48. Rotate Image
给定一个 n × n 的二维矩阵表示一个图像。
将图像顺时针旋转 90 度。
说明：
你必须在原地旋转图像，这意味着你需要直接修改输入的二维矩阵。请不要使用另一个矩阵来旋转图像。
示例 1:
Input: matrix = [[1,2,3],[4,5,6],[7,8,9]]
Output: [[7,4,1],[8,5,2],[9,6,3]]
示例 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]]
示例 3:
Input: matrix = [[1]]
Output: [[1]]
示例 4:
Input: matrix = [[1,2],[3,4]]
Output: [[3,1],[4,2]]
模拟法
O(N^2)
首先垂直旋转:
[1, 2, 3] [7, 8, 9]
[4, 5, 6] => [4, 5, 6]
[7, 8, 9] [1, 2, 3]
然后从左上到右下对角线互换:
\
[7, 8, 9] [7, 4, 1]
\
[4, 5, 6] => [8, 5, 2]
\
[1, 2, 3] [9, 6, 3]
\
代码如下:
class Solution:
def rotate(self, matrix: List[List[int]]) -> None:
"""
Do not return anything, modify matrix in-place instead.
"""
count = len(matrix)
top = 0
bottom = count - 1
while top < bottom: # 垂直翻转
matrix[top], matrix[bottom] = matrix[bottom], matrix[top]
top += 1
bottom -= 1
for i in range(count): # 对角线翻转
for j in range(i + 1, count):
matrix[i][j], matrix[j][i] = matrix[j][i], matrix[i][j]
–End–