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One Dimension, Two Dimensions

Reference > Science > Technology > Beginner Programming Tips
 

In my previous tip, I talked about how to find a one dimensional index into a two dimensional array. If you are ever in a situation where you need to do that, there's a good chance you'll need to do the opposite as well!

Let's say you have a one-dimensional array MyArray(99). This is an array with 100 elements. But you want to think of these 100 elements as being laid out in a 10x10 grid, assigning X and Y "coordinates" to each one:
 

MyArray(0)   (0,0)
MyArray(1)   (0,1)
MyArray(2)   (0,2)
...
MyArray(9)   (0,9)
MyArray(10)  (1,0)
MyArray(11)  (1,1)
...
MyArray(97)  (9,7)
MyArray(98)  (9,8)
MyArray(99)  (9,9)


To do this, there are two nice little operations you should know about. Here they are:

Integer Division: Normally when you divide, you write your division like this:

X = Y / 10


But there's another way to divide, and it looks like this:

X = Y \ 10


What does this do? It takes the integer part of the division Y / 10. In other words, it's essentially the same as writing:

X = Int(Y / 10)


Modulus The Mod operator calculates the remainderwhen one value is divided by another. For example: 

X = 12 Mod 7


When you divide 12 by 7, you get an answer of 1, with a remainder of 5. So in this example, X would equal 5.

Now, with these two tools in our toolbox, we can write the following functions:

Dim MyArray(99)

'Get the X Coordinate
Public Function XCoordinate(Index As Integer)
   XCoordinate = Index Mod 10
End Function

'Get the Y Coordinate
Public Function YCoordinate(Index As Integer)
   YCoordinate = Index \ 10
End Function


This time I have two functions, because in converting the one dimensional array to a two dimensional array, the array index has two coordinates instead of just one.

Now suppose, instead of our easy 10x10 array, we've got a 5x12 array. How does that change our code? Take a look, and make sure you understandwhy it has changed this way.
 

Dim MyArray(59)

'Get the X Coordinate
Public Function XCoordinate(Index As Integer)
   XCoordinate = Index Mod 12
End Function

'Get the Y Coordinate
Public Function YCoordinate(Index As Integer)
   YCoordinate = Index \ 12
​End Function


In both functions we used the twelve, but not the five! Of course, this is because we wanted to lay out the array as a 5x12 "grid". If we wanted to lay it out as a 12x5 grid, do you think we would have used the 5 instead? You bet we would! 

Questions

1.
Calculate: X = 20 Mod 5.
2.
Calculate: X = 20 Mod 7.
3.
Calculate: X = 15 Mod 12.
4.
Calculate: X = 8 Mod 7.
5.
Calculate: X = 7 Mod 8.
6.
Calculate: X = 20 \ 5.
7.
Calculate: X = 20 \ 7.
8.
Calculate: X = 15 \ 12.
9.
Calculate: X = 8 \ 7.
10.
Calculate: X = 7 \ 8.
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Two Dimensions, One DimensionTwo Dimensions, One Dimension
Removing an Array ElementRemoving an Array Element
 

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