Multi-Dimensional Arrays

Multi-Dimensional Arrays
An Introduction with Examples in Java

Prof. David Bernstein
James Madison University

Computer Science Department

bernstdh@jmu.edu

Review of Arrays

Some Awkward Code:
- x1 = 550.75; x2 = 25.60; x3 = 347.10; x4 = 120.45; x5 = 885.00; x6 = 10.99; x7 = 123.45;
How To Handle This in Math:
- \(x_i\)
How To Handle This in a Programming Language:
- Use an array (e.g., named x) and refer to particular elements using the square bracket operator (e.g., x[i])

Review of Arrays (cont.)

Fixed and Known Number of Elements:
- In order to be able to allocate a contiguous block of memory
Homogeneous Elements:
- In order to know how big each element/offset is

Review of Arrays (cont.)

Review of Arrays (cont.)

Memory Allocation:
- The new operator returns a memory address (reference) which is normally assigned to a variable
Starting Index:
- The first element has an index of 0 since this is an offset from the first memory address

Review of Arrays (cont.)

Arrays of Primitive Types:
- Each of the elements is a primitive of the same type
Arrays of Reference Types:
- Each of the elements is a reference (and all references, regardless of what they refer to, are the same size)

Motivation for Arrays of Arrays

Opinions?

// Keep track of the points scored in each game for week 0 int[] pointsScored0 = {58, 60}; // Keep track of the points scored in each game for week 1 int[] pointsScored1 = {72, 48, 61, 44}; // Keep track of the points scored in each game for week 2 int[] pointsScored2 = {60, 63, 51};

Motivation for Arrays of Arrays (cont.)

What We Have:
- A bunch of individual arrays, each with its own identifier
What We Want:
- An array of arrays (with one identifier)

Arrays of Arrays

Each Array:
- Is a reference
The Array of Arrays:
- We can achieve this with an array of Object objects (which is essentially an array of generic references)

Arrays of Arrays (cont.)

An Example

javaexamples/multidimensionalarrays/Sports1.java (Fragment: 0)

Arrays of Arrays (cont.)

A Quiz:
- When is the name table used?
- When is memory allocated from the heap?
A Question:
- Can you illustrate both the name table and the heap for the previous example?

Arrays of Arrays (cont.)

An Inconvenience:
- We have to cast each element of the Object array in order to use it
A Remedy:
- Declare the type of each element explicitly
What This Leads To:
- Multiple applications of the [] modifier in the declaration
- Multiple applications of the [] operator when accessing

Arrays of Arrays (cont.)

An Example

javaexamples/multidimensionalarrays/Sports2.java (Fragment: 0)

Arrays of Arrays (cont.)

An Observation:
- Each element of the array of arrays is a reference
An Implication:
- It is possible to re-assign (i.e., replace) an entire element
A Question:
- Can you illustrate both the name table and the heap for the previous example?

Rectangular Arrays of Arrays

A Special Case:
- Each array has the same number of elements and that number is known
An Implication:
- Both sizes are known when the memory is allocated
A Visualization: