Matrix Layer Rotation
Problem Statement
You are given a 2D matrix of dimension m x n and a positive integer r. You have to rotate the matrix r times and print the resultant matrix. Rotation should be in anti-clockwise direction.
Rotation of a 4 x 5 matrix is represented by the following figure. Note that in one rotation, you have to shift elements by one step only.
Matrix Rotation Algorithms
Matrix layer rotation is a problem in computer science that involves rotating the elements of a matrix by a specified number of layers. This problem can be solved using a variety of algorithms, each with its own advantages and disadvantages.
The brute-force algorithm O(n²)
The brute-force algorithm is the simplest way to rotate a matrix layer. It works by first copying the elements of the matrix into a temporary array. Then, it rotates the elements of the temporary array by the specified number of layers. Finally, it copies the elements of the temporary array back into the original matrix.
The brute-force algorithm is very simple to implement, but it is also very inefficient. The time complexity of the brute-force algorithm is O(n²), where n is the number of elements in the matrix.
The spiral algorithm O(n)
The spiral algorithm is a more efficient way to rotate a matrix layer. It works by rotating the elements of the matrix in a spiral pattern. The spiral algorithm:
- Starts by rotating the top left corner of the matrix.
- Then, it rotates the next row of elements, starting from the rightmost element.
- It continues rotating the elements of the matrix in this spiral pattern until all of the elements have been rotated.
The spiral algorithm is more efficient than the brute-force algorithm because it only needs to rotate a subset of the elements in the matrix at each step. The time complexity of the spiral algorithm is O(n), where n is the number of elements in the matrix.
The algorithm
My implementation is fairly based on the spiral algorithm but it suffers from little deviations for the worsts or the better.
- The function first iterates through the matrix in a spiral pattern and returns the layers that compose it. The
layersInSpriralfunction works by traversing the matrix in a spiral pattern and adding each row to a list. The spiral pattern starts at the top left corner of the matrix and moves counter-clockwise. The function continues traversing the matrix until all of the rows have been added to the list. - The next step is to rotate each layer in isolation. This is done by iterating through the list of layers and rotating each layer by the specified number of times. The rotation is performed by slicing the layer and then re-arranging the elements.
