the 2nd row and 3rd column.
- The element at the 3rd row and 4th column. (correct)
- The sum of 2 and 3.
- The product of 2 and 3.
In a 2D array, the first subscript typically represents the column, while the second represents the row.
In a 2D array, the first subscript typically represents the column, while the second represents the row.
False (B)
Explain the concept of 'arrays of arrays' in Java.
Explain the concept of 'arrays of arrays' in Java.
Arrays in Java are stored by _______.
Arrays in Java are stored by _______.
What is a 'ragged array'?
What is a 'ragged array'?
What is a common mathematical term for a 2D array of numbers?
What is a common mathematical term for a 2D array of numbers?
In scalar multiplication of a matrix, every element of the matrix is multiplied by the scalar value.
In scalar multiplication of a matrix, every element of the matrix is multiplied by the scalar value.
Describe what happens to the elements during matrix transposition.
Describe what happens to the elements during matrix transposition.
When a matrix's rows and columns are interchanged, this is known as _______.
When a matrix's rows and columns are interchanged, this is known as _______.
Match the array declaration with its correct description:
Match the array declaration with its correct description:
Explain how a 2D array is stored in memory.
Explain how a 2D array is stored in memory.
If timesTable is a 2D array initialized as int[][] timesTable = new int[6][6], what range of values for i and j would you use in nested loops to properly initialize all elements?
If timesTable is a 2D array initialized as int[][] timesTable = new int[6][6], what range of values for i and j would you use in nested loops to properly initialize all elements?
A 5-dimensional array cannot be created in Java.
A 5-dimensional array cannot be created in Java.
Why might you choose to use a ragged array in a real-world application?
Why might you choose to use a ragged array in a real-world application?
Flashcards
What are multi-dimensional arrays?
What are multi-dimensional arrays?
Arrays that contain other arrays as their elements, creating a grid-like structure.
How are multi-dimensional arrays implemented in Java?
How are multi-dimensional arrays implemented in Java?
Multi-dimensional arrays are implemented as 'arrays of arrays'.
How to declare a 2D array in Java?
How to declare a 2D array in Java?
Declaring a 2D array involves specifying the data type followed by two sets of square brackets: int[][] arrayName;
How are arrays stored in memory in Java?
How are arrays stored in memory in Java?
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What are Ragged Arrays?
What are Ragged Arrays?
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What is a matrix?
What is a matrix?
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What is Scalar Multiplication?
What is Scalar Multiplication?
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What is Matrix Transposition?
What is Matrix Transposition?
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How do you access elements in a 2D array?
How do you access elements in a 2D array?
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What about arrays of higher dimension?
What about arrays of higher dimension?
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Study Notes
Multi-Dimensional Arrays
- Arrays worked with so far are 1-dimensional
- 1-dimensional arrays are a single list of elements, like a row in a spreadsheet
- 2-dimensional arrays are possible
- They can represent data similar to a spreadsheet
- This is implemented as an array of arrays in Java
2-Dimensional Arrays
- A table represents a simple multiplication table
- To find the product of two numbers, look it up in the table
- Array indexes start at zero, even for multi-dimensional arrays
- Finding 5x6 would be timesTable[4][5]
- The array can be declared as int[][] timesTable = {{1, 2, 3, 4, 5, 6},{2, 4, 6, 8, 10, 12},{3, 6, 9, 12, 15, 18},{4, 8, 12, 16, 20, 24},{5, 10, 15, 20, 25, 30},{6, 12, 18, 24, 30, 36}};
- The entire array is enclosed in {}
- Each row is enclosed in a nested {}
- Use int[][] to denote the array is 2D
- This array is said to be in row-order
- The first subscript represents the row, while the second is the column
- timesTable[2][4] is the third row and the fifth column
- Multi-dimensional arrays doesn't have column or row headers like the table had
- The programmer must know what the rows and columns represent
- Arrays are stored by reference
- A 2D array is an array that references other arrays
- Since each sub-array is of type int, actual values are stored
Creating a 2D-Array
- An array of arrays can be initialized
- An empty 2D array can be defined and have values assigned later
- Another way to create multiplication table:
- int[][] timesTable = new int[6][6];
- Creates a first loop where i = 0, and the loop continues as long as i < 6, increment one after each loop
- Inside that loop a second loop is created where j = 0, and the loop continues as long as j < 6, increment one after each loop
- Inside the nested loops, timesTable[i][j] = (i+1) * (j+1)
Ragged Arrays
- Multi-dimensional arrays in Java are implemented as an array of arrays
- Sub-arrays can be of different lengths
- If there is data for 5 salesman, each may have a different number of sales
- Example: double[][] sales = {{49.99, 120.00, 30.10},{50.00, 10.00, 20.00, 42.42},{5.00, 5.00, 5.00},{5.00},{100.00, 48.00, 34.00, 60.00, 40.00, 155.00}}
- Need determination of how many sales each person had
- Need Total sales amount?
- Need Total number of sales?
Matrices
- A 2D construct of rows and columns in math is called a matrix
- We may often see 2D arrays referred to as matrices
- Likewise, 1D arrays may often be referred to as vectors
Matrix Operations
- Many standard mathematical operations are defined for matrices
- Addition, subtraction, scalar multiplication, transposition, multiplication, etc
- Scalar multiplication is multiplying a matrix (2D array) by a scalar (a single number)
- Denoted c * A, where c is a scalar, and A is a matrix
- c * A is computed by multiplying every element of A by c
- Matrix Addition is when you add 2 arrays together
- Adding the corresponding elements of each matrix together
- Matrix subtraction works the same way
- Matrix Transposition is when a matrix's rows and columns are interchanged
- Also called taking the transpose of a matrix
- Denoted with a superscript T
Higher Dimensions
- Arrays of more than 2 dimensions are possible
- Implementation in code and in memory follow from 2 dimensional arrays int[][][] myArray = new int[10][10][10];
- Stored in memory as an array of arrays of arrays
- It can be hard to visualize more than 3 dimensions, but implementing multidimensional arrays is fairly simple int[][][][] myComplexArray = new int[10][10][10][10];
- Stored in memory as an array of arrays of arrays of arrays
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Description
Explore the concept of multi-dimensional arrays in Java, focusing on 2-dimensional arrays. Learn how these arrays can represent data in a table format, similar to a spreadsheet. Understand row-order representation and how to declare and access elements within 2D arrays.
