Step by Step solution about How to resolve the algorithm Random Latin squares step by step in the Ruby programming language

The provided Ruby code generates and prints a Latin square of size N. A Latin square is an N x N grid filled with N unique values, with no repeats in any row or column.

• The code begins by setting the size of the square to N, which is 5 in this case.

• It then defines a method called generate_square that generates a Latin square. The method first creates a list of all possible permutations of the numbers from 1 to N. It then shuffles the list to create a random order.

• Next, the method creates an empty square. It then iterates through the rows of the square, and for each row, it selects a random permutation from the list of permutations.

• It checks that the chosen permutation does not have any duplicates in any column and then adds the chosen permutation to the square. It then removes all permutations from the list that have any duplicates in any column with the chosen permutation.

• After generating the Latin square, the code defines a method called print_square that prints the square to the console. The method first calculates the size of each cell in the square based on the number of digits in the largest number in the square.

• It then converts each row of the square to a string, padding each number with spaces to ensure that all cells are the same size. Finally, it prints the square to the console.

• The main part of the code calls the generate_square and print_square methods twice, generating and printing two different Latin squares of size 5.

N = 5

def generate_square
  perms  =  (1..N).to_a.permutation(N).to_a.shuffle
  square = []
  N.times do
    square << perms.pop
    perms.reject!{|perm| perm.zip(square.last).any?{|el1, el2| el1 == el2} }
  end
  square
end

def print_square(square)
  cell_size = N.digits.size + 1
  strings = square.map!{|row| row.map!{|el| el.to_s.rjust(cell_size)}.join }
  puts strings, "\n"
end

2.times{print_square( generate_square)}