A 2d grid map ofmrows andncolumns is initially filled with water. We may perform anaddLandoperation which turns the water at position (row, col) into a land. Given a list of positions to operate,count the number of islands after eachaddLandoperation. An island is surrounded by water and is formed by connecting adjacent lands horizontally or vertically. You may assume all four edges of the grid are all surrounded by water.

Example:

Input:
 m = 3, n = 3, positions = [[0,0], [0,1], [1,2], [2,1]]

Output:
 [1,1,2,3]

Explanation:

Initially, the 2d gridgridis filled with water. (Assume 0 represents water and 1 represents land).

0 0 0
0 0 0
0 0 0

Operation #1: addLand(0, 0) turns the water at grid[0][0] into a land.

1 0 0
0 0 0   Number of islands = 1
0 0 0

Operation #2: addLand(0, 1) turns the water at grid[0][1] into a land.

1 1 0
0 0 0   Number of islands = 1
0 0 0

Operation #3: addLand(1, 2) turns the water at grid[1][2] into a land.

1 1 0
0 0 1   Number of islands = 2
0 0 0

Operation #4: addLand(2, 1) turns the water at grid[2][1] into a land.

1 1 0
0 0 1   Number of islands = 3
0 1 0

Follow up:

Can you do it in time complexity O(k log mn), where k is the length of thepositions?

class Solution {
    private class UnionFind{
        int count;
        int[] father;

        public UnionFind(int m, int n){
            father = new int[m * n];

            for (int i = 0; i < m; i++){
                for (int j = 0; j < n; j++){
                    father[i * n + j] = i * n + j;
                }
            }

            count = 0;
        }

        public int find(int x){
            if (x == father[x]){
                return x;
            }

            return father[x] = find(father[x]);
        }

        public void union(int a, int b){
            int father_a = find(a);
            int father_b = find(b);

            if (father_a != father_b){
                father[father_a] = father_b;
                count--;
            }
        }

        public void addIsland(){
            count++;
        }

        public int query(){
            return count;
        }
    }

    public List<Integer> numIslands2(int m, int n, int[][] positions) {
        List<Integer> ans = new ArrayList<>();

        UnionFind uf = new UnionFind(m, n);
        Set<Integer> set = new HashSet<>();
        int[][] dirs = {{0, 1}, {1, 0}, {0, -1}, {-1, 0}};
        for (int[] position : positions){
            int x = position[0];
            int y = position[1];
            int cord = x * n + y;
            set.add(cord);
            uf.addIsland();            

            for (int i = 0; i < 4; i++){
                int xx = x + dirs[i][0];
                int yy = y + dirs[i][1];
                if (xx < 0 || xx >= m || yy < 0 || yy >= n) continue;
                int cordd = xx * n + yy;

                if (set.contains(cordd)){
                    uf.union(cord, cordd);
                }
            }

            ans.add(uf.query());
        }

        return ans;
    }
}