305.Number of Islands II

    /*
     * 305.Number of Islands II
     * 2016-4-3 by Mingyang
     *Union Find 的题目，直接略过
     */
     private int[][] dir = {{0, 1}, {0, -1}, {-1, 0}, {1, 0}};
     public List<Integer> numIslands2(int m, int n, int[][] positions) {
            UnionFind2D islands = new UnionFind2D(m, n);
            List<Integer> ans = new ArrayList<Integer>();
            for (int[] position : positions) {
                int x = position[0], y = position[1];
                int p = islands.add(x, y);
                for (int[] d : dir) {
                    int q = islands.getID(x + d[0], y + d[1]);
                    if (q > 0 && !islands.find(p, q))
                        islands.unite(p, q);
                }
                ans.add(islands.size());
            }
            return ans;
        }
}
class UnionFind2D {
    private int[] id;
    private int[] sz;
    private int m, n, count;
    public UnionFind2D(int m, int n) {
        this.count = 0;
        this.n = n;
        this.m = m;
        this.id = new int[m * n + 1];
        this.sz = new int[m * n + 1];
    }
    public int index(int x, int y) { return x * n + y + 1; }
    public int size() { return this.count; }
    public int getID(int x, int y) {
        if (0 <= x && x < m && 0<= y && y < n)
            return id[index(x, y)];
        return 0;
    }
    public int add(int x, int y) {
        int i = index(x, y);
        id[i] = i; sz[i] = 1;
        ++count;
        return i;
    }
    public boolean find(int p, int q) {
        return root(p) == root(q);
    }
    public void unite(int p, int q) {
        int i = root(p), j = root(q);
        if (sz[i] < sz[j]) { //weighted quick union
            id[i] = j; sz[j] += sz[i];
        } else {
            id[j] = i; sz[i] += sz[j];
        }
        --count;
    }
    private int root(int i) {
        for (;i != id[i]; i = id[i])
            id[i] = id[id[i]]; //path compression
        return i;
    }
}