Is Cyclically Rotating a Grid easy or hard?

The problem is rated Medium because the core idea is simple but implementing layer boundaries and rotation correctly can be tricky. Handling perimeter length, rotation modulo, and edge traversal often causes off‑by‑one errors.

Cyclically Rotating a Grid Python/Java solution

Python and C++ implementations often use the layered rotation method with a temporary list for each ring. Java and JavaScript solutions can implement direct coordinate manipulation to compute the rotated position of every element without extra memory.

How to solve Cyclically Rotating a Grid in O(n)?

The optimal solution processes the matrix by layers and rotates each ring using k % perimeter_length. Since each element is moved only once during extraction and reinsertion, the total work across all layers is proportional to the number of cells, giving O(m*n) time.

What is the best approach for Cyclically Rotating a Grid?

The layered rotation method is the most practical approach. Treat each rectangular ring of the matrix as a circular array, compute the effective rotation using k % perimeter_length, rotate the elements, and write them back. This keeps the logic simple while running in O(m*n) time.

Is Cyclically Rotating a Grid asked at Google/Amazon/Meta?

Matrix rotation and layer traversal problems are common in interviews at companies like Amazon, Google, and Meta. Variants involving rotating rings, spiral traversal, or matrix simulations frequently appear in coding rounds and onsite interviews.

What data structure is used in Cyclically Rotating a Grid?

The solution primarily uses arrays and matrix traversal. In the layered approach, each ring of the matrix is temporarily stored in a list or array to perform cyclic rotation before writing values back into the grid.

What is the time complexity of Cyclically Rotating a Grid?

Both common solutions run in O(m*n) time because every element of the grid is processed at most a constant number of times. Layer extraction and coordinate‑based simulation both visit each cell once while handling rotations per layer.

Description Hints 2 Solution Video 20:56

1914. Cyclically Rotating a Grid

Medium74.2% acceptance3 companies

You are given an m x n integer matrix grid, where m and n are both even integers, and an integer k.

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

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:

Return the matrix after applying k cyclic rotations to it.

Example 1:

Input: grid = [[40,10],[30,20]], k = 1
Output: [[10,20],[40,30]]
Explanation: The figures above represent the grid at every state.

Example 2:

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.

Constraints:

m == grid.length
n == grid[i].length
2 <= m, n <= 50
Both m and n are even integers.
1 <= grid[i][j] <=5000
1 <= k <= 10⁹

Asked at 3 companies

Google Meta Amazon

Topics

Hints open one at a time

Hint 1

First, you need to consider each layer separately as an array.

Hint 2

Just cycle this array and then re-assign it.

20:56

Still stuck?Read 3 approaches, or watch a walkthrough.

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1class Solution:

2 def rotateGrid(self, grid: List[List[int]], k: int) -> List[List[int]]:

Starter codePython 3Spaces: 4

Examples

Case 1Case 2

Input

[[40,10],[30,20]]
1

Input

[[1,2,3,4],[5,6,7,8],[9,10,11,12],[13,14,15,16]]
2

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