18. Rotate Image

mediumAsked at Unity

Rotate an n×n matrix 90 degrees in-place — a direct model of the 2D texture rotation Unity applies when normalizing atlas sprites or computing orthographic transform matrices without allocating new buffers.

By Alex Chen, Founder, InterviewChamp.AI · Last verified 2026-05-26

Problem

You are given an n x n 2D matrix representing an image. Rotate the image by 90 degrees clockwise in-place. You must modify the input matrix directly without allocating another 2D matrix.

Constraints

n == matrix.length == matrix[i].length
1 <= n <= 20
-1000 <= matrix[i][j] <= 1000

Examples

Example 1

Input

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

Output

[[7,4,1],[8,5,2],[9,6,3]]

Explanation: Transpose then reverse each row gives a 90-degree clockwise rotation.

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]]

Approaches

1. Extra matrix

Allocate a copy; place matrix[i][j] at copy[j][n-1-i]. Then copy back. Clear but uses O(n^2) extra space.

Time: O(n^2)
Space: O(n^2)

function rotate(matrix) {
  const n = matrix.length;
  const copy = matrix.map(r => [...r]);
  for (let i = 0; i < n; i++) {
    for (let j = 0; j < n; j++) {
      matrix[j][n - 1 - i] = copy[i][j];
    }
  }
}

Tradeoff:

2. Transpose then reverse rows

Step 1: transpose in-place (swap matrix[i][j] with matrix[j][i] for j>i). Step 2: reverse each row. Achieves 90-degree clockwise rotation with O(1) extra space.

Time: O(n^2)
Space: O(1)

function rotate(matrix) {
  const n = matrix.length;
  // transpose
  for (let i = 0; i < n; i++) {
    for (let j = i + 1; j < n; j++) {
      [matrix[i][j], matrix[j][i]] = [matrix[j][i], matrix[i][j]];
    }
  }
  // reverse each row
  for (let i = 0; i < n; i++) {
    matrix[i].reverse();
  }
}

Tradeoff:

Unity-specific tips

Unity engineers expect you to name the two-step pattern (transpose + row-reverse) and connect it to how a rotation matrix decomposes — saying 'this mirrors what Matrix4x4.TRS does for 2D orthographic cases' signals you understand transform math, not just array mechanics.

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