Solution: Number of Islands II

Understand how to apply the union find algorithm to dynamically calculate the number of islands in a 2D grid as land is added. This lesson guides you through implementing the algorithm with an emphasis on time and space efficiency, enabling you to handle connectivity problems in coding interviews.

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Statements
Solution
- Time complexity
- Space complexity

Statements

You are given a $2D$ binary grid of size $m × n$ . In this grid, $0$ represents water and $1$ represents land. At the beginning, every cell in the grid contains water (i.e., all cells are $0$ ).

You can perform an add land operation that changes a water cell into land. An array positions is provided, where each element positions[i] = [r_i, c_i] indicates the cell (r_i, c_i), where the i_th operation is applied.

Your task is to return an array of integers answer, where answer[i] gives the number of islands present in the grid after executing the i_th operation.

An island is defined as a cluster of land cells connected horizontally or vertically (diagonal connections are not considered). The grid is assumed to be completely enclosed by water along its four boundaries.

Constraints:

$1 <=$ ...