Huffman编码介绍
Huffman编码 处理的是字符以及字符对应的二进制的编码配对问题,分为编码和解码,目的是压缩字符对应的二进制数据长度。我们知道字符存贮和传输的时候都是二进制的(计算机只认识0/1),那么就有字符与二进制之间的mapping关系。字符属于字符集(Charset), 字符需要通过编码(encode)为二进制进行存贮和传输,显示的时候需要解码(decode)回 字符,字符集与编码方法是一对多关系(Unicode可以用UTF-8,UTF-16等编码)。理解了字符集,编码以及解码,满天飞的乱码问题也就游刃而 解了。以英文字母小写a为例, ASCII编码中,十进制为97,二进制为01100001。ASCII的每一个字符都用8个Bit(1Byte)编码,假如有1000个字符要传输,那 么就要传输8000个Bit。问题来了,英文中字母e的使用频率为12.702%,而z为0.074%,前者是后者的100多倍,但是确使用相同位数的二 进制。可以做得更好,方法就是可变长度编码,指导原则就是频率高的用较短的位数编码,频率低的用较长位数编码。Huffman编码算法就是处理这样的问 题。
Huffman编码Java实现
Huffman编码算法主要用到的数据结构是完全二叉树(full binary tree)和优先级队列。后者用的是java.util.PriorityQueue,前者自己实现(都为内部类),代码如下:
package huffman;
/**
* 构建完全二叉树(full binary tree)
* @author fh
*
*/
public class Tree {
private Node root;
public Node getRoot() {
return root;
}
public void setRoot(Node root) {
this.root = root;
}
static class Node implements Comparable<Node> {
private String val = "";
private int frequence = 0;
private Node parent;
private Node leftNode;
private Node rightNode;
@Override
public int compareTo(Node n) {
return this.frequence - n.frequence;
}
//是否是叶子节点
public boolean isleaf(){
return this.leftNode==null&&this.rightNode==null;
}
public boolean isRoot(){
return this.parent==null;
}
public boolean isLeftChild(){
return this.parent!=null&&this==this.parent.leftNode;
}
public String getVal() {
return val;
}
public void setVal(String val) {
this.val = val;
}
public int getFrequence() {
return frequence;
}
public void setFrequence(int frequence) {
this.frequence = frequence;
}
public Node getParent() {
return parent;
}
public void setParent(Node parent) {
this.parent = parent;
}
public Node getLeftNode() {
return leftNode;
}
public void setLeftNode(Node leftNode) {
this.leftNode = leftNode;
}
public Node getRightNode() {
return rightNode;
}
public void setRightNode(Node rightNode) {
this.rightNode = rightNode;
}
}
}
package huffman;
import huffman.Tree.Node;
import java.util.ArrayList;
import java.util.HashMap;
import java.util.List;
import java.util.Map;
import java.util.concurrent.PriorityBlockingQueue;
public class Huffman {
public static void main(String[] args) {
String oriStr = "Huffman codes compress data very effectively: savings of 20% to 90% are typical, "
+ "depending on the characteristics of the data being compressed. 中华崛起";
// 测试编码
Map<Character, Integer> statistics = collect(oriStr.toCharArray());
String encodedBinariStr = encode(oriStr, statistics);
System.out.println(encodedBinariStr);
String decodedBinariStr = decode(encodedBinariStr, statistics);
System.out.println(decodedBinariStr);
}
/**
* 1,统计数据:统计词频
*
* @param charArray
* @return
*/
static Map<Character, Integer> collect(char[] charArray) {
Map<Character, Integer> map = new HashMap<Character, Integer>();
for (int i = 0; i < charArray.length; i++) {
Character character = new Character(charArray[i]);
if (map.containsKey(character)) {
map.put(character, map.get(character) + 1);
} else {
map.put(character, 1);
}
}
return map;
}
/**
* 2,构建树:完全二叉树
*
* 构建树是Huffman编码算法的核心步骤。思想是把所有的字符挂到一颗完全二叉树的叶子节点,任何一个非页子
