Quarter-Turn the Photo

MediumMatrix

Problem

A photo editor stores a square image as an n × n grid of pixel values. Rotate the image 90 degrees clockwise, modifying grid in place.

Do not allocate a second n × n grid; O(1) extra memory is expected. The function returns nothing.

Example 1

Input:
grid = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
Output:
[[7, 4, 1], [8, 5, 2], [9, 6, 3]]

The left column 1, 4, 7 read from the bottom becomes the top row 7, 4, 1.

Example 2

Input:
grid = [[1, 2], [3, 4]]
Output:
[[3, 1], [4, 2]]

Constraints

  • 1 ≤ n ≤ 500
  • -1000 ≤ grid[i][j] ≤ 1000

Hint

Show the first hint

Where does the pixel at (r, c) end up after a clockwise quarter turn?

Walkthrough

How to approach it

01Clarify before coding

  • Clockwise or counter-clockwise? Clockwise.
  • Is the grid always square? Yes, which is what makes an in-place rotation possible.
  • Can I build a new grid and copy it back? No, O(1) extra memory.

02Brute force

Allocate a new grid and write out[c][n - 1 - r] = grid[r][c] for every cell, then copy it back.

Cost: O(n²) time and O(n²) extra memory, which breaks the in-place requirement.

The rest of the walkthrough is in the app

The full walkthrough (key insight, step-by-step, dry run, complexity, edge cases, pitfalls, follow-ups) and solutions in Python and JavaScript are in the app, next to an editor and a terminal that runs your code against the tests.

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This problem is part of Pro.