- For more information, see Array data structure on Wikipedia.
An array is an ordered collection of elements with each element accessible by an index or multiple indices (like a coordinate) in the case of a multi-dimensional array. A 1-dimensional array is similar to a list, however, arrays are more specific and simpler in their implementation, being generally a portion of memory where every element is the same type and their locations are known directly from their indices.
The first element index is often either 0 or 1 and said to be using zero-based indexing or one-based indexing, respectively.
Uses
Arrays are versatile and have countless uses. 1-dimensional arrays in particular can be used to build other collections such as lists and strings.
Higher dimensions can be used to store:
- pixels in a raster image
- matrices
- tiles in a 2D game
- voxels in a 3D game
Multidimensional Arrays in Scratch
Scratch does not support arrays however lists are functionally similar to 1-dimensional arrays. It is possible to pack multi-dimensional data into arrays of lower dimensions, thus allowing for one or more lists to be used.
Methodology
Any multidimensional array can flattened into a 1-dimensional array. The indices can be calculated knowing the size of the multidimensional array along each dimension.
- For a 2D array indexed from 0, the index in the 1D array is , where and are the offsets along the x and y dimensions, and is the size of the array along the x dimension.
- For a 3D array indexed from 0, the index in the 1D array is .
Addition of 1 is needed if the 1-dimensional array uses 1-based indexing, such as when represented by a Scratch list.
2D
The following shows how a 2D array can be implemented in Scratch using a list.
The list will be simply called "array" and two variables will be used to store its size: (size x) and (size y)
Initialization
The number of items in the list are equivalent to multiplying the sizes of the x and y dimensions. To initialize the array with empty values, clear the list and add all the items as needed.
delete all of [array v] repeat ((size x) * (size y)) add [] to [array v] end
Index
To get the index of a list item, use:
set [i v] to ((((iy) * (size x)) + (ix)) + (1))
"ix" and "iy" must be ≥0 and less than the size of their corresponding dimension.
To go the other way and get the dimension offsets from index, use:
set [ix v] to (((i) - (1)) mod (size x)) set [iy v] to ([floor v] of (((i) - (1)) / (size x)))
"i" must be ≥0 and less than the number of items in the list.
Set Value
To set a value, use the above calculated index:
replace item ((((iy) * (size x)) + (ix)) + (1)) of [array v] with [value]
Get Value
Similarly, to get a value:
(item ((((iy) * (size x)) + (ix)) + (1)) of [array v])
3D
A 3D array is much the same as the 2D array, except the indices are calculated with the 3rd dimension.
To get the index of a list item, use:
set [i v] to (((((iz) * ((size x) * (size y))) + ((iy) * (size x))) + (ix)) + (1))
To go the other way and get the dimension offsets from index, use:
set [ix v] to (((i) - (1)) mod (size x)) set [iy v] to (([floor v] of (((i) - (1)) / (size x))) mod (size y)) set [iz v] to ([floor v] of (((i) - (1)) / ((size x) * (size y))))
