Problem
You are given an n x n 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]
]
Notes
Naive solution, to do it one by one.
Important:
You go from the outside into the middle. So the main loop is half of the dimension.
The inner loop should also shrink its size everytime. Begins at i and ends and n-2-i, not n-1-i.
Because you don’t want to swap the last one. The last one n-1-i has already been swapped with the i.
Another solution: how to rotate a matrix faster
Swap the diagnoal elements and reverse each line in the matrix.
| 1 | 2 | 3 | swap | 1 | 4 | 7 | reverse | 7 | 4 | 1 |
|---|---|---|---|---|---|---|---|---|---|---|
| 4 | 5 | 6 | —> | 2 | 5 | 8 | ——> | 8 | 5 | 2 |
| 7 | 8 | 9 | 3 | 6 | 9 | 9 | 6 | 3 |
Solution
Solution 1: Straightforward
class Solution(object):
def rotate(self, matrix):
"""
:type matrix: List[List[int]]
:rtype: None Do not return anything, modify matrix in-place instead.
"""
n = len(matrix)
for i in range(n//2):
# Shrink the dimension
# Do not include the last element
for j in range(i, n-i-1):
tmp = matrix[i][j]
matrix[i][j] = matrix[n-1-j][i]
matrix[n-1-j][i] = matrix[n-1-i][n-1-j]
matrix[n-1-i][n-1-j] = matrix[j][n-1-i]
matrix[j][n-1-i] = tmp
matrix = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
Solution().rotate(matrix)
[print(*line) for line in matrix]
Solution 2:
class Solution(object):
def rotate(self, matrix):
"""
:type matrix: List[List[int]]
:rtype: None Do not return anything, modify matrix in-place instead.
"""
n = len(matrix)
for i in range(n):
for j in range(i, n):
matrix[i][j], matrix[j][i] = matrix[j][i], matrix[i][j]
for i in range(n):
matrix[i].reverse()
matrix = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
Solution().rotate(matrix)
[print(*line) for line in matrix]