Task

Produce a zig-zag array.



A   zig-zag   array is a square arrangement of the first   N2   natural numbers,   where the

numbers increase sequentially as you zig-zag along the array's   anti-diagonals.

For a graphical representation, see   JPG zigzag   (JPG uses such arrays to encode images).



For example, given   5,   produce this array:

 0  1  5  6 14
 2  4  7 13 15
 3  8 12 16 21
 9 11 17 20 22
10 18 19 23 24



Related tasks

   Spiral matrix
   Identity matrix
   Ulam spiral (for primes)


See also

   Wiktionary entry:   anti-diagonals


# Create an m x n matrix
 def matrix(m; n; init):
   if m == 0 then []
   elif m == 1 then [range(0;n)] | map(init)
   elif m > 0 then
     matrix(1;n;init) as $row
     | [range(0;m)] | map( $row )
   else error("matrix\(m);_;_) invalid")
   end ;
 
# Print a matrix neatly, each cell occupying n spaces
def neatly(n):
  def right: tostring | ( " " * (n-length) + .);
  . as $in
  | length as $length
  | reduce range (0;$length) as $i
      (""; . + reduce range(0;$length) as $j
      (""; "\(.) \($in[$i][$j] | right )" ) + "\n" ) ;
 