List Every Original Root-to-Leaf Value Path
Company: Bloomberg
Role: Software Engineer
Category: Coding & Algorithms
Difficulty: easy
Interview Round: Other
### Problem
Return every root-to-leaf path in the binary tree as a string with values joined by "->". A leaf has no children. The source permits any output order. Keep the TreeNode* root interface and retain path multiplicity even if distinct paths spell the same values.
```cpp
vector<string> binaryTreePaths(TreeNode* root);
```
### Examples
```text
root = [5,2,8,null,3] -> ["5->2->3","5->8"]
root = [-2] -> ["-2"]
```
### Constraints
- There are 1 through 100 nodes.
- Values lie in [-100,100].
### Follow-up Questions
Explain how the permitted output freedom is preserved without losing required values or occurrences.
### What a Strong Answer Covers
Depth-first traversal maintains the current value path and records a formatted copy only at leaves. Explain why every produced result satisfies the source contract and why no required result is omitted.
Overview: List Every Original Root-to-Leaf Value Path. Return every tree path from root to leaf, joining node values with a right-pointing arrow separator. Preserve every path occurrence; output order is unrestricted.