17. Rotate Image

mediumAsked at Tesla

Rotate an n×n matrix 90 degrees in-place — Tesla's vision pipeline applies this exact transformation when fusing camera frames from different sensor orientations into a unified bird's-eye-view grid for Autopilot.

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

Problem

You are given an n×n 2D matrix representing an image. Rotate the matrix 90 degrees clockwise in-place without allocating a new matrix.

Constraints

n == matrix.length == matrix[i].length
1 <= n <= 20
-1000 <= matrix[i][j] <= 1000
Must be done in-place with O(1) extra space

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 achieves 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 copy

Allocate a new n×n matrix, compute the rotated index mapping directly, then copy back. Clean 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(row => [...row]);
  for (let r = 0; r < n; r++) {
    for (let c = 0; c < n; c++) {
      matrix[c][n - 1 - r] = copy[r][c];
    }
  }
}

Tradeoff:

2. Transpose then reverse rows

First transpose the matrix (swap matrix[i][j] with matrix[j][i]), then reverse each row in-place. Two clean passes, O(1) extra space.

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

function rotate(matrix) {
  const n = matrix.length;
  // Step 1: 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]];
    }
  }
  // Step 2: reverse each row
  for (let i = 0; i < n; i++) {
    matrix[i].reverse();
  }
}

Tradeoff:

Tesla-specific tips

Tesla asks this to test spatial reasoning, which maps directly to how engineers think about camera-to-BEV coordinate transforms. They want to hear you derive the transpose-then-reverse trick rather than recall it — walk through a 2×2 example live to prove you understand the math. Also discuss how in real sensor pipelines you'd compose multiple rotations as matrix multiplications to avoid multiple passes.

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