Sort Every Concentric Matrix Border Clockwise
Company: Capital One
Role: Software Engineer
Category: Coding & Algorithms
Difficulty: medium
Interview Round: Take-home Project
# Sort Every Concentric Matrix Border Clockwise
Given a nonempty rectangular integer matrix, process each concentric layer independently.
For a layer, list its coordinates clockwise starting at that layer's top-left cell. Sort the values from that border in ascending order, then write them back along the same clockwise coordinate order. Return the transformed matrix.
The innermost layer may be a single row, a single column, or one cell. Every matrix cell belongs to exactly one layer.
## Function Signature
```python
def sort_matrix_borders(matrix: list[list[int]]) -> list[list[int]]:
...
```
## Constraints
- `1 <= len(matrix) <= 200`
- `1 <= len(matrix[0]) <= 200`
- Every row has the same length.
- `-1_000_000_000 <= matrix[r][c] <= 1_000_000_000`
## Example
```text
Input:
[[9, 8, 7],
[6, 5, 4],
[3, 2, 1]]
Output:
[[1, 2, 3],
[9, 5, 4],
[8, 7, 6]]
```
The outer values are written in ascending order along the clockwise path from the top-left cell; the center cell forms its own layer.
Quick Answer: Sort the values on each concentric border of a rectangular matrix, then write them back clockwise from the layer's top-left cell. The exercise tests precise coordinate traversal and edge cases where an inner layer collapses to a row, column, or single cell.
