算法（Algorithms）第4版 练习 1.5.14

package com.qiusongde;

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

public class UFWQuickUnionByHeight {

    private int[] id;//parent link(site indexed)
    private int[] treeheight;//size of component for roots(site indexed)
    private int count;//number of components

    public UFWQuickUnionByHeight(int N) {

        count = N;

        id = new int[N];
        for(int i = 0; i < N; i++)
            id[i] = i;

        treeheight = new int[N];
        for(int i = 0; i < N; i++)
            treeheight[i] = 0;

    }

    public int count() {
        return count;
    }

    public boolean connected(int p, int q) {
        return find(p) == find(q);
    }

    public int find(int p) {

        int root = p;//initialize root

        //find root(id[p] save the parent of p)
        while(root != id[root])
            root = id[root];

        return root;

    }

    public void union(int p, int q) {

        int pRoot = find(p);
        int qRoot = find(q);

        if(pRoot == qRoot)
            return;

        //make smaller root point to larger one
        if(treeheight[pRoot] < treeheight[qRoot]) {
            id[pRoot] = qRoot;
        }
        else if(treeheight[pRoot] == treeheight[qRoot]) {
            id[qRoot] = pRoot;
            treeheight[pRoot]++;
        }
        else {
            //treeheight[pRoot] > treeheight[qRott]
            id[qRoot] = pRoot;
        }

        count--;

    }

    @Override
    public String toString() {
        String s = "";

        for(int i = 0; i < id.length; i++) {
            s += id[i] + " ";
        }
        s += "\n";

        for(int i = 0; i < treeheight.length; i++) {
            s += treeheight[i] + " ";
        }
        s += "\n" + count + " components";

        return s;
    }

    public static void main(String[] args) {

        //initialize N components
        int N = StdIn.readInt();
        UFWQuickUnionByHeight uf = new UFWQuickUnionByHeight(N);
        StdOut.println(uf);

        while(!StdIn.isEmpty()) {

            int p = StdIn.readInt();
            int q = StdIn.readInt();

            if(uf.connected(p, q)) {//ignore if connected
                StdOut.println(p + " " + q + " is connected");
                StdOut.println(uf);
                continue;
            }

            uf.union(p, q);//connect p and q
            StdOut.println(p + " " + q);
            StdOut.println(uf);
        }

    }

}

运行结果：

0 1 2 3 4 5 6 7 8 9
0 0 0 0 0 0 0 0 0 0
10 components
4 3
0 1 2 4 4 5 6 7 8 9
0 0 0 0 1 0 0 0 0 0
9 components
3 8
0 1 2 4 4 5 6 7 4 9
0 0 0 0 1 0 0 0 0 0
8 components
6 5
0 1 2 4 4 6 6 7 4 9
0 0 0 0 1 0 1 0 0 0
7 components
9 4
0 1 2 4 4 6 6 7 4 4
0 0 0 0 1 0 1 0 0 0
6 components
2 1
0 2 2 4 4 6 6 7 4 4
0 0 1 0 1 0 1 0 0 0
5 components
8 9 is connected
0 2 2 4 4 6 6 7 4 4
0 0 1 0 1 0 1 0 0 0
5 components
5 0
6 2 2 4 4 6 6 7 4 4
0 0 1 0 1 0 1 0 0 0
4 components
7 2
6 2 2 4 4 6 6 2 4 4
0 0 1 0 1 0 1 0 0 0
3 components
6 1
6 2 6 4 4 6 6 2 4 4
0 0 1 0 1 0 2 0 0 0
2 components
1 0 is connected
6 2 6 4 4 6 6 2 4 4
0 0 1 0 1 0 2 0 0 0
2 components
6 7 is connected
6 2 6 4 4 6 6 2 4 4
0 0 1 0 1 0 2 0 0 0
2 components

证明可参照P229页的Proposition H的证明。