public class QuickUnion {
    private int[] id;    // id[i] = parent of i
    private int count;   // number of components

    // instantiate N isolated components 0 through N-1
    public QuickUnion(int N) {
        id = new int[N];
        count = N;
        for (int i = 0; i < N; i++) {
            id[i] = i;
        }
    }

    // return number of connected components
    public int count() {
        return count;
    }

    // return root of component corresponding to element p
    public int find(int p) {
        while (p != id[p])
            p = id[p];
        return p;
    }

    // are elements p and q in the same component?
    public boolean connected(int p, int q) {
        return find(p) == find(q);
    }

    // merge components containing p and q
    public void union(int p, int q) {
        int i = find(p);
        int j = find(q);
        if (i == j) return;
        id[i] = j;
        count--;
    }
}