Rotate Image medium

Problem Statement

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]]

Example 2:

Input: matrix = [[5,1,9,11],[2,4,8,10],[13,3,6,7],[15,14,12,16]]
Output: [[15,13,2,5],[14,3,4,1],[12,6,8,9],[16,7,10,11]]

Steps

The core idea is to perform the rotation in four steps:

  1. Transpose: First, transpose the matrix. Transposing a matrix swaps rows and columns. Element at matrix[i][j] becomes matrix[j][i].

  2. Reverse Columns: After transposing, reverse each row (column in the original matrix). This completes the 90-degree clockwise rotation.

Explanation

Let's illustrate with a 3x3 matrix:

Original Matrix:

1  2  3
4  5  6
7  8  9

Step 1: Transpose

1  4  7
2  5  8
3  6  9

Step 2: Reverse each row

7  4  1
8  5  2
9  6  3

This is the 90-degree clockwise rotated matrix. This approach avoids the need for creating a new matrix, achieving in-place rotation.

Code (Java)

class Solution {
    public void rotate(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;
            }
        }
    }
}

Complexity

  • Time Complexity: O(n²) - We iterate through the matrix twice (transposing and reversing).
  • Space Complexity: O(1) - The rotation is done in-place; we don't use any extra space proportional to the input size.