* 节点的左节点出现频率不大于右节点。算法为把统计信息转为Node存放到一个优先级队列里面,每一次从队列里面弹出两个最小频率的节点,构建一个新的父
* Node(非叶子节点),
* 字符内容刚弹出来的两个节点字符内容之和,频率也是它们的和,最开始的弹出来的作为左子节点,后面一个作为右子节点,并且把刚构建的父节点放到队列里面。
* 重复以上的动作N-1次,N为不同字符的个数(每一次队列里面个数减1)。结束以上步骤,队列里面剩一个节点,弹出作为树的根节点。
*/
static Tree buildTree(Map<Character, Integer> collect, List<Node> list) {
Tree tree = new Tree();
// 根据Node的构造函数及compartor判断优先级
PriorityBlockingQueue<Node> priorityBlockingQueue = new PriorityBlockingQueue<>();
Character[] keys = collect.keySet().toArray(new Character[0]);
// 转换成节点,存储到队列、链表中
for (Character c : keys) {
Node node = new Node();
node.setVal(c.toString());
node.setFrequence(collect.get(c));
priorityBlockingQueue.offer(node);
list.add(node);
}
// 构建二叉树
while (priorityBlockingQueue.size() != 1) {
Node node1 = priorityBlockingQueue.poll();
Node node2 = priorityBlockingQueue.poll();
Node parentNode = new Node();
parentNode.setVal(node1.getVal() + node2.getVal());
parentNode
.setFrequence(node1.getFrequence() + node2.getFrequence());
parentNode.setLeftNode(node1);
parentNode.setRightNode(node2);
node1.setParent(parentNode);
node2.setParent(parentNode);
priorityBlockingQueue.offer(parentNode);
}
tree.setRoot(priorityBlockingQueue.poll());
return tree;
}
/**
* 编码 :
*
* 某个字符对应的编码为,从该字符所在的叶子节点向上搜索,如果该字符节点是父节点的左节点,编码字符之前加0,反之如果是右节点,加1,直到根节点。
* 只要获取了字符和二进制码之间的mapping关系,编码就非常简单.
*
* 给出字符串,输出二进制码010101010
*/
static String encode(String input, Map<Character, Integer> collect) {
if (input == null || input.length() == 0) {
return "";
}
StringBuilder out = new StringBuilder();
// 预处理
char[] chars = input.toCharArray();
List<Node> list = new ArrayList<>();
Tree tree = buildTree(collect, list);
// 生成密码本:a=0101,b=0011
Map<Character, String> encodInfo = buildEncodingInfo(list);
// 比对
for (char c : chars) {
out.append(encodInfo.get(c));
}
return out.toString();
}
/**
* 生成密码本:a=0101,b=0011
*
* @param list
* @return
*/
private static Map<Character, String> buildEncodingInfo(List<Node> list) {
Map<Character, String> map = new HashMap<Character, String>();
for (Node n : list) {
Character character = n.getVal().toCharArray()[0];
StringBuilder stringBuilder = new StringBuilder();
do {
if (n.isLeftChild()) {
stringBuilder.append("0");
} else {
stringBuilder.append("1");
}
n = n.getParent();
} while (n.getParent() != null);
map.put(character, stringBuilder.reverse().toString());
}
return map;
}
/**
* 解码
* 因为Huffman编码算法能够保证任何的二进制码都不会是另外一个码的前缀,解码非常简单,依次取出二进制的每一位,从树根向下搜索,1向右,0向左
* ,到了叶子节点(命中),退回根节点继续重复以上动作。
*/
static String decode(String input, Map<Character, Integer> collect) {
if (input == null || input.equals("")) {
return "";
}
StringBuilder outBuilder = new StringBuilder();
// 预处理
char[] chars = input.toCharArray();
List<Node> list = new ArrayList<>();
Tree tree = buildTree(collect, list);
int i = 0;
while (i < chars.length) {
Node root = tree.getRoot();
while (!root.isleaf()) {
if (chars[i] == '0') {
root = root.getLeftNode();
} else {
root = root.getRightNode();
}
++i;
}
outBuilder.append(root.getVal());
}
return outBuilder.toString();
}
}