WeightedQuickUnionPathCompressionUF.java


Below is the syntax highlighted version of WeightedQuickUnionPathCompressionUF.java from §1.5 Case Study: Union-Find.


/******************************************************************************
 *  Compilation:  javac WeightedQuickUnionPathCompressionUF.java
 *  Execution:  java WeightedQuickUnionPathCompressionUF < input.txt
 *  Dependencies: StdIn.java StdOut.java
 *  Data files:   http://algs4.cs.princeton.edu/15uf/tinyUF.txt
 *                http://algs4.cs.princeton.edu/15uf/mediumUF.txt
 *                http://algs4.cs.princeton.edu/15uf/largeUF.txt
 *
 *  Weighted quick-union with path compression.
 *
 ******************************************************************************/

/**
 *  The {@code WeightedQuickUnionPathCompressionUF} class represents a
 *  union–find data structure.
 *  It supports the <em>union</em> and <em>find</em> operations, along with
 *  methods for determining whether two sites 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> sites 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 sites in tree rooted at i
                           // Note: not necessarily correct if i is not a root node
    private int count;     // number of components

    /**
     * Initializes an empty union–find data structure with {@code n} sites
     * {@code 0} through {@code n-1}. Each site is initially in its own 
     * component.
     *
     * @param  n the number of sites
     * @throws IllegalArgumentException if {@code n < 0}
     */
    public WeightedQuickUnionPathCompressionUF(int n) {
        count = n;
        parent = new int[n];
        size = new int[n];
        for (int i = 0; i < n; i++) {
            parent[i] = i;
            size[i] = 1;
        }
    }

    /**
     * Returns the number of components.
     *
     * @return the number of components (between {@code 1} and {@code n})
     */
    public int count() {
        return count;
    }
  

    /**
     * Returns the component identifier for the component containing site {@code p}.
     *
     * @param  p the integer representing one site
     * @return the component identifier for the component containing site {@code p}
     * @throws IllegalArgumentException unless {@code 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;
    }

   /**
     * Returns true if the the two sites are in the same component.
     *
     * @param  p the integer representing one site
     * @param  q the integer representing the other site
     * @return {@code true} if the two sites {@code p} and {@code q} are in the same component;
     *         {@code false} otherwise
     * @throws IllegalArgumentException unless
     *         both {@code 0 <= p < n} and {@code 0 <= q < n}
     */
    public boolean connected(int p, int q) {
        return find(p) == find(q);
    }

    // validate that p is a valid index
    private void validate(int p) {
        int n = parent.length;
        if (p < 0 || p >= n) {
            throw new IllegalArgumentException("index " + p + " is not between 0 and " + (n-1));  
        }
    }  

    /**
     * Merges the component containing site {@code p} with the 
     * the component containing site {@code q}.
     *
     * @param  p the integer representing one site
     * @param  q the integer representing the other site
     * @throws IllegalArgumentException unless
     *         both {@code 0 <= p < n} and {@code 0 <= q < n}
     */
    public void union(int p, int q) {
        int rootP = find(p);
        int rootQ = find(q);
        if (rootP == rootQ) return;

        // 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--;
    }

    /**
     * Reads in a sequence of pairs of integers (between 0 and n-1) from standard input, 
     * where each integer represents some site;
     * if the sites are in different components, merge the two components
     * and print the pair to standard output.
     *
     * @param args the command-line arguments
     */
    public static void main(String[] args) {
        int n = StdIn.readInt();
        WeightedQuickUnionPathCompressionUF uf = new WeightedQuickUnionPathCompressionUF(n);
        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");
    }

}


Copyright © 2000–2017, Robert Sedgewick and Kevin Wayne.
Last updated: Fri Jul 7 09:50:58 EDT 2017.