How do I split a 9x9 array into 9 3x3 components - arrays

Question

I have a 9x9 multidimensional array that represents a sudoku game. I need to break it into it's 9 3x3 many components. How would this be done? I have absolutely no idea where to begin, here.
game = [
[1, 3, 2, 5, 7, 9, 4, 6, 8],
[4, 9, 8, 2, 6, 1, 3, 7, 5],
[7, 5, 6, 3, 8, 4, 2, 1, 9],
[6, 4, 3, 1, 5, 8, 7, 9, 2],
[5, 2, 1, 7, 9, 3, 8, 4, 6],
[9, 8, 7, 4, 2, 6, 5, 3, 1],
[2, 1, 4, 9, 3, 5, 6, 8, 7],
[3, 6, 5, 8, 1, 7, 9, 2, 4],
[8, 7, 9, 6, 4, 2, 1, 5, 3]
]
Split into chunks, it becomes
chunk_1 = [
[1, 3, 2],
[4, 9, 8],
[7, 5, 6]
]
chunk_2 = [
[5, 7, 9],
[2, 6, 1],
[3, 8, 4]
]
...and so on

Answer 1

That was a fun exercise!
Answer
game.each_slice(3).map{|stripe| stripe.transpose.each_slice(3).map{|chunk| chunk.transpose}}.flatten(1)
It would be cumbersome and not needed to define every chunk_1, chunk_2, ....
If you want chunk_2, you can use extract_chunks(game)[1]
It outputs [chunk_1, chunk_2, chunk_3, ..., chunk_9], so it's an Array of Arrays of Arrays :
1 3 2
4 9 8
7 5 6
5 7 9
2 6 1
3 8 4
4 6 8
3 7 5
2 1 9
6 4 3
5 2 1
...
You can define a method to check if this grid is valid (it is) :
def extract_chunks(game)
game.each_slice(3).map{|stripe| stripe.transpose.each_slice(3).map{|chunk| chunk.transpose}}.flatten(1)
end
class Array # NOTE: Use refinements if you don't want to patch Array
def has_nine_unique_elements?
self.flatten(1).uniq.size == 9
end
end
def valid?(game)
game.has_nine_unique_elements? &&
game.all?{|row| row.has_nine_unique_elements? } &&
game.all?{|column| column.has_nine_unique_elements? } &&
extract_chunks(game).all?{|chunk| chunk.has_nine_unique_elements? }
end
puts valid?(game) #=> true
Theory
The big grid can be sliced in 3 stripes, each containing 3 rows of 9 cells.
The first stripe will contain chunk_1, chunk_2 and chunk_3.
We need to cut the strip vertically into 3 chunks. To do so :
We transpose the strip,
Cut it horizontally with each_slice,
transpose back again.
We do the same for stripes #2 and #3.
To avoid returning an Array of Stripes of Chunks of Rows of Cells, we use flatten(1) to remove one level and return an Array of Chunks of Rows of Cells. :)

