算法（Algorithms）第4版 练习 1.5.4

代码实现：

package com.qiusongde;

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

public class UFWeightedQuickUnion {

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

    private static int totalcost = 0;//for the test of array access

    public UFWeightedQuickUnion(int N) {

        count = N;

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

        treesize = new int[N];
        for(int i = 0; i < N; i++)
            treesize[i] = 1;

    }

    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];
            totalcost += 2;
        }
        totalcost++;

        return p;

    }

    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(treesize[pRoot] < treesize[qRoot]) {
            id[pRoot] = qRoot;
            treesize[qRoot] += treesize[pRoot];
            totalcost += 5;
        } else {
            id[qRoot] = pRoot;
            treesize[pRoot] += treesize[qRoot];
            totalcost += 5;
        }

        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 < treesize.length; i++) {
            s += treesize[i] + " ";
        }
        s += "\n" + count + " components";

        return s;
    }

    public static void main(String[] args) {

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

        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("totalcost: " + totalcost);
                StdOut.println();
                continue;
            }

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

    }

}

reference input：

10
4 3
3 8
6 5
9 4
2 1
8 9
5 0
7 2
6 1
1 0
6 7

结果：

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

4 3
0 1 2 4 4 5 6 7 8 9
1 1 1 1 2 1 1 1 1 1
9 components
totalcost: 9

3 8
0 1 2 4 4 5 6 7 4 9
1 1 1 1 3 1 1 1 1 1
8 components
totalcost: 22

6 5
0 1 2 4 4 6 6 7 4 9
1 1 1 1 3 1 2 1 1 1
7 components
totalcost: 31

9 4
0 1 2 4 4 6 6 7 4 4
1 1 1 1 4 1 2 1 1 1
6 components
totalcost: 40

2 1
0 2 2 4 4 6 6 7 4 4
1 1 2 1 4 1 2 1 1 1
5 components
totalcost: 49

8 9 is connected
totalcost: 55

5 0
6 2 2 4 4 6 6 7 4 4
1 1 2 1 4 1 3 1 1 1
4 components
totalcost: 68

7 2
6 2 2 4 4 6 6 2 4 4
1 1 3 1 4 1 3 1 1 1
3 components
totalcost: 77

6 1
6 2 6 4 4 6 6 2 4 4
1 1 3 1 4 1 6 1 1 1
2 components
totalcost: 90

1 0 is connected
totalcost: 98

6 7 is connected
totalcost: 104

worst-case input：

8
0 1
2 3
4 5
6 7
0 2
4 6
0 4

结果：

0 1 2 3 4 5 6 7
1 1 1 1 1 1 1 1
8 components

0 1
0 0 2 3 4 5 6 7
2 1 1 1 1 1 1 1
7 components
totalcost: 9

2 3
0 0 2 2 4 5 6 7
2 1 2 1 1 1 1 1
6 components
totalcost: 18

4 5
0 0 2 2 4 4 6 7
2 1 2 1 2 1 1 1
5 components
totalcost: 27

6 7
0 0 2 2 4 4 6 6
2 1 2 1 2 1 2 1
4 components
totalcost: 36

0 2
0 0 0 2 4 4 6 6
4 1 2 1 2 1 2 1
3 components
totalcost: 45

4 6
0 0 0 2 4 4 4 6
4 1 2 1 4 1 2 1
2 components
totalcost: 54

0 4
0 0 0 2 0 4 4 6
8 1 2 1 4 1 2 1
1 components
totalcost: 63