Rotate Image medium

Problem Statement

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]]

Steps:

1. Transpose the matrix: A transpose swaps rows and columns. This is a crucial first step towards rotation.

2. Reverse each row: After transposing, each row represents a column in the rotated image. Reversing each row completes the 90-degree clockwise rotation.

Explanation:

Let's illustrate with a 3x3 matrix:

Original Matrix:

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

Step 1: Transpose

Swapping rows and columns:

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

Step 2: Reverse each row

Reversing each row:

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

This final matrix is the 90-degree clockwise rotation of the original.

Code (TypeScript):

function rotate(matrix: number[][]): void {
    // Transpose the matrix
    for (let i = 0; i < matrix.length; i++) {
        for (let j = i; j < matrix[0].length; j++) {
            [matrix[i][j], matrix[j][i]] = [matrix[j][i], matrix[i][j]];
        }
    }

    // Reverse each row
    for (let i = 0; i < matrix.length; i++) {
        matrix[i].reverse();
    }
};

Complexity:

• Time Complexity: O(n²) - We iterate through the matrix twice (once for transposition and once for reversal).
• Space Complexity: O(1) - We perform the rotation in-place; no extra space is used proportional to the input size. The space used by the variable matrix is not considered additional space.