Matrix rotation 90 degrees

Transpose • Comparing algorithms

13.12.2021

Consider the algorithm for rotating a matrix 90 degrees clockwise and anticlockwise. This algorithm is similar to matrix transpose, with the difference that here, for each point, one of the coordinates is mirrored.

// matrix transpose — rows and columns are swapped
swapped[j][i] = matrix[i][j];
// clockwise ↻ — rows are mirrored
rotated[j][i] = matrix[m-i-1][j];
// anticlockwise ↺ — columns are mirrored
rotated[j][i] = matrix[i][n-j-1];

Similar algorithm: Matrix rotation 180 degrees.

Let’s write a method in Java to rotate a matrix {m×n} 90 degrees. The additional parameter sets the direction of rotation: clockwise or anticlockwise. As an example, let’s take a rectangular matrix {4×3}.

/**
 * @param m      number of rows of the original matrix
 * @param n      number of columns of the original matrix
 * @param clock  direction of rotation: 
 *               clockwise ↻ or anticlockwise ↺
 * @param matrix the original matrix
 * @return the rotated matrix
 */
public static int[][] rotateMatrix(int m, int n, boolean clock, int[][] matrix) {
    // new matrix, the number of rows and columns are swapped
    int[][] rotated = new int[n][m];
    // bypass the rows of the original matrix
    for (int i = 0; i < m; i++)
        // bypass the columns of the original matrix
        for (int j = 0; j < n; j++)
            if (clock) // clockwise rotation ↻
                rotated[j][i] = matrix[m-i-1][j];
            else // anticlockwise rotation ↺
                rotated[j][i] = matrix[i][n-j-1];
    return rotated;
}

// start the program and output the result
public static void main(String[] args) {
    // incoming data
    int m = 4, n = 3;
    int[][] matrix = {{11, 12, 13}, {14, 15, 16}, {17, 18, 19}, {20, 21, 22}};
    // rotate the matrix and output the result
    outputMatrix("Original matrix:", matrix);
    outputMatrix("Clockwise ↻:", rotateMatrix(m, n, true, matrix));
    outputMatrix("Anticlockwise ↺:", rotateMatrix(m, n, false, matrix));
}

// helper method, prints the matrix to the console row-wise
public static void outputMatrix(String title, int[][] matrix) {
    System.out.println(title);
    for (int[] row : matrix) {
        for (int el : row)
            System.out.print(" " + el);
        System.out.println();
    }
}

Output:

Original matrix:
 11 12 13
 14 15 16
 17 18 19
 20 21 22
Clockwise ↻:
 20 17 14 11
 21 18 15 12
 22 19 16 13
Anticlockwise ↺:
 13 16 19 22
 12 15 18 21
 11 14 17 20