Dynamic Island Counts

# Dynamic Island Counts Implement `island_counts(rows: int, columns: int, additions: list[list[int]]) -> list[int]`. Begin with a `rows` by `columns` grid containing only water. Each addition `[row, column]` changes that cell to land. After every addition, return the current number of islands, where land connects only through shared horizontal or vertical edges. ### Input Domain - `1 <= rows, columns <= 100,000` and `rows * columns <= 10^9`. - `0 <= len(additions) <= 200,000`. - Every addition contains exactly two valid zero-based coordinates. - The same coordinate may be added more than once. ### Output Rules - Preserve the order of additions. - Adding a cell that is already land changes nothing but still produces an output count. - Diagonal neighbors do not connect islands. - Return an empty list when there are no additions. ### Constraints - The result after each operation must be exact. - Space should depend on the number of distinct added cells, not on `rows * columns`. ### Examples #### Example 1 Input: `rows = 3, columns = 3, additions = [[0,0],[0,1],[1,2],[2,1]]` Output: `[1,1,2,3]` #### Example 2 Input: `rows = 2, columns = 3, additions = [[0,0],[0,2],[0,1],[0,1]]` Output: `[1,2,1,1]` ```hint Merge newly connected components A new land cell begins as one component, then each union with a distinct neighboring component reduces the count by one. ```