Problem: in a ocean there are islands marked by 1. water s represented as 0. Determine how many unique shapes(no rotation or mirror) among these islands. 4-directional connection.

Example input:
[[ 1, 1, 1, 1, 0, 0],
[ 1, 1, 0, 0, 0, 1],
[ 0, 0, 1, 1, 0, 1]
[ 1, 1, 0, 0, 0, 0]
[ 0, 0, 1, 1, 1, 1],
[ 1, 0, 1, 1, 0, 0],
]

Example answer: 4. (the 2 6-sized island, the 2 2-sized island, the 1 2-sized island, the 1 1-sized island)

Standard BFS/DFS problem with a translation of the starting point to origin of each island. I got it done correctly and optimally with O(n) complexity.

The following up is: now allows rotation and mirroring, shapes are considered the same if they can be rotated and mirrored to the same. The only way i can think of is to enumerate all the rotations and mirroring combinations of an island and checking for uniqueness in a set. But i dont feel optimal, and the interviewer hinted by saying how do you normalize a shape. I did not get to it. How to do normalization of shapes to avoid enumerate all the rotations and mirroring combinations?