- Pre-order walk can create a expression tree in Polish notation
- Post-order walk can create a expression tree in reverse-Polish notation
https://en.wikipedia.org/wiki/Tree_traversal#Uses has a concise example.
This usage is fairly popular in my past coding interviews.
In fact, the wikipedia article goes on to say that pre/post order walk can create a “representation of a binary tree” … see my blogposts for details.