Step by Step solution about How to resolve the algorithm Magic squares of doubly even order step by step in the Ruby programming language

This Ruby code defines two methods to create and display a double even magic square:

double_even_magic_square(n):

• It takes one argument, n, which must be an even multiple of 4 (e.g., 8, 12, 16, 20).
• It raises an ArgumentError if n is not a multiple of 4.
• It calculates various constants based on n: block_size (n/4) and max (n*n).
• It defines a pre_pat list to create a pattern that alternates between 'true' and 'false'. This pattern is used to generate a sequence of numbers that form the magic square.
• It flattens and repeats the pre_pat pattern to create a single array pattern of length n*n.
• It creates a flat array flat_ar by iterating through pattern and converting 'true' elements to numbers ranging from 1 to max and 'false' elements to numbers ranging from max to 1.
• It slices the flat_ar into rows of size n and returns a 2D array representing the magic square.

to_string(square):

• It takes one argument, square, which is a 2D array representing the magic square.
• It calculates the number of columns n as the square's length.
• It defines a format string fmt to format the numbers with the correct width based on the number of digits in the largest number in the square.
• It iterates through the square, flattening each row and inserting the formatted row into a string.
• It returns the resulting string.

In the main block of the code:

• It calls double_even_magic_square(8) to create an 8x8 double even magic square.
• It calls to_string to format and display the magic square as a string.

def double_even_magic_square(n)
  raise ArgumentError, "Need multiple of four" if n%4 > 0
  block_size, max = n/4, n*n
  pre_pat = [true, false, false, true,
             false, true, true, false]
  pre_pat += pre_pat.reverse
  pattern = pre_pat.flat_map{|b| [b] * block_size} * block_size
  flat_ar = pattern.each_with_index.map{|yes, num| yes ? num+1 : max-num}
  flat_ar.each_slice(n).to_a
end

def to_string(square)
  n = square.size
  fmt = "%#{(n*n).to_s.size + 1}d" * n
  square.inject(""){|str,row| str << fmt % row << "\n"}
end

puts to_string(double_even_magic_square(8))