Rotate Every Rectangular Ring
Company: Google
Role: Software Engineer
Category: Coding & Algorithms
Difficulty: medium
Interview Round: Other
### Problem
Apply `k` counterclockwise rotations to every concentric rectangular layer of the even-by-even matrix `grid`, and return the resulting matrix. In one rotation, each value moves to the adjacent position in the counterclockwise direction along its own layer. Values never move between layers.
```cpp
class Solution {
public:
vector<vector<int>> rotateGrid(vector<vector<int>>& grid, int k);
};
```
### Examples
**Example 1:**
```text
grid = [[1,2],[3,4]], k = 1
Output: [[2,4],[1,3]]
Explanation: The top-left entry moves down along the left edge.
```
**Example 2:**
```text
grid = [[2,5],[7,9]], k = 2
Output: [[9,7],[5,2]]
Explanation: Two counterclockwise steps move every entry to the opposite ring position.
```
### Constraints
- `m == grid.length`, `n == grid[i].length`; `2 <= m,n <= 50`.
- Both dimensions are even.
- `1 <= grid[i][j] <= 5000`; `1 <= k <= 10^9`.
### Clarifying Questions
A layer is the boundary of a submatrix remaining after zero or more outer boundaries are removed. Each layer rotates independently.
```hint Inspect the structure
How can a ring be indexed once so that a large rotation becomes modular arithmetic?
```
### Reasoning checkpoints
- Match the stated counterclockwise movement on every layer, including corners and inner layers.
- Account for very large rotation counts and for layers with different perimeters.
### Optional extensions
What special handling would odd dimensions require for a remaining central row or column?
Overview: Rotate Every Rectangular Ring. Given the even-by-even integer matrix grid, rotate every concentric rectangular layer k steps counterclockwise. In one step each entry moves to the neighboring position along its own layer in the counterclockwise direction. Return the resulting matrix.