class Solution:
def rotate(self, matrix: List[List[int]]) -> None:
"""
Rotate the given n x n matrix 90 degrees clockwise in-place.
Parameters:
matrix (List[List[int]]): A 2D list representing an n x n matrix.
Returns:
None: The function modifies the matrix in-place.
"""
n = len(matrix) # 'n' is the size (number of rows/columns) of the square matrix.
# Step 1: Transpose the matrix.
# Transposing converts rows to columns.
for i in range(n):
for j in range(i + 1, n):
# Swap the elements at positions (i, j) and (j, i)
matrix[i][j], matrix[j][i] = matrix[j][i], matrix[i][j]
# Step 2: Reverse each row.
# Reversing each row yields the final rotated matrix.
for i in range(n):
# Reverse the current row in place.
matrix[i].reverse()
Summary of Techniques and Approaches:
Decomposition of the Problem: The solution is split into two clear and manageable steps: transposing the matrix and then reversing each row. This technique is useful for tackling complex problems by breaking them down into smaller sub-tasks.
Matrix Transformation: Understanding that rotating a matrix 90 degrees clockwise can be achieved by first transposing (swapping rows with columns) and then reversing each row demonstrates the importance of using inherent matrix properties. This insight is broadly applicable in problems involving matrix and geometric transformations.
In-Place Operations: The solution modifies the matrix directly without allocating extra space. This approach is beneficial in scenarios where memory efficiency is critical, particularly for in-place algorithms.
Two-Pointer Technique (via list.reverse()): The reversal of each row leverages the Python built-in reverse() method, which is efficient and succinct. Similar techniques can be applied in other array manipulation problems where elements need to be reordered.
These approaches can be identified and applied when dealing with problems that require transformation, rearrangement, or optimization of data structures in a memory- and time-efficient way.