48. Rotate Image

Published on June 1, 2023

Question

You are given an n x n 2D matrix representing an image, rotate the image by 90 degrees (clockwise).

You have to rotate the image in-place, which means you have to modify the input 2D matrix directly. DO NOT allocate another 2D matrix and do the rotation.

Example 1:

Input: matrix = [[1,2,3],[4,5,6],[7,8,9]]
Output: [[7,4,1],[8,5,2],[9,6,3]]

Algorithm

If you tried do it at one motion, you may not find the answer.

For matrix related questions, there are some useful movement, like image, flip(diagonal and anti-diagonal), if you are solving this kind of problem, try to do such things and find a pattern.

For this question, if you need to rotate a matrix, image first, and then flip once, then you will get the answer.

Code

class Solution {
    public void rotate(int[][] matrix) {
        image(matrix);
        flip(matrix);
    }
    
    private void image(int[][] matrix) {
        int m = matrix.length;
        for (int i = 0; i < m; i++) {
            for (int j = i; j < m; j++) {
                if (i != j) {
                    swap(matrix, i, j);
                }
            }
        }
    }
    
    private void flip(int[][] matrix) {
        int m = matrix.length - 1;
        for (int[] row : matrix) {
            int i = 0, j = m;
            while (i < j) {
                int temp = row[i];
                row[i] = row[j];
                row[j] = temp;
                i++;
                j--;
            }
        }
    }
    
    private void swap(int[][] matrix, int i, int j) {
        int temp = matrix[i][j];
        matrix[i][j] = matrix[j][i];
        matrix[j][i] = temp;
    }

}