I've just learned from a comment posted by the OP that I've solved the wrong problem, despite the fact that the OP's question seems quite clear, especially the example, and is consistent with my interpretation. I will leave this solution to the following problem: "Given an array arr such that Matrix(*arr) is an NxM matrix, and a matrix location i,j, return an array [d,a], where elements d and a are elements on the diagonal and antidiagonal that pass through [d,a] but do not include [d,a] and are each rotated so that row index of the first element is i+1 if i < arr.size-1 and is 0 otherwise.
Code
def diagonals(arr, row_idx, col_idx)
ncols = arr.first.size
sum_idx = row_idx+col_idx
diff_idx = row_idx-col_idx
a = Array.new(arr.size * arr.first.size) { |i| i.divmod(ncols) } -[[row_idx, col_idx]]
[a.select { |r,c| r-c == diff_idx }, a.select { |r,c| r+c == sum_idx }].
map do |b| b.sort_by { |r,_| [r > row_idx ? 0:1 , r] }.
map { |r,c| arr[r][c] }
end
end
All elements of the array arr must be equal in size but there is no requirement that arr.size = arr.first.size.
Example
arr = [
[ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10],
[11, 12, 13, 14, 15, 16, 17, 18, 19, 20],
[21, 22, 23, 24, 25, 26, 27, 28, 29, 30],
[31, 32, 33, 34, 35, 36, 37, 38, 39, 40],
[41, 42, 43, 44, 45, 46, 47, 48, 49, 50],
[51, 52, 53, 54, 55, 56, 57, 58, 59, 60],
[61, 62, 63, 64, 65, 66, 67, 68, 69, 70],
[71, 72, 73, 74, 75, 76, 77, 78, 79, 80],
[81, 82, 83, 84, 85, 86, 87, 88, 89, 90],
[91, 92, 93, 94, 95, 96, 97, 98, 99, 100]
]
diagonals(arr, 4, 4)
#=> [[56, 67, 78, 89, 100, 1, 12, 23, 34],
# [54, 63, 72, 81, 9, 18, 27, 36]]
Explanation
Suppose
arr = (1..16).each_slice(4).to_a
#=> [[ 1, 2, 3, 4],
# [ 5, 6, 7, 8],
# [ 9, 10, 11, 12],
# [13, 14, 15, 16]]
row_idx = 2
col_idx = 1
The steps are as follows.
a = Array.new(arr.size) { |i| Array.new(arr.first.size) { |j| [i,j] } }
#=> [[[0, 0], [0, 1], [0, 2], [0, 3]],
# [[1, 0], [1, 1], [1, 2], [1, 3]],
# [[2, 0], [2, 1], [2, 2], [2, 3]],
# [[3, 0], [3, 1], [3, 2], [3, 3]]]
ncols = arr.first.size
#=> 4
sum_idx = row_idx+col_idx
#=> 3
diff_idx = row_idx-col_idx
#=> 1
a = Array.new(arr.size * arr.first.size) { |i| i.divmod(ncols) } - [[row_idx, col_idx]]
#=> [[0, 0], [0, 1], [0, 2], [0, 3], [1, 0], [1, 1], [1, 2], [1, 3],
# [2, 0], [2, 2], [2, 3], [3, 0], [3, 1], [3, 2], [3, 3]]
Select and sort the locations [r, c] on the top-left to bottom-right diagonal that passes through [row_idx, col_idx].
b = a.select { |r,c| r-c == diff_idx }
#=> [[1, 0], [3, 2]]
c = b.sort_by { |r,_| [r > row_idx ? 0:1 , r] }
#=> [[3, 2], [1, 0]]
Select and sort the locations [r, c] on the top-right bottom-left diagonal that passes through [row_idx, col_idx].
d = a.select { |r,c| r+c == sum_idx }
#=> [[0, 3], [1, 2], [3, 0]]
e = d.sort_by { |r,c| [r > row_idx ? 0:1 , r] }
#=> [[3, 0], [0, 3], [1, 2]]
[c, e].map { |f| f.map { |r,c| arr[r][c] }
#=> [c, e].map { |f| f.map { |r,c| arr[r][c] } }
#=> [[15, 5], [13, 4, 7]]
