I knew the general shape of the solution pretty quickly.
Use BFS to identify one island, then multi-source BFS from all cells of that island to find the shortest path to the other island. The number of steps (or layers) until reaching the second island gives the minimum number of 0s to flip.
Pro tip: Clarify that flipping 0s to 1s is equivalent to finding the shortest path through water cells; mention that you can optimize by only expanding from the smaller island to reduce BFS queue size.
Traverse the matrix to find the first '1' and use BFS/DFS to mark all cells of that island. The remaining unvisited '1's belong to the second island.
Select the island with fewer cells as the source to minimize the initial BFS queue size, though either works.
Initialize a queue with all cells of the source island and perform BFS, expanding to neighboring water cells (0s) and unvisited land cells. Track the distance (number of water cells crossed).
When a cell belonging to the second island is reached, return the current distance (number of 0s flipped).
Discuss time and space complexity (O(n^2)), and consider if the islands are already connected (though problem states exactly two islands, so they are separate).
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.