$2.$ Finding the door in a wall: Imagine you are facing a wall that does not end in either direction. 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 $($as you pass 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.

What makes this run in O$($n$)$ time? that is the part that doesn't make sense to me$.$ Let's say the door is n$-10$ steps to the right. If I take $2^$i steps in both directions during each iteration, I will take $54$ steps before finding the door, which is much greater than $10.$