Answer 2

The method Matrix#minor is tailor-made for this:
require 'matrix'
def sub3x3(game, i, j)
Matrix[*game].minor(3*i, 3, 3*j, 3).to_a
end
chunk1 = sub3x3(game, 0, 0)
#=> [[1, 3, 2], [4, 9, 8], [7, 5, 6]]
chunk2 = sub3x3(game, 0, 1)
#=> [[5, 7, 9], [2, 6, 1], [3, 8, 4]]
chunk3 = sub3x3(game, 0, 2)
#=> [[4, 6, 8], [3, 7, 5], [2, 1, 9]]
chunk4 = sub3x3(game, 1, 0)
#=> [[6, 4, 3], [5, 2, 1], [9, 8, 7]]
...
chunk9 = sub3x3(game, 2, 2)
#=> [[6, 8, 7], [9, 2, 4], [1, 5, 3]]
Ruby has not concept of "rows" and "columns" of arrays. For convenience, therefore, I will refer to the 3x3 "subarray" of game, at offsets i and j (i = 0,1,2, j = 0,1,2), as the 3x3 submatrix of m = Matrix[*game] whose upper left value is at row offset 3*i and column offset 3*j of m, converted to an array.
This is relatively inefficient as a new matrix is created for the calculation of each "chunk". Considering the size of the array, this is not a problem, but rather than making that more efficient you really need to rethink the overall design. Creating nine local variables (rather than, say, an array of nine arrays) is not the way to go.
Here's a suggestion for checking the validity of game (that uses the method sub3x3 above) once all the open cells have been filled. Note that I've used the Wiki description of the game, in which the only valid entries are the digits 1-9, and I have assumed the code enforces that requirement when players enter values into cells.
def invalid_vector_index(game)
game.index { |vector| vector.uniq.size < 9 }
end
def sub3x3_invalid?(game, i, j)
sub3x3(game, i, j).flatten.uniq.size < 9
end
def valid?(game)
i = invalid_vector_index(game)
return [:ROW_ERR, i] if i
j = invalid_vector_index(game.transpose)
return [:COL_ERR, j] if j
m = Matrix[*game]
(0..2).each do |i|
(0..2).each do |j|
return [:SUB_ERR, i, j] if sub3x3_invalid?(game, i, j)
end
end
true
end
valid?(game)
#=> true
Notice this either returns true, meaning game is valid, or an array that both signifies that the solution is not valid and contains information that can be used to inform the player of the reason.
Now try
game[5], game[6] = game[6], game[5]
so
game
#=> [[1, 3, 2, 5, 7, 9, 4, 6, 8],
# [4, 9, 8, 2, 6, 1, 3, 7, 5],
# [7, 5, 6, 3, 8, 4, 2, 1, 9],
# [6, 4, 3, 1, 5, 8, 7, 9, 2],
# [5, 2, 1, 7, 9, 3, 8, 4, 6],
# [2, 1, 4, 9, 3, 5, 6, 8, 7],
# [9, 8, 7, 4, 2, 6, 5, 3, 1],
# [3, 6, 5, 8, 1, 7, 9, 2, 4],
# [8, 7, 9, 6, 4, 2, 1, 5, 3]]
valid?(game)
#=> [:SUB_ERR, 1, 0]
The rows and columns are obviously still valid, but this return value indicates that at least one 3x3 subarray is invalid and the array
[[6, 4, 3],
[5, 2, 1],
[2, 1, 4]]
was the first found to be invalid.

Answer 3

You could create a method that generates a single 3X3 chunk from a given index. since the sudoku board is of length 9, that will produce 9 3X3 chunks for you. see below.
#steps
#you'll loop through each index of the board
#to get the x value
#you divide the index by 3 and multiply by 3
#to get the y value
#you divide the index by 3, take remainder and multiply by 3
#for each x value, you can get 3 y values
#this will give you a single 3X3 box from one index so
def three_by3(index, sudoku)
#to get x value
x=(index/3)*3
#to get y value
y=(index%3)*3
(x...x+3).each_with_object([]) do |x,arr|
(y...y+3).each do |y|
arr<<sudoku[x][y]
end
end
end
sudoku = [ [1,2,3,4,5,6,7,8,9],
[2,3,4,5,6,7,8,9,1],
[3,4,5,6,7,8,9,1,2],
[1,2,3,4,5,6,7,8,9],
[2,3,4,5,6,7,8,9,1],
[3,4,5,6,7,8,9,1,2],
[1,2,3,4,5,6,7,8,9],
[2,3,4,5,6,7,8,9,1],
[3,4,5,6,7,8,9,1,2]]
p (0...sudoku.length).map {|i| three_by3(i,sudoku)}
#output:
#[[1, 2, 3, 2, 3, 4, 3, 4, 5],
# [4, 5, 6, 5, 6, 7, 6, 7, 8],
# [7, 8, 9, 8, 9, 1, 9, 1, 2],
# [1, 2, 3, 2, 3, 4, 3, 4, 5],
# [4, 5, 6, 5, 6, 7, 6, 7, 8],
# [7, 8, 9, 8, 9, 1, 9, 1, 2],
# [1, 2, 3, 2, 3, 4, 3, 4, 5],
# [4, 5, 6, 5, 6, 7, 6, 7, 8],
# [7, 8, 9, 8, 9, 1, 9, 1, 2]]