Average Binary-Tree Values at Each Depth
Company: Amazon
Role: Software Engineer
Category: Coding & Algorithms
Difficulty: easy
Interview Round: Other
### Problem
Return the average node value at every depth of the binary tree, starting with the root level. TreeNode exposes val,left,right. Answers within 10^-5 of the mathematical averages are accepted.
```cpp
class Solution {
public:
vector<double> averageOfLevels(TreeNode* root);
};
```
### Examples
**Example 1:**
```text
root = [4,2,9,1,7]
Output: [4.0,5.5,4.0]
Explanation: Level sums are 4,11,8 with counts 1,2,2.
```
**Example 2:**
```text
root = [-3,-5,1]
Output: [-3.0,-2.0]
Explanation: The second level averages (-5+1)/2.
```
### Constraints
- Tree size: 1..10000 nodes. Each node stores a signed-32-bit value, from -2147483648 to 2147483647.
### Clarifying Questions
Compute arithmetic means per level and preserve the stated numeric acceptance tolerance.
```hint Read the boundary condition
How can the queue size identify the boundary between two levels?
```
### Contract considerations
Compute arithmetic means per level and preserve the stated numeric acceptance tolerance.
Overview: Average Binary-Tree Values at Each Depth. Return the average node value at every depth of the binary tree, starting with the root level.
