Weighted Quick-Union with Path Compression algorithm

Question

There is a \"Weighted Quick-Union with Path Compression\" algorithm.

The code:

public class WeightedQU 
{
    private int[] id;
    private int[] iz;

           


        

Answer 1

id[i] = id[id[i]]; // this line represents "path compression"

The above code is "Simpler one-pass variant" as mentioned in the slide of Union Find (Algorithms, Part I by Kevin Wayne and Robert Sedgewick). Therefore your guess for question 1 is correct. Each examined node points to its grandparent.

To make each examined node points to the root we will need two-pass implementation:

  /**
 * Returns the component identifier for the component containing site p.
 * @param p the integer representing one site
 * @return the component identifier for the component containing site p
 * @throws java.lang.IndexOutOfBoundsException unless 0 <= p < N
 */
public int find(int p) {
    int root = p;
    while (root != id[root])
        root = id[root];
    while (p != root) {
        int newp = id[p];
        id[p] = root;
        p = newp;
    }
    return root;
}

Reference: http://algs4.cs.princeton.edu/15uf/WeightedQuickUnionPathCompressionUF.java.html