What is the optimal time complexity of solving Rotate Image?

The optimized solution achieves a time complexity of O(n) by using sorting, mathematical shortcuts, or hash table lookups.

What is the auxiliary space complexity for Rotate Image?

The space complexity is O(n) since we only use a minimal/constant amount of extra memory for tracking variables (or auxiliary space if dynamic structures are allocated).

What are the typical edge cases we must handle in Rotate Image?

Key edge cases include empty collections, negative or large bounds causing integer overflow, arrays with only one element, or inputs where target criteria are not met.

How can we optimize the brute force approach for Rotate Image?

Brute force methods often inspect all possible combinations. We optimize this by sorting the input list to enable binary search, or tracking processed items in a set to avoid redundant nested loop lookups.

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Rotate Image

Learn how to solve the 'Rotate Image' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

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.

Implement a function rotate(matrix: list) -> list that rotates the matrix in-place and returns it.

Constraints

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

Examples

Example 1

Input

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

Output

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

Explanation

The matrix is rotated 90 degrees clockwise. The first column [1,4,7] becomes the first row [7,4,1] reversed.

Example 2

Input

[[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]]

Explanation

Each layer of the 4x4 matrix is rotated 90 degrees clockwise.

Need a Hint?

Analyze the input constraints. Try sorting first (O(n log n)) or using a hash map/set to track seen elements in O(n) time.

Edge Cases to Watch

Empty list or null input variables
Single item lists/arrays
Extremely large input bounds causing integer or stack overflow

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