Weighted Quick Union Path Compression UF

package edu.princeton.cs.algs4;

/******************************************************************************
 * Compilation: javac WeightedQuickUnionPathCompressionUF.java Execution:
 * java WeightedQuickUnionPathCompressionUF < input.txt Dependencies:
 * StdIn.java StdOut.java Data files:
 * https://algs4.cs.princeton.edu/15uf/tinyUF.txt
 * https://algs4.cs.princeton.edu/15uf/mediumUF.txt
 * https://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="https://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;
        // we find the root, then we have two choices almost as fast
        while (root != parent[root])
            root = parent[root];

        // option 1: with grand parent path compression
        while (p != root) {
            int newp = parent[p];
            parent[p] = root;
            p = newp;
        }

       // option 2: with full path compression
       // in practice linear time m log n
        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 2002-2016, Robert Sedgewick and Kevin Wayne.
 *
 * This file is part of algs4.jar, which accompanies the textbook
 *
 * Algorithms, 4th edition by Robert Sedgewick and Kevin Wayne, Addison-Wesley
 * Professional, 2011, ISBN 0-321-57351-X. http://algs4.cs.princeton.edu
 *
 *
 * algs4.jar is free software: you can redistribute it and/or modify it under
 * the terms of the GNU General Public License as published by the Free Software
 * Foundation, either version 3 of the License, or (at your option) any later
 * version.
 *
 * algs4.jar is distributed in the hope that it will be useful, but WITHOUT ANY
 * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
 * A PARTICULAR PURPOSE. See the GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License along with
 * algs4.jar. If not, see http://www.gnu.org/licenses.
 ******************************************************************************/