Minimum flips to make Matrix identical for all rotations

Given a binary matrix Mat[][] of size N*N, the task is to find the minimum number of flips to be performed such that the matrix is identical for all rotations.

Examples:

Input: Mat[][] = {{1, 0, 0}, {0, 1, 0}, {1, 0, 1}}
Output: 1
Explanation:  Change the element at row = 1, col =  3 from 0 to 1.
Now for all the rotations the matrix is identical.

Input: {{0}}
Output: 0

Approach: To solve the problem follow the below idea:

Rotate the matrix 4 times and for every position check how many of elements needs to be changed based on their positions in each rotation.

Follow the steps mentioned below to implement the observation:

• Initialize a matrix of size N² with 0 to store the count of 1 at that position for every rotation.
• Rotate the matrix 4 times and count 1 for every position of the matrix.
• Initialize Sum = 0 and count min(count of 1, count of 0) for every position of Mat[][].
• Return Sum/4, as we count the same position 4 times.

Below is the implementation of the above approach:

1

Time Complexity: O(N²)
Auxiliary Space: O(N²)