• + 1 comment

    Think of it this way, @marcotuliorr. Imagine if that '3' node had three consecutive children "7 - 8 - 9" (each node is the left child of its parent.) Would that branch cross over the long "4 - 5 - 6" branch and make the top-down view of the tree "9 - 2 - 1 - 3 - 6"? Of course not!

    Every node's child must retain the positional properties of its parent, I.E. if 2 is to the left of 1, then 4 and 5 must also be to the left of 1. If 5 is to the left of 1, 6 must be to the left of 1 as well, etc. There's no way a branch not on the leftmost or rightmost path could be visible from the top down.