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


/** Missing scalar multiplication, but we don't need it. */
def makeVector2(x, y) {
  return def vector {
    to x() { return x }
    to y() { return y }
    to add(other) { return makeVector2(x + other.x(), y + other.y()) }
    to clockwise() { return makeVector2(-y, x) }
  }
}
 
/** Bugs: (1) The printing is specialized. (2) No bounds check on the column. */
def makeFlex2DArray(rows, cols) {
  def storage := ([null] * (rows * cols)).diverge()
  return def flex2DArray {
    to __printOn(out) {
      for y in 0..!rows {
        for x in 0..!cols {
          out.print(<import:java.lang.makeString>.format("%3d", [flex2DArray[y, x]]))
        }
        out.println()
      }
    }
    to get(r, c) { return storage[r * cols + c] }
    to put(r, c, v) { storage[r * cols + c] := v }
  }
}