Rotate Image

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

Solution 1: Rotate Groups of Four Cells

n = len(matrix)
for i in range(n // 2 + n % 2):
    for j in range(i, n - i - 1):
        (
            matrix[i][j],
            matrix[j][-(i + 1)],
            matrix[-(i + 1)][-(j + 1)],
            matrix[-(j + 1)][i],
        ) = (
            matrix[-(j + 1)][i],
            matrix[i][j],
            matrix[j][-(i + 1)],
            matrix[-(i + 1)][-(j + 1)],
        )

The key lies in carefully examine the range for i and j! Draw matrices of different sizes and experiment with the indices. Complexity = $O(n^2)$ as each cell is processed once.

Solution 2: Transpose and Reflect

def transpose(matrix):
    n = len(matrix)
    for i in range(n):
        for j in range(i + 1, n):
            matrix[j][i], matrix[i][j] = matrix[i][j], matrix[j][i]
 
def reflect(matrix):
    n = len(matrix)
    for i in range(n):
        for j in range(n // 2):
            (
                matrix[i][j],
                matrix[i][-j - 1]
            ) = (
                matrix[i][-j - 1],
                matrix[i][j],
            )
 
def rotate(matrix):
    transpose(matrix)
    reflect(matrix)

Same complexity but twice as many read/write access.