Number of Islands II

A 2d grid map of m rows and n columns is initially filled with water. We may perform an addLand operation which turns the water at position (row, col) into a land. Given a list of positions to operate, count the number of islands after each addLand operation. 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:

Given m = 3, n = 3, positions = [[0,0], [0,1], [1,2], [2,1]].
Initially, the 2d grid grid is 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

We return the result as an array: [1, 1, 2, 3]

The easiest solution for this problem utilizes union-find. Each time we add a land, first increment the size of the total number of islands, then for each of its neighbors, union them if the neighbor is also an island.

public class NumberOfIslands {
    private int[] rankArray;

    int size, cols, rows;

    public NumberOfIslands (int m, int n) {
        rankArray = new int[m * n];
        this.size = 0;
        this.cols = n;
        this.rows = m;
        Arrays.fill(rankArray, rows * cols + 1);
    }

    public int add(int x, int y) {
        int index = getIndex(x, y);
        rankArray[index] = -1;
        size++;
        int[] neighbors = getNeighbors(x, y);
        for (int n : neighbors) {
            if (n < 0 || rankArray[n] == rows * cols + 1) {
                continue;
            }
            union(index, n);
        }
        return size;
    }

    private int getIndex(int x, int y) {
        return x * cols + y;
    }

    //left, right, down, up
    private int[] getNeighbors(int x, int y) {
        int[] neighbors = new int[4];
        neighbors[0] = x - 1 >= 0 ? getIndex(x - 1, y) : -1;
        neighbors[1] = x + 1 < rows ? getIndex(x + 1, y) : -1;
        neighbors[2] = y - 1 >= 0 ? getIndex(x, y - 1) : -1;
        neighbors[3] = y + 1 < cols ? getIndex(x, y + 1) : -1;
        return neighbors;
    }

    private void union(int index1, int index2) {
        int root1 = find(index1);
        int root2 = find(index2);
        if (root1 == root2)  {
            size--;
            return;
        }
        if (rankArray[root2] < rankArray[root1]) {
            rankArray[root1] = root2;
            size--;
        } else {
            if (rankArray[root1] == rankArray[root2]) {
                rankArray[root1]--;
            }
            rankArray[root2] = root1;
            size--;
        }
    }

    private int find(int index) {
        if (rankArray[index] < 0) {
            return index;
        }
        int root = find(rankArray[index]);
        rankArray[index] = root;
        return root;
    }
}