Another Puzzle for You!!!!

Ok, here it is.

You are facing a wall that stretches infinitely in both directions.
There is a door in the wall, but you know neither how far away nor in which
direction. You can see the door only when you are right next to it.

Design an algorithm that enables you to reach the door by walking at most O(n)
steps where n is the (unknown to you) number of steps between your initial position
and the door.

I also thought this cannot be solved ;

but was able to solve it eventually.

So don't give up.