48_Rotate Image
You are given an nxn
2D matrix representing an image.
Rotate the image by 90 degrees (clockwise).
Note:
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 1:
Given input matrix =
[
[1,2,3],
[4,5,6],
[7,8,9]
],
rotate the input matrix in-place such that it becomes:
[
[7,4,1],
[8,5,2],
[9,6,3]
]
Example 2:
Given input matrix =
[
[ 5, 1, 9,11],
[ 2, 4, 8,10],
[13, 3, 6, 7],
[15,14,12,16]
],
rotate the input matrix in-place such that it becomes:
[
[15,13, 2, 5],
[14, 3, 4, 1],
[12, 6, 8, 9],
[16, 7,10,11]
]
Solution 1:
If there is no constraint of in-place rotation, a brute force method is to initiate a new nxn
matrix and put each row in the original matrix into the column of the new matrix in a reversed order.
Solution 2:
Idea: (In-place rotation)
split the whole matrix into 4 parts: upper-left, upper-right, bottom-right, bottom-left, loop over all the elements in the upper left part, and rotate the corresponding 3 elements in the other 3 parts.
Time Complexity:
Space Complexity:
def rotate(matrix):
"""
:type matrix: List[List[int]]
:rtype: void Do not return anything, modify matrix in-place instead.
"""
n = len(matrix)
for i in range(n//2):
for j in range(n-n//2):
matrix[i][j], matrix[j][~i], matrix[~i][~j], matrix[~j][i] \
= matrix[~j][i], matrix[i][j], matrix[j][~i], matrix[~i][~j]
Note that [~i]
means [n-1-i],
and it's easier to read.
Reference: https://leetcode.com/problems/rotate-image/discuss/18884/Seven-Short-Solutions-(1-to-7-lines)
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