Leetcode 48 : Rotate Image

Problem Statement :

You are given an n x n 2D matrix representing an image, rotate the image by 90 degrees (clockwise).

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.

Test Cases :

Example 1:

Input: matrix = [[1,2,3],[4,5,6],[7,8,9]]
Output: [[7,4,1],[8,5,2],[9,6,3]]

Example 2:

Input: matrix = [[5,1,9,11],[2,4,8,10],[13,3,6,7],[15,14,12,16]]
Output: [[15,13,2,5],[14,3,4,1],[12,6,8,9],[16,7,10,11]]

Example 3:

Input: matrix = [[1]]
Output: [[1]]
Example 4:

Input: matrix = [[1,2],[3,4]]
Output: [[3,1],[4,2]]

Constraints:

• matrix.length == n
• matrix[i].length == n
• 1 <= n <= 20
• -1000 <= matrix[i][j] <= 1000

Algorithm :

The simple idea is, consider this matrix

matrix = [[1,2,3],[4,5,6],[7,8,9]]

1 2 3
4 5 6
7 8 9
Just take the transpose and lets see what we got :
1 2 3      1 4 7
4 5 6. =>  2 5 8 
7 8 9      3 6 9

So we got the above after doing the transpose operation.

for (int i=0; i<row; i++) {
 for (int j=0; j<i; j++) {
     swap(matrix, i, j);
  }
 }

Now let’s compare it with our possible answer.
Our transpose is :
1 4 7                    7 4 1
2 5 8. and our answer is 8 5 2
3 6 9                    9 6 3

So what we observe, answer is just reversing each row after doing the transpose.

1 4 7.after reversing  7 4 1
2 5 8 after reversing  8 5 2
3 6 9 after reversing  9 6 3

which is what we needed as our answer.

So algorithm is pretty simple :

1) Take the transpose of the given matrix
2) Reverse each row

Note : The above is 90 degree clockwise direction. What if, we need to rotate 90 degree anti clockwise direction.
Same way, just take the transpose.
1 2 3     1 4 7
4 5 6. => 2 5 8 
7 8 9     3 6 9

Now what will be our possible answer if we do anti clockwise 90 degree rotation on given matrix.

1 2 3     3 6 9
4 5 6. => 2 5 8 
7 8 9     1 4 7

Now we can just observe the answer along with the transpose of the matrix

1 4 7                    3 6 9
2 5 8. and our answer is 2 5 8
3 6 9                    1 4 7

So we can observe that if we just reverse all the column, we will get the desired output.

1 4 7. after reversing column wise 3 6 9
2 5 8                              2 5 8
3 6 9                              1 4 7
```

Complexity :

Time complexity is O(row * col) and since we are doing in-place, space complexity is O(1).

Code : (Clockwise 90 degree rotation)

class Solution {
 public void rotate(int[][] matrix) {
 if (matrix == null || matrix.length == 0) {
 return;
 }
 int row = matrix.length;
 int col = matrix[0].length;
 for (int i=0; i<row; i++) {
 for (int j=0; j<i; j++) {
 swap(matrix, i, j);
 }
 }
 for (int [] rowWise : matrix) {
 reverse(rowWise, 0, col — 1);
 }
 }
 
 private void swap(int [][] matrix, int i, int j) {
 int temp = matrix[i][j];
 matrix[i][j] = matrix[j][i];
 matrix[j][i] = temp;
 }
 
 private void reverse(int [] nums, int i, int j) {
 while (i < j) {
 int temp = nums[i];
 nums[i] = nums[j];
 nums[j] = temp;
 i++;
 j — ;
 }
 }
}

Github :

https://github.com/Rohithv07/LeetCode

https://github.com/Rohithv07/LeetCodeTopInterviewQuestions