cyclically-rotating-a-grid

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Algorithms

You are given an <code>m x n</code> integer matrix <code>grid</code>​​​, where <code>m</code> and <code>n</code> are both even integers, and an integer <code>k</code>.

The matrix is composed of several layers, which is shown in the below image, where each color is its own layer:

<img alt="" src="https://assets.leetcode.com/uploads/2021/06/10/ringofgrid.png" style="width: 231px; height: 258px;" />

A cyclic rotation of the matrix is done by cyclically rotating each layer in the matrix. To cyclically rotate a layer once, each element in the layer will take the place of the adjacent element in the counter-clockwise direction. An example rotation is shown below:
<img alt="" src="https://assets.leetcode.com/uploads/2021/06/22/explanation_grid.jpg" style="width: 500px; height: 268px;" />
Return the matrix after applying <code>k</code> cyclic rotations to it.

&nbsp;
Example 1:
<img alt="" src="https://assets.leetcode.com/uploads/2021/06/19/rod2.png" style="width: 421px; height: 191px;" />
<pre>
Input: grid = [[40,10],[30,20]], k = 1
Output: [[10,20],[40,30]]
Explanation: The figures above represent the grid at every state.
</pre>

Example 2:
<img alt="" src="https://assets.leetcode.com/uploads/2021/06/10/ringofgrid5.png" style="width: 231px; height: 262px;" /> <img alt="" src="https://assets.leetcode.com/uploads/2021/06/10/ringofgrid6.png" style="width: 231px; height: 262px;" /> <img alt="" src="https://assets.leetcode.com/uploads/2021/06/10/ringofgrid7.png" style="width: 231px; height: 262px;" />

<pre>
Input: grid = [[1,2,3,4],[5,6,7,8],[9,10,11,12],[13,14,15,16]], k = 2
Output: [[3,4,8,12],[2,11,10,16],[1,7,6,15],[5,9,13,14]]
Explanation: The figures above represent the grid at every state.
</pre>

&nbsp;
Constraints:

<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 even integers.</li>
	<li><code>1 &lt;= grid[i][j] &lt;= 5000</code></li>
	<li><code>1 &lt;= k &lt;= 109</code></li>
</ul>

rotateGrid

Cyclically Rotating a Grid

Array

Matrix

Simulation

给你一个大小为 <code>m x n</code> 的整数矩阵 <code>grid</code>​​​ ，其中 <code>m</code> 和 <code>n</code> 都是 偶数 ；另给你一个整数 <code>k</code> 。

矩阵由若干层组成，如下图所示，每种颜色代表一层：

<img alt="" src="https://assets.leetcode.com/uploads/2021/06/10/ringofgrid.png" style="width: 231px; height: 258px;">

矩阵的循环轮转是通过分别循环轮转矩阵中的每一层完成的。在对某一层进行一次循环旋转操作时，层中的每一个元素将会取代其 逆时针 方向的相邻元素。轮转示例如下：
<img alt="" src="https://assets.leetcode.com/uploads/2021/06/22/explanation_grid.jpg" style="width: 500px; height: 268px;">
返回执行 <code>k</code> 次循环轮转操作后的矩阵。

 

示例 1：
<img alt="" src="https://assets.leetcode.com/uploads/2021/06/19/rod2.png" style="width: 421px; height: 191px;">
<pre>输入：grid = [[40,10],[30,20]], k = 1
输出：[[10,20],[40,30]]
解释：上图展示了矩阵在执行循环轮转操作时每一步的状态。</pre>

示例 2：
<img alt="" src="https://assets.leetcode.com/uploads/2021/06/10/ringofgrid5.png" style="width: 231px; height: 262px;"> <img alt="" src="https://assets.leetcode.com/uploads/2021/06/10/ringofgrid6.png" style="width: 231px; height: 262px;"> <img alt="" src="https://assets.leetcode.com/uploads/2021/06/10/ringofgrid7.png" style="width: 231px; height: 262px;">

<pre>输入：grid = [[1,2,3,4],[5,6,7,8],[9,10,11,12],[13,14,15,16]], k = 2
输出：[[3,4,8,12],[2,11,10,16],[1,7,6,15],[5,9,13,14]]
解释：上图展示了矩阵在执行循环轮转操作时每一步的状态。
</pre>

 

提示：

<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><code>m</code> 和 <code>n</code> 都是 偶数</li>
	<li><code>1 &lt;= grid[i][j] &lt;= 5000</code></li>
	<li><code>1 &lt;= k &lt;= 109</code></li>
</ul>