Rotate an Image 90 Degree Counterclockwise

Given an image represented by m x n matrix, rotate the image by 90 degrees in counterclockwise direction. Please note the dimensions of the result matrix are going to n x m for an m x n input matrix.

Input:
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16
Output:
4 8 12 16
3 7 11 15
2 6 10 14
1 5 9 13

Input:
1 2 3 4
5 6 7 8
9 10 11 12
Output:
4 8 12
3 7 11
2 6 10
1 5 9

[Best Approach] – O(m x n) Time

We mainly need to move first row elements to first column in revers order, second row elements to second column in reverse order.

Let us first try to find out a pattern to solve the problem for n = 4 (second example matrix above)

mat[0][0] goes to mat[3][0]
mat[0][1] goes to mat[2][0]
………………………………………
mat[1][0] goes to mat[3][1]
……………………………………..
mat[3][3] goes to mat[0][3]

Do you see a pattern? Mainly we need to move mat[i][j] to mat[n-j-1][i].

9 5 1 
10 6 2 
11 7 3 
12 8 4 

[Alternate Approach] – O(m x n) Time

When you think about rotating a matrix 90 degrees counterclockwise, each element moves to a new position. The top row becomes the leftmost column, the second row becomes the second-left column, and so forth. If we first transpose the matrix, and then reverse individual columns, we get the desired result.

Follow the given steps to solve the problem:

• Perform Transpose of the matrix
• Reverse Individual Columns

4 8 12 
2 6 10 
3 7 11 
1 5 9 

Note : We can alternatively do

1. Reverse individual rows
2. Transpose Matrix