Ambiguity with the Top View of a binary tree
I think what they are trying to define is the following.

Given a rooted binary tree $T$, let $V(T)$ be the set of vertices of $T$. For $v \in V(G)$, let $P_v$ the unique path from the root of $T$ to $v$.
We will call an edge $(u,w) \in P_v$ a left edge if $w$ is the left child of $u$, and a right edge otherwise. 

Let $\ell_v$ and $r_v$ be the number of left and right edges in $P_v$, respectively, and define $\delta(v) = \ell_v - r_v = 2\ell_v - |P_v|$.

Let $h(u)$ be the depth of vertex $u$ in $T$ and define $\Delta(v) = \{ \delta_u \, : u \in V(T) \wedge h(u) &lt; h(v) \}$.
The top view of $T$ is the set $\{ v \in V(T) :  \delta_v \not\in \Delta(v)  \}$.

In your example the top view would be $\{1, 2, 12, 14, 15 \}$. In general, you can compute the top view in $O(|V(T)|)$ time thought a preorder DFS visit.

I have no idea why this is important, sorry.