[techdragon]

The description makes me think of a loud sound echoing through the maze, each branch further divides the volume of the sound, but a loud enough sound will "exit" in the optimal "O(1)" time because the sound wave "explores" every branch of the maze in "parallel".

Is this a reasonable mental model of what your describing?

[adamnemecek]

In your description you are still expending extra energy to explore the branches. Also it's not O(1), it's just that every step you take is bound to be optimal. So in O(1), you are literally one step closer to the solution.