Took me a minute to even figure out how to separate the two islands first.
Model the problem as finding the shortest path between the two islands where the cost of entering a water cell is 1 and land cell is 0. Use multi-source BFS from one island to compute the minimum water cells needed to reach the other island.
Pro tip: Clarify assumptions upfront: whether diagonal moves are allowed and if the grid is guaranteed to have exactly two islands. This shows attention to detail and avoids incorrect solutions.
Use DFS or BFS to label each island and collect all cells belonging to each. This separates the problem into two distinct regions.
Treat water cells as cost 1 and land cells as cost 0. The goal is to find the minimum total cost to connect any cell of island A to any cell of island B.
Initialize a queue with all cells of island A and a distance array where land cells have distance 0. Perform BFS, updating distances by adding 1 when moving to a water cell, 0 when moving to land.
During BFS, when a cell of island B is reached, the current distance is the minimum water cells needed. Return that distance.
Time complexity is O(n^2) since each cell is processed once. Discuss edge cases like islands already adjacent (answer 0) or grid boundaries.
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