1. 310201 Fundamental Programming
Introduction to Multidimensional Arrays

2. Introduction to two-dimensional arrays
There are many problems where the data being processed can be naturally organised as a table.
A two dimensional array provides a way to build such a software model.

3. A 2D Array
<Type of array> <Array Name> [<num rows>] [<num columns>]
Example :
float Sales_Array [3] [12]
// Hold 3 years of monthly sales data.

4. A 2D Array Example to hold character for a computer screen :
const int NumRows = 24, NumColumns = 80;
char Screen1 [NumRows] [NumColumns];
// Table : rows 0-23 columns 0-79

5. Getting to elements
The variable Screen1 is a two-dimensional array in which the notation
Screen1[0][0] is the element at row 1 and column 1
Screen1[22][60] is the element at row 23 and column 61
cout << Screen1[12][12]
// display element stored row 13 col 13
Screen[23][79] = ‘*’;
// store element at row 24 col 80

6. Getting to elements
Accessing all elements of the table using nested loops
for (int row = 0; row < NumRows; row++) {
for (int col = 0; col < NumColumns; col++)
cout << Screen1[row][col];
// display all columns
cout << endl;
// skip a line to display next row }

7. Passing 2D arrays to functions
An example :
int main() {
char DisplayScreen [24] [80]; …
Initialise(DisplayScreen); }

8. Passing 2D arrays to functions
void Initialise(Screen [ ] [ ])
// Initialise the Screen Array – set all values to spaces. {
for (int row = 0; row < NumRows; row++)
for (int col = 0; col < NumColumns; col++)
Screen[row][col] = ‘ ‘; }

9. Initialising 2 D Arrays For example const int ROWS = 4, COLS = 3;
float TempTable[ROWS][COLS] = {17.0}; or
float TempTable[ROWS][COLS] =
{ {65.5, 68.3, 62.0}, // Row 1
{68.8, 68.9, 64.5}, // Row {70.4, 69.4, 66.3}, // Row 3
{68.8, 68.9, 64.5}, // Row 4
} ; // using double braces

10. 3D Arrays - Example
So far we have looked at 2D arrays or tables now we will investigate arrays with a greater number of dimensions. i.e. have more than 2 indices

11. 3D Arrays - Example
To define a 3D array which holds prices for ice-creams:
const int Flavors = 12, Sizes = 3, Conetypes = 2;
float Prices[Flavors][Sizes][Conetypes];

12. 3D Arrays - Example To address individual elements
cout << Prices[8][2][1];
// price of flavor 9, size 3, conetype 2.
Price[10][0][1] = 4.75;
// price of flavor 11, size 1, conetype 2.

13. 3D Arrays – Example (cont …)
If you wish to loop through higher dimensional arrays displaying or setting all elements, then you require a loops for each dimension.
For 2D arrays, you need 2 nested loops.

14. 3D Arrays – Example (cont …)
For 3D arrays, you need 3 nested loops:
for(int f = 0; f < Flavors; f++)
for(int s = 0; s < Sizes; s++)
for(int c = 0; c < Conetypes; c++)
Price[f][s][c] = 5.50;
// loop thru’ 12*3*2 (72) times

15. 3D Arrays – Example (cont …)
It is easy to visualize the array in three dimensions:
Size
Flavor
Conetype

16. Greater than 3D arrays
You may declare and use greater than 3D arrays, but these are hard to visualise at first.
In business, you may well be dealing with 7 dimension, 10 dimension, or higher arrays.
Just think as each of the elements of the array as having more than three attributes which describes it uniquely.

17. Example : 4D Array
For example, a company may wish to track its actual and forecast sales by year, month, region, and product, as follows :
Years , 1998, 1999, 2000, 2001, 2002
Months - Jan,Feb,Mar,Apr,May,Jun,Jul,Aug,Sep,Oct,Nov,Dec
Regions - NSW, Qld, Vic, Tas, SA, WA, NT
Products - Toaster, Fridge, Jug, Washing_Machine
int actual_sales[6][12][7][4];
int forecast_sales[6][12][7][4];

18. Example : 4D Array (cont ….)
Using a 4D array, it would be possible to store the sales details by year, month, region, and product.
So, for example, to record the actual number of sales of toasters in Qld in Dec 2000, we would do so as follows :
Actual_Sales [3][11][1][0] = 1500;

19. Example : 4D Array (cont ….)
To set a Forecast Sales for Toasters in Qld in Dec 2001, we may increase the 2000 value by 10% as follows :
Forecast_Sales [4][11][1][0] =
Actual_Sales [3][11][1][0] * 1.10;

20. Example : 4D Array (cont ….)
In fact, we could set all 2001 Forecast values to be the 2000 Actuals increased by 10% as follows :
for(int month = 0; month < 12; month++)
for(int region = 0; region < 7 ; region++)
for(int prod = 0; prod < 4; prod++)
Forecast_Sales [4][month][region][prod] =
Actual_Sales [3][month][region][prod] * 1.10;

21. Things to watch out for and be aware of :
The order of dimensions is very important – you must always list the array’s dimensions in the same order in which they were originally defined !
If you define an array eg
Int Whatever[10][8][6]
then valid subscripts are 0-9, 0-7, and 0-5 respectively!!!

22. Example : 4D Array (cont ….)
A diagram of the 4D array may help to visualize it :
Regions
Years
Months
Products

23. 5D Arrays
Using a 5D array, it would be possible to store the sales details by year, month, region, product, and salesperson.

24. 6D Arrays Using a 6D array, we could store numbers of students by
Mode of study (eg Internal, External),
Campus (eg Bundy, Rocky, Melbourne, Sydney),
Gender (eg M, F),
Program (eg BIT, BMM, BAT, BComms),
Year of enrolment (eg 1999, 2000, 2001),
Background (eg School leaver, TAFE, Mature age)

25. Summary
Multidimensional arrays are just extensions of the ideas introduced when discussing one-dimensional arrays!