updated.rb

### ALGORITHM ###

# for each index 0 .. last_index
  #for each index i .. 0
    # during each iteration of the inner loop
    # we store one member of a diagonal from the upper-left half
    # and the element that reflects it across the line y=x (the middle diagonal)
    # the member from the upper-left half is at index [i-j][i]
    # we push this member into the final array at index i

    # the member from the bottom half, that mirrors the above member
    # is at the above index plus an offset of (last_index - i),(last_index - i)

    # we push this member into the final array at index i + (2 * offset)
    # in order to avoid double counting the elements from the middle diagonal
    # we check to see that that mirror_diagonal is not the same as the middle_diagonal
    # in the case that they are the same, we are at the middle diagonal, 
    # so we avoid inserting the element (the mirror of the middle diagonal is itself)


matrix = ('a'..'y').each_slice(5).to_a

def all_diagonals(m)
  len = m[0].length
  
  diagonals = Array.new(2*len - 1){[]} #Create array of empty arrays 
                                   #The num of diagonals is 2 * (matrix length) - 1
  
  middle_diagonal_index = last_index = len - 1
    
  0.upto(last_index) do |i|
    offset = last_index - i
    mirror_diagonal_index = i + 2*offset
    
    i.downto(0) do |j|
      diagonals[i] << m[i-j][j]
      if mirror_diagonal_index != middle_diagonal_index
        diagonals[mirror_diagonal_index] << m[i-j+offset][j+offset]
      end
    end
    
  end
  diagonals
end


matrix.each { |i| p i }

puts; puts;

p all_diagonals(matrix)