Measure Infection Time from One Valued Binary-Tree Node
Company: Amazon
Role: Software Engineer
Category: Coding & Algorithms
Difficulty: medium
Interview Round: Other
### Problem
At minute zero, the unique node with value `start` in a binary tree becomes infected. Each subsequent minute, infection spreads simultaneously across parent-child edges to uninfected neighboring nodes. Return the number of minutes until every node in the tree rooted at `root` is infected.
```cpp
class Solution {
public:
int amountOfTime(TreeNode* root, int start);
};
```
### Examples
**Example 1:**
```text
Input: root = [5,2,9, null,3], start = 3
Output: 3
Explanation: Infection reaches value 2 at minute 1, value 5 at minute 2, and value 9 at minute 3.
```
**Example 2:**
```text
Input: root = [8,4,12], start = 8
Output: 1
Explanation: Both children become infected simultaneously at minute 1.
```
### Constraints
- The tree contains 1 through 100000 nodes.
- Values are unique integers in [1,100000].
- A node with value start exists.
### Clarifying Questions
- Is `start` a value or a node index? It is a value guaranteed to exist in the tree.
- Can infection spread toward a parent? Yes, as well as toward children.
- Do multiple neighbors become infected simultaneously? Yes.
- What if the tree has only its starting node? Return 0.
```hint Check the boundary
Trace a start at a leaf, where infection must travel toward the root before reaching another branch.
```
Overview: Measure how many minutes infection needs to reach every binary-tree node from a specified starting value through parent-child edges.
