48. Rotate Image

You are given annxn2D matrix representing an image.

Rotate the image by 90 degrees (clockwise).

Note:
You have to rotate the imagein-place, which means you have to modify the input 2D matrix directly.DO NOTallocate 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]
]
``````

[Thoughts]

``````class Solution {
int n;
public:
void rotate(vector<vector<int>>& matrix) {
if (matrix.size() == 0) return;
n = matrix.size();

for (int i = 0; i < (n+1)/2; i++ ){
for (int j = 0; j < n/2 ; j++){
// here i and j only needs one to be (n+1)/2 and the other be n/2
// [i,j] -> [j][n-1-i] -> [n-1-i][n-1-j]->[n-1-j][i]
//   ^                                        |
//   |----------------------------------------|
int temp = matrix[j][n-1-i]; // who is the temp does not matter
matrix[j][n-1-i] = 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] = temp;
}
}
}
};
``````

[Code2: reverse up down + swap symmetry (Recommend)]

``````/*
* clockwise rotate
* first reverse up to down, then swap the symmetry
* 1 2 3     7 8 9     7 4 1
* 4 5 6  => 4 5 6  => 8 5 2
* 7 8 9     1 2 3     9 6 3
*/
void rotate(vector<vector<int> > &matrix) {
reverse(matrix.begin(), matrix.end());
for (int i = 0; i < matrix.size(); ++i) {
for (int j = i + 1; j < matrix[i].size(); ++j)
swap(matrix[i][j], matrix[j][i]);
}
}
``````

Extension: counter-clockwise: reverse left to right + swap the symmetry

``````/*
* anticlockwise rotate
* first reverse left to right, then swap the symmetry
* 1 2 3     3 2 1     3 6 9
* 4 5 6  => 6 5 4  => 2 5 8
* 7 8 9     9 8 7     1 4 7
*/
void anti_rotate(vector<vector<int> > &matrix) {
for (auto vi : matrix) reverse(vi.begin(), vi.end());
for (int i = 0; i < matrix.size(); ++i) {
for (int j = i + 1; j < matrix[i].size(); ++j)
swap(matrix[i][j], matrix[j][i]);
}
}
``````