Cyclically Rotating a Grid
<p>You are given an <code>m x n</code> integer matrix <code>grid</code>​​​, where <code>m</code> and <code>n</code> are both <strong>even</strong> integers, and an integer <code>k</code>.</p>

<p>The matrix is composed of several layers, which is shown in the below image, where each color is its own layer:</p>

<p><img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/1900-1999/1914.Cyclically%20Rotating%20a%20Grid/images/ringofgrid.png" style="width: 231px; height: 258px;" /></p>

<p>A cyclic rotation of the matrix is done by cyclically rotating <strong>each layer</strong> in the matrix. To cyclically rotate a layer once, each element in the layer will take the place of the adjacent element in the <strong>counter-clockwise</strong> direction. An example rotation is shown below:</p>

<img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/1900-1999/1914.Cyclically%20Rotating%20a%20Grid/images/explanation_grid.jpg" style="width: 500px; height: 268px;" />

<p>Return <em>the matrix after applying </em><code>k</code> <em>cyclic rotations to it</em>.</p>

<p>&nbsp;</p>

<p><strong class="example">Example 1:</strong></p>

<img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/1900-1999/1914.Cyclically%20Rotating%20a%20Grid/images/rod2.png" style="width: 421px; height: 191px;" />

<pre>

<strong>Input:</strong> grid = [[40,10],[30,20]], k = 1

<strong>Output:</strong> [[10,20],[40,30]]

<strong>Explanation:</strong> The figures above represent the grid at every state.

</pre>

<p><strong class="example">Example 2:</strong></p>

<strong><img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/1900-1999/1914.Cyclically%20Rotating%20a%20Grid/images/ringofgrid5.png" style="width: 231px; height: 262px;" /></strong> <strong><img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/1900-1999/1914.Cyclically%20Rotating%20a%20Grid/images/ringofgrid6.png" style="width: 231px; height: 262px;" /></strong> <strong><img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/1900-1999/1914.Cyclically%20Rotating%20a%20Grid/images/ringofgrid7.png" style="width: 231px; height: 262px;" /></strong>

<pre>

<strong>Input:</strong> grid = [[1,2,3,4],[5,6,7,8],[9,10,11,12],[13,14,15,16]], k = 2

<strong>Output:</strong> [[3,4,8,12],[2,11,10,16],[1,7,6,15],[5,9,13,14]]

<strong>Explanation:</strong> The figures above represent the grid at every state.

</pre>

<p>&nbsp;</p>

<p><strong>Constraints:</strong></p>

<ul>

    <li><code>m == grid.length</code></li>

    <li><code>n == grid[i].length</code></li>

    <li><code>2 &lt;= m, n &lt;= 50</code></li>

    <li>Both <code>m</code> and <code>n</code> are <strong>even</strong> integers.</li>

    <li><code>1 &lt;= grid[i][j] &lt;=<sup> </sup>5000</code></li>

    <li><code>1 &lt;= k &lt;= 10<sup>9</sup></code></li>

</ul>
Array; Matrix; Simulation
class Solution:
    def rotateGrid(self, grid: List[List[int]], k: int) -> List[List[int]]:
        def rotate(p: int, k: int):
            nums = []
            for j in range(p, n - p - 1):
                nums.append(grid[p][j])
            for i in range(p, m - p - 1):
                nums.append(grid[i][n - p - 1])
            for j in range(n - p - 1, p, -1):
                nums.append(grid[m - p - 1][j])
            for i in range(m - p - 1, p, -1):
                nums.append(grid[i][p])
            k %= len(nums)
            if k == 0:
                return
            nums = nums[k:] + nums[:k]
            k = 0
            for j in range(p, n - p - 1):
                grid[p][j] = nums[k]
                k += 1
            for i in range(p, m - p - 1):
                grid[i][n - p - 1] = nums[k]
                k += 1
            for j in range(n - p - 1, p, -1):
                grid[m - p - 1][j] = nums[k]
                k += 1
            for i in range(m - p - 1, p, -1):
                grid[i][p] = nums[k]
                k += 1

        m, n = len(grid), len(grid[0])
        for p in range(min(m, n) >> 1):
            rotate(p, k)
        return grid
