Huffman树、霍夫曼编码

Huffman树指的是带权路径长度WPL最小的二叉树

WPL=路径*权值

Huffman常用于压缩编码，正常传输ABCDEF这些字母需要3位二进制树来描述，但由于一篇文章中ABCDEF这些字母出现的概率不同，用较多的二进制位数表示出现概率低的字母，而用较少的二进制位数表示概率高的字母。

Huffman编码实现：

package HuffmanTree;

import java.util.ArrayList;
import java.util.Collections;
import java.util.HashMap;
import java.util.LinkedList;
import java.util.List;
import java.util.Map;
import java.util.Queue;

import javax.xml.crypto.Data;

//Huffman树压缩
public class HuffmanTree<T>{

    public static Map<Object, String> map=new HashMap<Object,String>();

    //创建Huffman树
    public static <T> Node<T> createTree(List<Node<T>> nodes) {
        while (nodes.size() > 1) {
            Collections.sort(nodes);
            Node<T> left = nodes.get(nodes.size() - 1);
            Node<T> right = nodes.get(nodes.size() - 2);
            Node<T> parent = new Node<T>(null, left.getWeight()
                    + right.getWeight());
            parent.setLeft(left);
            parent.setRight(right);
            nodes.remove(left);
            nodes.remove(right);
            nodes.add(parent);
        }
        return nodes.get(0);
    }

    //保存Huffman树
    public static <T> List<Node<T>> breath(Node<T> root) {
        List<Node<T>> list = new ArrayList<Node<T>>();
        Queue<Node<T>> queue = new LinkedList<>();
        queue.add(root);
        while (!queue.isEmpty()) {
            Node<T> pNode = queue.poll();
            list.add(pNode);
            if (pNode.getLeft() != null) {
                queue.add(pNode.getLeft());
            }
            if (pNode.getRight() != null) {
                queue.add(pNode.getRight());
            }
        }
        return list;
    }

    //编码
    public static<T> void encoding(Node<T> node,String str)
    {
        if(node==null)
        {
            return;
        }
        if(node.getLeft()==null&&node.getRight()==null)
        {
            //            System.out.println(node.getData()+":"+str);
            map.put(node.getData(),str);
            return;
        }
        encoding(node.getLeft(), str+"0");
        encoding(node.getRight(), str+"1");
    }
}

//二叉树结点
class Node <T> implements Comparable<Node<T>>{

    private T data;
    private int weight;
    private Node<T> left;
    private Node<T> right;

    public Node(T data, int weight) {
        this.data = data;
        this.weight = weight;
    }

    @Override
    public String toString() {
        // TODO Auto-generated method stub
        return "data:" + this.data + ",weight:" + this.weight + ";   ";
    }

    @Override
    public int compareTo(Node<T> o) {
        // TODO Auto-generated method stub
        if (o.weight > this.weight) {
            return 1;
        } else if (o.weight < this.weight) {
            return -1;
        }
        return 0;
    }

    public T getData() {
        return data;
    }

    public void setData(T data) {
        this.data = data;
    }

    public int getWeight() {
        return weight;
    }

    public void setWeight(int weight) {
        this.weight = weight;
    }

    public Node<T> getLeft() {
        return left;
    }

    public void setLeft(Node<T> left) {
        this.left = left;
    }

    public Node<T> getRight() {
        return right;
    }

    public void setRight(Node<T> right) {
        this.right = right;
    }
}

测试：

package HuffmanTree;

import java.util.ArrayList;
import java.util.Iterator;
import java.util.List;
import java.util.Map;
import java.util.Map.Entry;

public class App {

    public static void main(String[] args) {
        // TODO Auto-generated method stub
        List<Node<String>> nodes = new ArrayList<Node<String>>();
        nodes.add(new Node<String>("A", 27));
        nodes.add(new Node<String>("B", 8));
        nodes.add(new Node<String>("C", 15));
        nodes.add(new Node<String>("D", 15));
        nodes.add(new Node<String>("E", 30));
        nodes.add(new Node<String>("F", 5));
        Node<String> root = HuffmanTree.createTree(nodes);
        HuffmanTree<String> h=new HuffmanTree<String>();
        h.encoding(root, "");
                Iterator<Entry<Object, String>> entries = HuffmanTree.map.entrySet().iterator();
                String string="";
                while (entries.hasNext()) {
                  Entry<Object, String> entry = entries.next();
                  string+=entry.getValue();
                  System.out.println("Key = " + entry.getKey() + ", Value = " + entry.getValue());
                }
                System.out.println("ABCDEF的编码为:"+string);
    }
}

结果：

Key = A, Value = 01
Key = B, Value = 1001
Key = C, Value = 00
Key = D, Value = 101
Key = E, Value = 11
Key = F, Value = 1000
ABCDEF的编码为:01100100101111000