HeightedQuickUnionUF.java

public class HeightedQuickUnionUF {
    private int[] id;    // id[i] = parent of i
    private int[] height;    // sz[i] = number of objects in subtree rooted at i
    private int count;   // number of components

    // Create an empty union find data structure with N isolated sets.
    public HeightedQuickUnionUF(int N) {
        count = N;
        id = new int[N];
        height = new int[N];
        for (int i = 0; i < N; i++) {
            id[i] = i;
            height[i] = 0;
        }
    }

    // Return the number of disjoint sets.
    public int count() {
        return count;
    }

    // Return component identifier for component containing p
    public int find(int p) {
        while (p != id[p]) {
            id[p] = id[id[p]]; //point element to its grandparent, path compression, works in practice.
            p = id[p];
        }
        return p;
    }

    // Are objects p and q in the same set?
    public boolean connected(int p, int q) {
        return find(p) == find(q);
    }


    // Replace sets containing p and q with their union.
    public void union(int p, int q) {
        int i = find(p);
        int j = find(q);
        if (i == j) return;

        // make smaller root point to larger one
        if   (height[i] < height[j]) { id[i] = j;}
        else {
            id[j] = i;
            if (height[i] == height[j]) //only h[i] == h[j], we need update height
                height[i] += 1; //update height by adding 1
        }
        count--;
    }

}

Network.java

public class Network {
  private WeightedQuickUnionUF wuf;
  public Network(int n) {
    wuf = new WeightedQucikUnionUF(n);
  }
  pulic void connect(int i, int j) {
    wuf.union(i, j);
  }
  public boolean isAllConnected() {
    return wuf.count == 1;
  }
  public static int main(String[] args) {
    int m = Integer.parseInt(args[0]);
    In in = new In(args[1]); // input file.every line is t, i, j
    Network net = new Network(m);
    while (!in.isEmpty()) {
      int t = in.readInt();
      int i = in.readInt();
      int j = in.readInt();
      net.connect(i,j)
      if (net.isAllConnected()) {
        return t;
      } 
    }
  }
}

WeightedQuickUnionLargestUF.java

/****************************************************************************
 *  Compilation:  javac WeightedQuickUnionLargestUF.java
 *  Execution:  java WeightedQuickUnionLargestUF < input.txt
 *  Dependencies: StdIn.java StdOut.java
 *
 *  Weighted quick-union (with one line variant path compression).
 *
 ****************************************************************************/

public class WeightedQuickUnionLargestUF {
    private int[] id;    // id[i] = parent of i
    private int[] sz;    // sz[i] = number of objects in subtree rooted at i
    private int[] largest; // largest[i] = largest element in the subtree rooted at i
    private int count;   // number of components

    // Create an empty union find data structure with N isolated sets.
    public WeightedQuickUnionLargestUF(int N) {
        count = N;
        id = new int[N];
        sz = new int[N];
        largest = new int[N];
        for (int i = 0; i < N; i++) {
            id[i] = i;
            largest[i] = i;
            sz[i] = 1;
        }
    }

    // Return the number of disjoint sets.
    public int count() {
        return count;
    }

    // Return component identifier for component containing p
    public int realFind(int p) {
        while (p != id[p]) {
            id[p] = id[id[p]]; //point element to its grandparent, path compression, works in practice.
            p = id[p];
        }
        return p;
    }

    // fake find, return the largest element in the component
    public int find(int p) {
        int root = realFind(p);
        return largest[root];
    }

    // Are objects p and q in the same set?
    public boolean connected(int p, int q) {
        return realFind(p) == realFind(q);
    }


    // Replace sets containing p and q with their union.
    public void union(int p, int q) {
        int i = realFind(p);
        int j = realFind(q);
        if (i == j) return;

        // make smaller root point to larger one
        if   (sz[i] < sz[j]) { id[i] = j; sz[j] += sz[i]; largest[j] = Math.max(largest[i], largest[j]); }
        else                 { id[j] = i; sz[i] += sz[j]; largest[i] = Math.max(largest[i], largest[j]); }
        count--;
    }


    public static void main(String[] args) {
        int N = StdIn.readInt();
        WeightedQuickUnionUF uf = new WeightedQuickUnionUF(N);

        // read in a sequence of pairs of integers (each in the range 0 to N-1),
        // calling find() for each pair: If the members of the pair are not already
        // call union() and print the pair.
        while (!StdIn.isEmpty()) {
            int p = StdIn.readInt();
            int q = StdIn.readInt();
            if (uf.connected(p, q)) continue;
            uf.union(p, q);
            StdOut.println(p + " " + q);
        }
        StdOut.println(uf.count() + " components");
    }

}