Multidimensional Arrays

Overview

The number of indices needed to specify an element is called the dimension or dimensionality of the array. A two-dimensional array, or table, may be stored as a one-dimensional array of one-dimensional arrays (rows of columns) and accessed with double indexing (array[row][column] in typical notation).^[1]

Discussion

An array is a sequenced collection of elements of the same data type with a single identifier name. As such, the array data type belongs to the “Complex” category or family of data types. Arrays can have multiple axes (more than one axis). Each axis is a dimension. Thus a single dimension array is also known as a list. A two-dimension array is commonly known as a table (a spreadsheet like Excel is a two dimension array). In real life, there are occasions to have data organized into multiple dimensioned arrays. Consider a theater ticket with section, row, and seat (three dimensions).

We refer to the individual values as members (or elements) of the array. Multidimensional arrays use one set of square brackets per dimension or axis of the array. For example, a table which has two dimensions would use two sets of square brackets to define the array variable and two sets of square brackets for the index operators to access the members of the array. Programming languages implement the details of arrays differently. The total number of dimensions allowed in an array is language-specific and also limited by available memory.

Pseudocode

Function Main
    Declare String Array game[3][3]
    
    Assign game = [ ["X", "O", "X"], ["O", "O", "O"], ["X", "O", "X"] ]

    DisplayGame(game)
End

Function DisplayGame (String Array game)
    Declare Integer row
    Declare Integer column
    
    Output "Tic-Tac-Toe"
    For row = 0 to 2
        For column = 0 to 2
            Output game[row][column]
            If column < 2 Then
                Output " | "
            End
        End
    End
End

Output

Tic-Tac-Toe
X | O | X
O | O | O
X | O | X

Key Terms

array member

An element or value in an array.

dimension

An axis of an array.

index

An operator that allows us to reference a member of an array.

list

A single dimension array.

offset

The method of referencing array members by starting at zero.

table

A two-dimension array.

References

• cnx.org: Programming Fundamentals – A Modular Structured Approach using C++