Understanding Time Complexity: $O(m+n)$

You've got it spot on! The time complexity of $O(m+n)$ perfectly captures the nature of this problem.

Why $O(m+n)$?

1. Every Node Visited Once: In the process of merging, each node in both trees is visited exactly once.
2. Single Operation Per Node: At each visit, we perform a constant amount of work (i.e., summing node values and creating a new node).

Considering that there are $m$ nodes in the first tree and $n$ nodes in the second tree, it's quite straightforward to conclude that the overall time complexity is $O(m+n)$.

The Intuition

Think of it like two separate lists that you need to merge into one. You have to look at each element at least once in both lists to accomplish this. In our case, the lists are just a bit more complex, structured as binary trees. But the fundamental idea remains the same: you have to touch every node at least once.