48. Rotate Image
Problem
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.
https://leetcode.com/problems/rotate-image/
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].length1 <= n <= 20-1000 <= matrix[i][j] <= 1000
Test Cases
class Solution:
def rotate(self, matrix: List[List[int]]) -> None:
"""
Do not return anything, modify matrix in-place instead.
"""solution_test.py下载完整源码
import pytest
from solution import Solution
@pytest.mark.parametrize('matrix, expected', [
([[1,2,3],[4,5,6],[7,8,9]], [[7,4,1],[8,5,2],[9,6,3]]),
([[5,1,9,11],[2,4,8,10],[13,3,6,7],[15,14,12,16]], [[15,13,2,5],[14,3,4,1],[12,6,8,9],[16,7,10,11]]),
])
class Test:
def test_solution(self, matrix, expected):
sol = Solution()
sol.rotate(matrix)
assert matrix == expected
Thoughts
从外到内一圈一圈处理。如果 n 是奇数，中心格子无需旋转。因此 0 <= i < n // 2。
对于第 i 圈，依次处理 i 行的 i <= j < n - 1 -i 列，跟另外三条边的对应位置做轮换。
[i][j] 对应的其他三个位置分别为 [j][-i-1]、[-i-1][-j-1] 和 [-j-1][i]。
Code
solution.py下载完整源码
from typing import List
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 >> 1):
for j in range(i, n - 1 - i):
temp = matrix[i][j]
matrix[i][j] = matrix[-j-1][i]
matrix[-j-1][i] = matrix[-i-1][-j-1]
matrix[-i-1][-j-1] = matrix[j][-i-1]
matrix[j][-i-1] = temp
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