48. Rotate Image

Array, Math, Matrix · 31 Aug 2023

Problem Statement

link: https://leetcode.com/problems/rotate-image/ https://leetcode.cn/problems/rotate-image/

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:

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

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]]

Solution Approach

The solution employs an in-place approach by first flipping the matrix horizontally and then transposing it (i.e., swapping elements across its primary diagonal).

Algorithm

Horizontal Flip: Swap rows symmetrically from top to bottom.
Transpose: Swap elements across the primary diagonal.
Ensure iteration ranges are selected to avoid double swaps.

Implement

    class Solution:
      def rotate(self, matrix: List[List[int]]) -> None:
          l = len(matrix)
          for i in range(l // 2):#notice the range
              for j in range(l):
                  matrix[i][j], matrix[l - 1 - i][j] = matrix[l - 1 - i][j], matrix[i][j]
          for i in range(l):
              for j in range(i):#notice the range
                  matrix[i][j], matrix[j][i] = matrix[j][i], matrix[i][j]