Solution: Rotate Image

Statement#

Given an $n \times n$ matrix, rotate the matrix 90 degrees clockwise. The performed rotation should be in place, i.e., the given matrix is modified directly without allocating another matrix.

Note: The function should only return the modified input matrix.

Constraints:

• matrix.length $=$ matrix[i].length
• $1 \leq$ matrix.length $\leq 20$
• $-10^3 \leq$ matrix[i][j] $\leq 10^3$

Solution#

The idea is to make groups of four cells and rotate them by 90 degrees clockwise.

Here’s how the algorithm works:

1. We run a loop where row ranges from 0 to n / 2.

   1. Within this loop, we run a nested loop where col ranges from row to n - row - 1. These loops traverse the groups of four cells in the matrix. In this nested loop, we perform three swaps:

      1. The value of the top-left cell is swapped with the value of the top-right cell.

      2. The value of the top-left cell is swapped with the value of the bottom-right cell.

      3. The value of the top-left cell is swapped with the value of the bottom-left cell.

   2. The current group of four cells has been rotated by $90$ degrees. We now move to the next iteration of the outer loop to rotate the next group.

2. We repeat the process above until the whole matrix has been rotated.

Let’s look at the following illustration to get a better understanding of the solution:

Let’s have a look at the code for the algorithm we just discussed:

Time complexity#

The time complexity of this solution is $O(n^2)$ since each cell is read and written once.

Space complexity#

The space complexity of this solution is $O(1)$ since no extra space is used.