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.