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46. Rotate Image

mediumAsked at Plaid

Rotate an NxN matrix 90 degrees clockwise in place. Plaid asks this because in-place 2D transforms are the same shape as their column-major to row-major balance-history transposition for charts.

By Alex Chen, Founder, InterviewChamp.AI · Last verified

Source citations

Public interview reports confirming this problem appears in Plaid loops.

  • Glassdoor (2025)— Plaid SWE II OA — matrix transform.
  • LeetCode Discuss (2026)— Plaid in-place classic.

Problem

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.

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]]

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. Allocate new matrix

Build a fresh matrix with rotated indices; copy back.

Time
O(n^2)
Space
O(n^2)
function rotate(matrix) {
  const n = matrix.length;
  const r = Array.from({ length: n }, () => new Array(n));
  for (let i = 0; i < n; i++) for (let j = 0; j < n; j++) r[j][n - 1 - i] = matrix[i][j];
  for (let i = 0; i < n; i++) for (let j = 0; j < n; j++) matrix[i][j] = r[i][j];
}

Tradeoff: Violates the in-place constraint. Mention only as the warm-up.

2. Transpose then reverse each row

Swap matrix[i][j] with matrix[j][i] (transpose). Then reverse each row. Composition = 90° clockwise rotation.

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 (const row of matrix) row.reverse();
}

Tradeoff: In-place. Two clean phases — easy to debug, easy to test. The j = i+1 (not 0) in transpose prevents double-swap.

Plaid-specific tips

Plaid grades this on the transpose-then-reverse decomposition because it's the readable production approach. The 4-way cycle swap is more clever but harder to debug. Bonus signal: derive the composition out loud — transpose followed by horizontal flip equals 90° clockwise.

Common mistakes

  • Starting j from 0 in the transpose — double-swaps and ends up with the original matrix.
  • Reversing columns instead of rows — produces a 90° counter-clockwise rotation.
  • Allocating a new matrix — fails the in-place constraint.

Follow-up questions

An interviewer at Plaid may pivot to one of these next:

  • Rotate counter-clockwise (transpose then reverse columns).
  • Rotate by 180° (reverse rows then reverse columns).
  • Rotate a non-square matrix.

Solve it now

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Output

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FAQ

Why does transpose + reverse work?

Transpose maps (i,j) to (j,i). Row reverse maps (j,i) to (j, n-1-i). Composition: (i,j) -> (j, n-1-i), which is the 90° clockwise formula.

Could you do this with a single cycle-swap pass?

Yes — four cells form a cycle: (i,j) -> (j, n-1-i) -> (n-1-i, n-1-j) -> (n-1-j, i) -> back. One temp variable per cycle. Equivalent asymptotic, fewer writes.

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