## Problem Statement

You are given an 2D matrix(n x n) representing an image/matrix, rotate the matrix by **90** degrees (clockwise). You have to rotate the image/matrix **in-place**, which means you have to modify the input matrix directly. **DO NOT** allocate another matrix and do the rotation.

**Optimal Solution** **for rotation by 90 Degree**

The optimal solution to rotating a matrix by 90 degrees is to use the following algorithm:

- Reverse the rows of the matrix.
- Transpose the matrix.

Reversing rows and transposing a matrix are both relatively simple operations, achievable in a single pass through the matrix. This makes the optimal solution to rotating a matrix by 90 degrees very efficient.

## Java Implementation for rotation by 90 degrees

import java.util.Arrays; public class OptimalMatrixRotation { public static void rotateMatrixClockwise(int[][] matrix) { int n = matrix.length; // Reverse the rows for (int i = 0; i < n; i++) { for (int j = 0; j < n / 2; j++) { int temp = matrix[i][j]; matrix[i][j] = matrix[i][n - 1 - j]; matrix[i][n - 1 - j] = temp; } } // Transpose the matrix for (int i = 0; i < n; i++) { for (int j = i + 1; j < n; j++) { int temp = matrix[i][j]; matrix[i][j] = matrix[j][i]; matrix[j][i] = temp; } } } public static void main(String[] args) { int[][] matrix = { {1, 2, 3}, {4, 5, 6}, {7, 8, 9} }; System.out.println("Original Matrix:"); for (int[] row : matrix) { System.out.println(Arrays.toString(row)); }rotateMatrixClockwise(matrix); System.out.println("Matrix after 90-degree clockwise rotation:"); for (int[] row : matrix) { System.out.println(Arrays.toString(row)); } } }

**Time Complexity:** O(N*N) + O(N*N). First one O(N*N) is for transposing the matrix and the second one is for reversing the matrix.

**Space Complexity: **O(1).

## Benefits of the Optimal Solution

The optimal solution for matrix rotation in Java offers several advantages:

- Efficiency: The combination of transpose and row reversal minimizes the number of operations, making it highly efficient for large matrices.
- In-Place: The rotation is performed in-place, meaning no additional memory is required, making it memory-efficient.
- Simplicity: The straightforward implementation allows for easy integration into various applications.

### Conclusion

As a Java developer, adding this essential technique to your toolkit will empower you to tackle complex matrix rotation challenges with ease. Embrace the power of the optimal solution, which offers a time complexity of O(n^2), and grow your programming skills to new heights!

[…] the 4Sum Problem: Efficient Algorithms in Java with Time and Space Complexity Rotation by 90 Degrees: Mastering Efficient Matrix Rotation in Java Top 10 Emerging Technologies Shaping India’s Engineering Landscape Stock Buy and Sell […]