How do you approach Rotate Image?

First transpose the matrix (swap rows and columns).

What is the time complexity of Rotate Image?

Time complexity: O(n²). Space complexity: O(1).

What are common mistakes on Rotate Image?

Transposing row and column in the index. It reads fine and fails on any non-square input. Overwriting cells a later iteration still needs to read - most in-place matrix problems want a marker pass first. Bounds checks that cover only some of the four edges.

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Rotate Image

MediumAlgorithms

Description

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]]

Constraints

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

Rotate Image: approach, complexity and pitfalls

A medium matrix problem, graded against 4 test cases (1 of them hidden).

The pattern: Matrix

2D grid traversal, rotation, and in-place manipulation.

Reach for it when you see: A grid input, spiral or diagonal traversal, or an in-place transformation constraint.

More Matrixproblems →

If you are stuck

Show the 3-step hint ladder

First transpose the matrix (swap rows and columns).
Then reverse each row.
This achieves a 90-degree clockwise rotation.

The optimal approach

Show the approach: Transpose + Reverse

1. Transpose the matrix (swap matrix[i][j] with matrix[j][i])

2. Reverse each row

Time: O(n²)
Space: O(1)

The full reference solution in every supported language stays in the editor above - reveal it there once you have had a real attempt.

What the tests check

Read off this problem's own test suite, so these are the cases a submission actually has to survive.

Single element. A one-element case is included. Two-pointer and window solutions frequently return the wrong thing when the two indices start out equal.

Common Matrix mistakes

These apply to the pattern as a whole, not just this problem.

Transposing row and column in the index. It reads fine and fails on any non-square input.
Overwriting cells a later iteration still needs to read - most in-place matrix problems want a marker pass first.
Bounds checks that cover only some of the four edges.