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48. Rotate Image — Step-by-Step Visualization

mediumLeetCode #48ArrayMathMatrix

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]]`

Algorithm Pattern

Transpose & Reverse

Key Idea

A 90-degree clockwise rotation can be achieved in two elegant in-place steps: 1. Transpose the matrix (swap matrix[i][j] with matrix[j][i]). 2. Reverse each row.

Step-by-Step Approach

  1. Iterate through the matrix using two nested loops: `i` from 0 to `n` and `j` from `i+1` to `n`.
  2. Swap `matrix[i][j]` with `matrix[j][i]` to transpose the matrix.
  3. After transposition, iterate through each row and reverse its elements using a two-pointer swap.
  4. The result is a 90-degree clockwise rotation without extra memory.

Common Gotchas

  • Ensure you skip the diagonal during transposition (`j = i + 1`), otherwise, you'll swap and then swap back, doing nothing.
  • The problem strictly requires in-place modification.

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