Coursera Algorithms week1 查并集 练习测验：2 Union-find with specific canonical element

题目原文：

Add a method find() to the union-find data type so that find(i) returns the largest element in the connected component containing i. The operations, union(), connected(), and find() should all take logarithmic time or better. 

import edu.princeton.cs.algs4.StdIn;
import edu.princeton.cs.algs4.StdOut;

public class FindLargestUF {
    private int[] id;
    private int count;
    public FindLargestUF(int n) {
        count = n;
        id = new int[n];
        for (int i = 0; i < n; i++)
            id[i] = i;
    }
    public int count(){
        return count;
    }
    public boolean connected(int p, int q){
        return (find(p)==find(q));
    }
    public int find(int p) {
        while (p != id[p])
            p = id[p];
        return p;
    }

    public void union(int p, int q) {
        int pRoot = find(p);
        int qRoot = find(q);
        StdOut.println("find("+p+")="+pRoot+",find("+q+")="+qRoot);
        if (pRoot == qRoot)
            return;
        else if (pRoot < qRoot)
            id[pRoot] = qRoot;
        else
            id[qRoot] = pRoot;
        count--;
    }

    public static void main(String[] args) {
        int n = StdIn.readInt();
        FindLargestUF uf = new FindLargestUF(n);
        while (!StdIn.isEmpty()) {
            int p = StdIn.readInt();
            int q = StdIn.readInt();
            if (uf.connected(p, q))
                continue;
            uf.union(p, q);
            StdOut.println("link points:" + p + " " + q);
        }
        StdOut.println(uf.count() + "components");
    }
}

For example, if one of the connected components is {1,2,6,9}, then the find() method should return 9 for each of the four elements in the connected components.

分析：

这一题很简单，要求find到的根是子集中的最大元素。因此只需要在union时，用两个子集中较大的root作为合并后的root就可以了。以下代码提交100