Zig-zag scan an N x N array

Question

I have a simple array. The array length always has a square root of an integer. So 16, 25, 36 etc.

$array = array(\'1\', \'2\', \'3\', \'4\' ... \'25\');
         


        

Answer 1

Example Python implementation:

def wave(size):
    curX = 0
    curY = 0
    direction = "down"
    positions = []
    positions.append((curX, curY))
    while not (curX == size-1 and curY == size-1):
        if direction == "down":
            if curY == size-1: #can't move down any more; move right instead
                curX += 1
            else:
                curY += 1
            positions.append((curX, curY))
            #move diagonally up and right
            while curX < size-1 and curY > 0:
                curX += 1
                curY -= 1
                positions.append((curX, curY))
            direction = "right"
            continue
        else: #direction == "right"
            if curX == size-1: #can't move right any more; move down instead
                curY += 1
            else:
                curX += 1
            positions.append((curX, curY))
            #move diagonally down and left
            while curY < size-1 and curX > 0:
                curX -= 1
                curY += 1
                positions.append((curX, curY))
            direction = "down"
            continue
    return positions

size = 5
for x, y in wave(size):
    index = 1 + x + (y*size)
    print index, x, y

Output:

1 0 0
6 0 1
2 1 0
3 2 0
7 1 1
11 0 2
16 0 3
12 1 2
8 2 1
4 3 0
5 4 0
9 3 1
13 2 2
17 1 3
21 0 4
22 1 4
18 2 3
14 3 2
10 4 1
15 4 2
19 3 3
23 2 4
24 3 4
20 4 3
25 4 4

Comedy one line implementation:

def wave(size):
    return [1+x+size*y for x,y in filter(lambda (x,y): x >=0 and x < size and y >= 0 and y < size, reduce(lambda x, y: x+y, [r if i==0 else list(reversed(r)) for i, r in enumerate([(x-delta, delta) for delta in range(size)] for x in range(size*2))], []))]

print wave(5)

output:

[1, 6, 2, 11, 7, 3, 16, 12, 8, 4, 21, 17, 13, 9, 5, 22, 18, 14, 10, 23, 19, 15, 24, 20, 25]

Answer 2

This is my take on it. Its similiar to qiuntus's response but more concise.

function wave($base) {
  $i = 1;
  $a = $base;
  $square = $base*$base;
  $out = array(1);

  while ($i < $square) {
    if ($i > ($square - $base)) { // hit the bottom
      $i++;
      $out[] = $i;
      $a = 1 - $base;
    } elseif ($i % $base == 0) { // hit the right
      $i += $base;
      $out[] = $i;
      $a = $base - 1;
    } elseif (($i - 1) % $base == 0) { // hit the left
      $i += $base;
      $out[] = $i;
      $a = 1 - $base;
    } elseif ($i <= $base) { // hit the top
      $i++;
      $out[] = $i;
      $a = $base - 1;
    }

    if ($i < $square) {
      $i += $a;
      $out[] = $i;
    }
  }

  return $out;
}