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 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]
]
There are 3 solutions.
1: use extra space O(n^2)
2. transpose + flip horizontally
class Solution {
void left2Right(int[][] matrix){
int n = matrix.length;
for(int i = 0; i<n; i++){//
for(int j = 0; j<(n/2); j++){//->
int temp = matrix[i][j];
matrix[i][j] = matrix[i][n-1-j];
matrix[i][n-1-j] = temp;
}
}
}
void up2Down(int[][] matrix){
int n = matrix.length;
for(int i = 0; i<n; i++){//->
for(int j = 0; j<(n/2); j++){//
int temp = matrix[j][i];
matrix[j][i] = matrix[n-1-j][i];
matrix[n-1-j][i] = temp;
}
}
}
void transpose(int[][] matrix){
int n = matrix.length;
for(int i = 0; i<n; i++){//->
for(int j = 0; j<i; j++){//
int temp = matrix[i][j];
matrix[i][j] = matrix[j][i];
matrix[j][i] = temp;
}
}
}
public void rotate(int[][] matrix) {
//up2Down(matrix);
transpose(matrix);
left2Right(matrix);
}
}
3: just one operation (pattern among the in-place element)
reference: https://blog.csdn.net/happyaaaaaaaaaaa/article/details/51563752
class Solution {
public void rotate(int[][] matrix) {
//three solutions
int n = matrix.length;
for(int i = 0; i<=n/2; i++){//why n/2
for(int j = i; j<n-1-i; j++){//why i < j
int temp = 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-i-1] = temp;
}
}
}
}
Caution: the boundary(pick the diagnosis)
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 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]
]