Rotate Matrix Elements

The problem at hand involves rotating the elements of a given matrix in a clockwise direction. In this scenario, the matrix is a 2D array with rows and columns, and we need to rotate its elements in a way that each element moves one step ahead in the clockwise direction along the outermost boundary of the matrix. This operation is performed iteratively for each "ring" or layer of the matrix, starting from the outermost layer and moving towards the center.

Problem Statement and Description

Given a matrix as input, the goal is to rotate its elements in a clockwise direction. For instance, consider the following matrix:

1  2  3  4  5
6  7  8  9  10
11 12 13 14 15
16 17 18 19 20
21 22 23 24 25

After performing the rotation operation, the matrix should become:

6  1  2  3  4
11 12 7  8  5
16 17 13 9  10
21 18 19 14 15
22 23 24 25 20

Idea to Solve the Problem

To solve this problem, we can divide it into subproblems. Each subproblem involves rotating the elements of one "ring" or boundary of the matrix. We start with the outermost ring and move towards the inner rings until we reach the center. To rotate the elements of a single ring, we perform four different operations (labeled as Case A, B, C, and D in the code):

1. Case A (Bottom Right to Left)

   This involves moving elements from the bottom row of the current ring, from right to left.

2. Case B (Bottom to Top)

   Here, we move elements from the rightmost column of the current ring, from bottom to top.

3. Case C (Left to Right)

   This operation involves moving elements from the top row of the current ring, from left to right.

4. Case D (Top to Bottom)

   Finally, we move elements from the leftmost column of the current ring, from top to bottom.

Algorithm

1. Initialize variables row and col to the number of rows and columns of the matrix, respectively.
2. Initialize size as the minimum of row and col. This will be used to determine the number of rings in the matrix.
3. Loop i over each ring, starting from 0 up to size/2 - 1. a. Decrement row and col by 1 to represent the current ring's dimensions. b. Call the rotateRing function with parameters matrix, row, col, and i to rotate the current ring's elements. c. Increment i to move to the inner ring.
4. Display the rotated matrix using the display function.

Code Solution

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Time Complexity

The time complexity of this algorithm mainly depends on the number of elements in the matrix, which is row * col. Since we iterate over each element once during the rotation process, the time complexity is O(row * col). The other operations involve constant time complexity, so they don't significantly impact the overall complexity.