Step by Step solution about How to resolve the algorithm Zig-zag matrix step by step in the Ruby programming language

The provided Ruby code defines two methods, zigzag and print_matrix, to generate and print a zigzag matrix. Here's how these methods work:

1. zigzag method:

   • It takes one argument, n, which represents the number of rows and columns in the desired zigzag matrix.
   • The method uses Ruby's product method to generate pairs of indices (x, y) for each cell in the matrix.
   • It then sorts these pairs using a custom sorting criteria based on the following logic:
     • Sort by the sum of x and y in ascending order.
     • If the sum is even, sort by y in ascending order.
     • If the sum is odd, sort by -y in descending order.
   • After sorting, the method converts the sorted pairs to a 1D array by extracting the second value from each pair (i.e., x).
   • Finally, it divides this 1D array into sub-arrays of length n to create the zigzag matrix and returns it.

2. print_matrix method:

   • It takes one argument, m, which is a 2D matrix.
   • The method calculates the maximum value in the flattened version of the matrix (i.e., the largest number in all cells).
   • It determines the formatting string format based on the length of this maximum value.
   • The method then iterates over each row of the matrix and prints it using the format string to ensure consistent spacing.

To demonstrate the functionality of these methods, the code includes a call to print_matrix with the result of zigzag(5). This will generate and print a 5x5 zigzag matrix.

For example, when n is 5, the zigzag method will produce the following zigzag matrix:

1  7 13 19 25
2  8 14 20 26
3  9 15 21 27
4 10 16 22 28
5 11 17 23 29

And the print_matrix method will format and print this matrix as shown above.

def zigzag(n)
  (seq=*0...n).product(seq)
    .sort_by {|x,y| [x+y, (x+y).even? ? y : -y]}
    .each_with_index.sort.map(&:last).each_slice(n).to_a
end

def print_matrix(m)
  format = "%#{m.flatten.max.to_s.size}d " * m[0].size
  puts m.map {|row| format % row}
end

print_matrix zigzag(5)