# 48. Rotate Image (Medium)

https://leetcode.com/problems/rotate-image/

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]
]
```

## Solutions

``````class Solution {

// It's so easy to get wrong with the index of the matrix, especially based on offsets for
// inner square.

public void rotate(int[][] matrix) {
if (matrix == null || matrix.length <= 1) {
return;
}

// inter panel, i is the thickness
// starting row index i, ending row index size - i - 1
// starting column index i, ending column index size - i - 1

for (int i = 0; i < matrix.length / 2; i++) {
int start = i; // inclusive
int end = matrix.length - i; // exclusive
int len = end - start;

// first backup the top row
int[] tmp = new int[len];
for (int j = 0; j < len; j++) {
tmp[j] = matrix[start][start + j];
}

// write over top row with left column
// copy from left column head to row tail, never use reverse order
for (int j = 0; j < len; j++) {
matrix[start][end - j - 1] = matrix[start + j][start];
}

// write over left column with bottom row
for (int j = 0; j < len; j++) {
matrix[start + j][start] = matrix[end-1][start+j];
}

// write over bottom row with right column
for (int j = 0; j < len; j++) {
matrix[end-1][start+j] = matrix[end-1-j][end-1];
}

// write right column with preserved top row
for (int j = 0; j < len; j++) {
matrix[start + j][end-1] = tmp[j];
}
}
}
}
``````

## Incorrect Solutions

``````class Solution {

// TODO Incorrect solution

public void rotate(int[][] matrix) {
int size = matrix.length;

// inter panel, i is the thickness
// starting row index i, ending row index size - i - 1
// starting column index i, ending column index size - i - 1

for (int i = 0; i < size / 2; i++) {
int start = i;
int end = size - 1 - i;

// 1. swap top and right
for (int j = 1; j < end; j++) {
swap(matrix, start, start + j, start + j, end);
}

swap(matrix, start, start, start, end);
swap(matrix, start, start, end, end);

int left = start + 1;
int right = end - 1;
while (left < right) {
swap(matrix, start, left, start, right);
left++;
right--;
}

// 2. swap top and bottom
for (int j = 0; j < end; j++) {
swap(matrix, start, start + j, end, start + j);
}

// 3. swap top and left
for (int j = 1; j < end; j++) {
swap(matrix, start, start + j, start + j, start);
}

left = start + 1;
right = end - 1;
while (left < right) {
swap(matrix, start, left, start, right);
left++;
right--;
}
}
}

private void swap(int[][] matrix, int ax, int ay, int bx, int by) {
int tmp = matrix[ax][ay];
matrix[ax][ay] = matrix[bx][by];
matrix[bx][by] = tmp;
}
}
``````