哈夫曼树---贪婪法

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哈夫曼算法

第一步：初始化n个单节点的树，并为它们标上字母表中的字符。把每个字符的概率记在树的根中，用来指出树的权重（更一般地来说，树的权重等于树中所有叶子节点的概率之和）

第二步：重复下面的步骤，直到只剩一棵单独的树。找到两棵权重最小的树，把它们作为新树中的左右子树，并把其权重之和作为新的权重记录在新树的根中。

上面的算法所构造的树称之为哈夫曼树。

哈夫曼节点代码：

public class Node<T> implements Comparable<Node<T>> {private T data;private double weight;private Node<T> left;private Node<T> right;public Node(T data, double weight){this.data = data;this.weight = weight;}public T getData() {return data;}public void setData(T data) {this.data = data;}public double getWeight() {return weight;}public void setWeight(double 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;}@Overridepublic String toString(){return "data:"+this.data+";weight:"+this.weight;}@Overridepublic int compareTo(Node<T> other) {if(other.getWeight() > this.getWeight()){return 1;}if(other.getWeight() < this.getWeight()){return -1;}return 0;}}

构造哈夫曼树和遍历哈夫曼树代码：

import java.util.ArrayDeque;import java.util.ArrayList;import java.util.Collections;import java.util.List;import java.util.Queue;public class HuffmanTree<T> {public static <T> Node<T> createTree(List<Node<T>> nodes){while(nodes.size() > 1){//假如用优先队列的话，排序算法的复杂度就可以变成插入优先队列的时间复杂度lognCollections.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);}public static <T> List<Node<T>> breadth(Node<T> root){List<Node<T>> list = new ArrayList<Node<T>>();Queue<Node<T>> queue = new ArrayDeque<Node<T>>();if(root != null){queue.offer(root);}while(!queue.isEmpty()){list.add(queue.peek());Node<T> node = queue.poll();if(node.getLeft() != null){queue.offer(node.getLeft());}if(node.getRight() != null){queue.offer(node.getRight());}}return list;}public static void main(String[] args) {// TODO Auto-generated method stubList<Node<String>> list = new ArrayList<Node<String>>();list.add(new Node<String>("a",7));list.add(new Node<String>("b",5));list.add(new Node<String>("c",4));list.add(new Node<String>("d",2));Node<String> root = HuffmanTree.createTree(list);System.out.println(HuffmanTree.breadth(root));//System.out.println(list);}}

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