014.md

48. Rotate Image

Difficulty: 🟡 Medium

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.

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]]

Constraints:

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

Solutions

O(n^2) solution

In order to rotate the matrix clockwise by 90 degrees, we can flip the matrix by its diagonals, and then reverse it.

1 2 3 1 4 7 7 4 1 4 5 6 => 2 5 8 => 8 5 2 7 8 9 3 6 9 9 6 3

Python3

class Solution:
    def rotate(self, matrix: List[List[int]]) -> None:
        """
        Do not return anything, modify matrix in-place instead.
        """
        n = len(matrix)
        for i in range(n):
            for j in range(i+1, n):
                matrix[i][j], matrix[j][i] = matrix[j][i], matrix[i][j]
                
        for i in range(n) :
            for j in range(n//2):
                matrix[i][j], matrix[i][-1-j] = matrix[i][-1-j], matrix[i][j]

The given solution solves the problem by performing the following steps:

1. Get the size of the matrix n.
2. Iterate over the matrix using two nested loops to perform two transformations:
   • Transpose: Swap elements along the main diagonal (i.e., matrix[i][j] with matrix[j][i]).
   • Reverse Rows: Swap elements along each row's middle column (i.e., matrix[i][j] with matrix[i][n-1-j]).
3. After the loop ends, the matrix will be rotated by 90 degrees clockwise.

Complexity Analysis

The time complexity of this algorithm is O(n^2) because we iterate over the entire matrix of size n x n.

The space complexity of the algorithm is O(1) because we modify the input matrix in-place without using any additional space.

Summary

The given solution rotates the image by 90 degrees clockwise by performing a transpose operation followed by a row reversal operation. It does this in-place, modifying the input matrix directly. The algorithm has a time complexity of O(n^2) and a space complexity of O(1), making it efficient for the given constraints.

NB: If you want to get community points please suggest solutions in other languages as merge requests.