code: package graphTheory.utils;
  
  	/****************************************************************************
  	 *  Compilation:  javac WeightedQuickUnionPathCompressionUF.java
  	 *  Execution:  java WeightedQuickUnionPathCompressionUF < input.txt
  	 *  Dependencies: StdIn.java StdOut.java
  	 *
  	 *  Weighted quick-union with path compression.
  	 *
  	 ****************************************************************************/
  
  import java.util.HashSet;
  import java.util.LinkedList;
  import java.util.List;
  
  /**
  	 *  The <tt>WeightedQuickUnionPathCompressionUF</tt> class represents a
  	 *  union-find data structure.
  	 *  It supports the <em>union</em> and <em>find</em> operations, along with
  	 *  methods for determinig whether two objects are in the same component
  	 *  and the total number of components.
  	 *  <p>
  	 *  This implementation uses weighted quick union (by size) with full path compression.
  	 *  Initializing a data structure with <em>N</em> objects takes linear time.
  	 *  Afterwards, <em>union</em>, <em>find</em>, and <em>connected</em> take
  	 *  logarithmic time (in the worst case) and <em>count</em> takes constant
  	 *  time. Moreover, the amortized time per <em>union</em>, <em>find</em>,
  	 *  and <em>connected</em> operation has inverse Ackermann complexity.
  	 *  <p>
  	 *  For additional documentation, see <a href="http://algs4.cs.princeton.edu/15uf">Section 1.5</a> of
  	 *  <i>Algorithms, 4th Edition</i> by Robert Sedgewick and Kevin Wayne.
  	 *     
  	 *  @author Robert Sedgewick
  	 *  @author Kevin Wayne
  	 */
  	public class WeightedQuickUnionPathCompressionUF {
  	    private int[] parent;  // parent[i] = parent of i
  	    private int[] size;    // size[i] = number of objects in subtree rooted at i
  	    private int count;     // number of components
  
  	    private int numberOfNodes;
  	    
  	    /**
  	     * Initializes an empty union-find data structure with N isolated components 0 through N-1.
  	     * @throws java.lang.IllegalArgumentException if N < 0
  	     * @param N the number of objects
  	     */
  	    public WeightedQuickUnionPathCompressionUF(int N) {
  	    	numberOfNodes = N;
  	        parent = new int[numberOfNodes];
  	        size = new int[numberOfNodes];
  	    	reinit();
  	    }
  
  	    public void reinit(){
  	    	count = numberOfNodes;
  	        for (int i = 0; i < numberOfNodes; i++) {
  	            parent[i] = i;
  	            size[i] = 1;
  	        }
  	    }
  	    
  	    /**
  	     * Returns the number of components.
  	     * @return the number of components (between 1 and N)
  	     */
  	    public int count() {
  	        return count;
  	    }
  
  	  
  	    /**
  	     * Are the two sites <tt>p</tt> and <tt>q</tt> in the same component?
  	     * @param p the integer representing one site
  	     * @param q the integer representing the other site
  	     * @return <tt>true</tt> if the two sites <tt>p</tt> and <tt>q</tt>
  	     *    are in the same component, and <tt>false</tt> otherwise
  	     * @throws java.lang.IndexOutOfBoundsException unless both 0 <= p < N and 0 <= q < N
  	     */
  	    public boolean connected(int p, int q) {
  	        return find(p) == find(q);
  	    }
  
  
  	    /**
  	     * Returns the component identifier for the component containing site <tt>p</tt>.
  	     * @param p the integer representing one site
  	     * @return the component identifier for the component containing site <tt>p</tt>
  	     * @throws java.lang.IndexOutOfBoundsException unless 0 <= p < N
  	     */
  	    public int find(int p) {
  	        validate(p);
  	        int root = p;
  	        while (root != parent[root])
  	            root = parent[root];
  	        while (p != root) {
  	            int newp = parent[p];
  	            parent[p] = root;
  	            p = newp;
  	        }
  	        return root;
  	    }
  
  	     
  	    // validate that p is a valid index
  	    private void validate(int p) {
  	        int N = parent.length;
  	        if (p < 0 || p >= N) {
  	            throw new IndexOutOfBoundsException("index " + p + " is not between 0 and " + N);
  	        }
  	    }  
  
  	    /**
  	     * Merges the component containing site<tt>p</tt> with the component
  	     * containing site <tt>q</tt>.
  	     * @param p the integer representing one site
  	     * @param q the integer representing the other site
  	     * @throws java.lang.IndexOutOfBoundsException unless both 0 <= p < N and 0 <= q < N
  	     */
  	  public boolean union(int p, int q) {
  	        int rootP = find(p);
  	        int rootQ = find(q);
  	        if (rootP == rootQ) return false;
  
  	        // make smaller root point to larger one
  	        if (size[rootP] < size[rootQ]) {
  	            parent[rootP] = rootQ;
  	            size[rootQ] += size[rootP];
  	        }
  	        else {
  	            parent[rootQ] = rootP;
  	            size[rootP] += size[rootQ];
  	        }
  	        count--;
  	        return true;
  	    }
  
  
  
  	    /**
  	     * Reads in a sequence of pairs of integers (between 0 and N-1) from standard input, 
  	     * where each integer represents some object;
  	     * if the objects are in different components, merge the two components
  	     * and print the pair to standard output.
  	     */
  	    public static void main(String[] args) {
  	        int n = 20;
  	        WeightedQuickUnionPathCompressionUF uf = new WeightedQuickUnionPathCompressionUF(n);
  //	        for(int i = 0; i<n*n;i++) {
  //	            int p = Math2.randomInt(n);
  //	            int q = Math2.randomInt(n);
  //	            System.out.print(p+" "+q);
  //	            if (uf.connected(p, q)) {
  //	            	System.out.println();
  //	            	continue;
  //	            }
  //	            uf.union(p, q);
  //	            System.out.println(" ok");
  //	        }
  	        uf.union(0, 1);
  	        uf.union(1, 2);
  	        uf.union(2, 3);
  	        uf.union(3, 4);
  	        System.out.println(uf.count() + " components");
  	    }
  
  }
  