How to initialise a three dimensional ruby array - arrays

Question

I want to initialise a three dimensional ruby array. For a two-dimensional array, I can do
a = Array.new(4){ Array.new(5, 0) }
so I have tried
a = Array.new(4) { Array.new(5, Array.new(6, 0)) }
but if I do a[1][2][3] = 5, it not only sets that element to 5, it sets the corresponding element to 5 in other sub arrays i.e.
[[[0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0]],
[[0, 0, 0, 5, 0, 0], [0, 0, 0, 5, 0, 0], [0, 0, 0, 5, 0, 0], [0, 0, 0, 5, 0, 0], [0, 0, 0, 5, 0, 0]],
[[0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0]],
[[0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0]]]

Answer 1

The issue is that if you pass the value as an argument, you will get an array where each value refers to that same object. You do exactly that with:
Array.new(5, Array.new(6, 0))
You can use Array#*, i.e array multiplication instead:
[[[0] * 6] * 5] * 4

Answer 2

Just use the same syntax (with a block instead of an argument : Array.new(n){...}) for all the dimensions.
a = Array.new(4) { Array.new(5) { Array.new(6, 0) } }
This way, your code will create 20 distincts Array.new(6, 0) sub-sub-arrays instead of replicating the same object 5 times.
require 'pp'
a = Array.new(4) { Array.new(5) { Array.new(6, 0) } }
a[1][2][3] = 5
pp a
# [[[0, 0, 0, 0, 0, 0],
# [0, 0, 0, 0, 0, 0],
# [0, 0, 0, 0, 0, 0],
# [0, 0, 0, 0, 0, 0],
# [0, 0, 0, 0, 0, 0]],
# [[0, 0, 0, 0, 0, 0],
# [0, 0, 0, 0, 0, 0],
# [0, 0, 0, 5, 0, 0],
# [0, 0, 0, 0, 0, 0],
# [0, 0, 0, 0, 0, 0]],
# [[0, 0, 0, 0, 0, 0],
# [0, 0, 0, 0, 0, 0],
# [0, 0, 0, 0, 0, 0],
# [0, 0, 0, 0, 0, 0],
# [0, 0, 0, 0, 0, 0]],
# [[0, 0, 0, 0, 0, 0],
# [0, 0, 0, 0, 0, 0],
# [0, 0, 0, 0, 0, 0],
# [0, 0, 0, 0, 0, 0],
# [0, 0, 0, 0, 0, 0]]]

Answer 3

The following worked properly.
a=Array.new(4){ Array.new(5) { Array.new(6,0) }}

Answer 4

You can use recursion to initialize the elements of a multidimensional array of any dimension.1
Code
def init(n, *rest)
rest.empty? ? Array.new(n, 0) : Array.new(n) { init(*rest) }
end
Examples
dims = [2, 3, 2]
a = init(*dims)
#=> [[[0, 0], [0, 0], [0, 0]], [[0, 0], [0, 0], [0, 0]]]
a[0][0][0] = 1
a #=> [[[1, 0], [0, 0], [0, 0]], [[0, 0], [0, 0], [0, 0]]]
dims = [2, 3, 2, 4, 2, 3]
a = init(*dims)
a.flatten.size
#=> 288 (= 2*3*2*4*2*3)
a[0][0][0][0][0][0] = 1
a.flatten.count(1)
#=> 1
Explanation
The steps are as follows.
Suppose, as in the example,
dims = [2, 3, 2]
Then
n, *rest = dims
#=> [2, 3, 2]
n #=> 2
rest
#=> [3, 2]
As rest.empty? #=> false, the method returns
Array.new(2) { init(*[3, 2]) } # (1)
#=> [[[0, 0], [0, 0], [0, 0]], [[0, 0], [0, 0], [0, 0]]]
To obtain this result, we execute the block
{ init(*[3, 2]) }
for each of the two elements of the array being constructed. This requires us to compute init([3, 2]) (same as { init(3, 2) }), which is done as follows.
n, *rest = [3, 2]
#=> [3, 2]
n #=> 3
rest
#=> [2]
Again, as rest.empty? #=> false, we return
Array.new(3) { init(*[2]) } # (2)
#=> [[0, 0], [0, 0], [0, 0]]
to expression (1) above. For each of the 3 elements of this array we execute the block
{ init(*[2]) }
This requires us to compute init([2]), which is done as follows.
n, *rest = [2]
#=> [2]
n #=> 2
rest
#=> []
This time, since rest.empty? #=> true, we compute and return
Array.new(2, 0)
#=> [0, 0]
to expression (2) above.
1 Yes, there's no such thing as a "multidimensional array" in Ruby, but I expect readers to know what I mean. The alternative is something like "...of an array containing nested arrays of equal size with any number of levels of nesting", but even that is incomplete as it fails to exclude, for example, [[1, [2,3]], [4,5]]. It would be helpful if Ruby had a name for such objects.