Rotate Matrix by 90 Degrees

Understanding the Problem

The goal is to rotate a given square matrix by 90 degrees clockwise.

Method 1: Using a Temporary Matrix

This method uses a temporary matrix to store the rotated values.

public class RotateMatrix {
    public static void rotateMatrix(int[][] matrix) {
        int n = matrix.length;
        int[][] temp = new int[n][n];

        // Store the rotated values in a temporary matrix
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                temp[j][n - 1 - i] = matrix[i][j];
            }
        }

        // Copy the temporary matrix back to the original matrix
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                matrix[i][j] = temp[i][j];
            }
        }
    }

    public static void printMatrix(int[][] matrix) {
        for (int[] row : matrix) {
            for (int value : row) {
                System.out.print(value + " ");
            }
            System.out.println();
        }
    }

    public static void main(String[] args) {
        int[][] matrix = {
            {1, 2, 3},
            {4, 5, 6},
            {7, 8, 9}
        };
        rotateMatrix(matrix);
        System.out.println("Rotated Matrix:");
        printMatrix(matrix);
    }
}
            

Output:

Rotated Matrix:
7 4 1 
8 5 2 
9 6 3 

Method 2: In-Place Rotation

This method rotates the matrix in place without using extra space.

public class RotateMatrix {
    public static void rotateMatrix(int[][] matrix) {
        int n = matrix.length;

        // Transpose the matrix
        for (int i = 0; i < n; i++) {
            for (int j = i; j < n; j++) {
                int temp = matrix[i][j];
                matrix[i][j] = matrix[j][i];
                matrix[j][i] = temp;
            }
        }

        // Reverse each row
        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;
            }
        }
    }

    public static void printMatrix(int[][] matrix) {
        for (int[] row : matrix) {
            for (int value : row) {
                System.out.print(value + " ");
            }
            System.out.println();
        }
    }

    public static void main(String[] args) {
        int[][] matrix = {
            {1, 2, 3},
            {4, 5, 6},
            {7, 8, 9}
        };
        rotateMatrix(matrix);
        System.out.println("Rotated Matrix:");
        printMatrix(matrix);
    }
}
            

Output:

Rotated Matrix:
7 4 1 
8 5 2 
9 6 3 

Method 3: Using Layer by Layer Rotation

This method rotates the matrix layer by layer.

public class RotateMatrix {
    public static void rotateMatrix(int[][] matrix) {
        int n = matrix.length;

        for (int layer = 0; layer < n / 2; layer++) {
            int first = layer;
            int last = n - 1 - layer;

            for (int i = first; i < last; i++) {
                int offset = i - first;
                // Save the top element
                int top = matrix[first][i];

                // Move left element to top
                matrix[first][i] = matrix[last - offset][first];

                // Move bottom element to left
                matrix[last - offset][first] = matrix[last][last - offset];

                // Move right element to bottom
                matrix[last][last - offset] = matrix[i][last];

                // Assign top element to right
                matrix[i][last] = top;
            }
        }
    }

    public static void printMatrix(int[][] matrix) {
        for (int[] row : matrix) {
            for (int value : row) {
                System.out.print(value + " ");
            }
            System.out.println();
        }
    }

    public static void main(String[] args) {
        int[][] matrix = {
            {1, 2, 3},
            {4, 5, 6},
            {7, 8, 9}
        };
        rotateMatrix(matrix);
        System.out.println("Rotated Matrix:");
        printMatrix(matrix);
    }
}
            

Output:

Rotated Matrix:
7 4 1 
8 5 2 
9 6 3