Ambiguity with the Top View of a binary tree What exactly is the top view of a binary tree?

I find great ambiguity and lack of clarity from the articles I find.

For example, this is what is used to demonstrate the top view on geeksforgeeks:

       1
    /     \
   2       3
  /  \    / \
 4    5  6   7



They go on to say that the top view is 4 2 1 3 7. The problem here is that they leave a lot of speculation on what isn't the top view. Consequently it becomes ambiguous to implement in code.

Stackoverflow examples are not any better. Hackerrank's example is even worse.

So I have signed up here hoping someone will tell me explicitly what the top view is because I have been trying to find out for 2 days. For instance, what is the top view of this tree:

      1
       \
        14
       /  \
      3    15
     / \
    2   7
       /  \
      4     13
     / \   /
    5   6 10
         /  \
        8    11
         \    \
          9    12



And if I may be bold to ask, why is it important?
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.