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

treeheight = new int
;
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。