grid traversal question

Question

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Looping in a spiral

Given a grid of any height and width, write an algorithm to traverse it in a spiral. (Starting at the top left and ending in the middle) without passing over previously visited nodes. Without using nested loops.

Answer 1

1. Set xmin = 0, xmax = grid.width - 1, ymin = 0, and ymax = grid.height - 1. These are the traversal limits.
2. Set dy = 0 and dx = 1. This is the traversal direction.
3. Set x = 0 and y = 0. This is your cursor.

While xmin <= xmax and ymin <= ymax:

1. Visit the node at (x, y).
2. If dx == 1 and x == xmax, set dx = 0, dy = 1, and ymin = y + 1.
3. If dy == 1 and y == ymax, set dx = -1, dy = 0, and xmax = x - 1.
4. If dx == -1 and x == xmin, set dx = 0, dy = -1, and ymax = y - 1.
5. If dy == -1 and y == ymin, set dx = 1, dy = 0, and xmin = x + 1.
6. Set x = x + dx and y = y + dy.

I have no idea what that algorithm is called; it just seemed apparent from the description. Nested loops would be a much more optimal solution; all those if statements will push the limits of an optimizer.

Answer 2

it should be done using one for loop and starting from bottom left, I'am in that coarse