详解Huffman编码算法之Java实现

详解Huffman编码算法之Java实现

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:

static class Tree {

private Node root;

public Node getRoot() {

return root;

}

public void setRoot(Node root) {

this.root = root;

}

}

static class Node implements Comparable {

private String chars = "";

private int frequence = 0;

private Node parent;

private Node leftNode;

private Node rightNode;

@Override

public int compareTo(Node n) {

return frequence - n.frequence;

}

public boolean isLeaf() {

return chars.length() == 1;

}

public boolean isRoot() {

return parent == null;

}

public boolean isLeftChild() {

return parent != nuhttp://ll && this == parent.leftNode;

}

public int getFrequence() {

return frequence;

}

public void setFrequence(int frequence) {

this.frequence = frequence;

}

public String getChars() {

return chars;

}

public void setChars(String chars) {

this.chars = chars;

}

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;

}

}

统计数据

既然要按频率来安排编码表，那么首先当然得获得频率的统计信息。我实现了一个方法处理这样的问题。如果已经有统计信息，那么转为Map即可。如果你得到的信息是百分比，乘以100或1000，或10000。总是可以转为整数。比如12.702%乘以1000为12702，Huffman编码只关心大小问题。统计方法实现如下：

public static Map statistics(char[] charArray) {

Map map = new HashMap();

for (char c : charArray) {

Character character = new Character(c);

if (map.containsKey(character)) {

map.put(character, map.get(character) + 1);

} else {

map.put(character, 1);

}

}

return map;

}

构建树

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。代码如下:

private static Tree buildTree(Map statistics,

List leafs) {

Character[] keys = statistics.keySet().toArray(new Character[0]);

PriorityQueue priorityQueue = new PriorityQueue();

for (Character character : keys) {

Node node = new Node();

node.chars = character.toString();

node.frequence = statistics.get(character);

priorityzpBDAQueue.add(node);

leafs.add(node);

}

int size = priorityQueue.size();

for (int i = 1; i <= size - 1; i++) {

Node node1 = priorityQueue.poll();

Node node2 = priorityQueue.poll();

Node sumNode = new Node();

sumNode.chars = node1.chars + node2.chars;

sumNode.frequence = node1.frequence + node2.frequence;

sumNode.leftNode = node1;

sumNode.rightNode = node2;

node1.parent = sumNode;

node2.parent = sumNode;

priorityQueue.add(sumNode);

}

Tree tree = new Tree();

tree.root = priorityQueue.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。代码如下:

public static String encode(String originalStr,

Map statistics) {

if (originalStr == null || originalStr.equals("")) {

return "";

}

char[] charArray = originalStr.toCharArray();

List leafNodes = new ArrayList();

buildTree(statistics, leafNodes);

Map encodInfo = buildEncodingInfo(leafNodes);

StringBuffer buffer = new StringBuffer();

for (char c : charArray) {

Character character = new Character(c);

buffer.append(encodInfo.get(character));

}

return buffer.toString();

}

private static Map buildEncodingInfo(List leafNodes) {

Map codewords = new HashMap();

for (Node leafNode : leafNodes) {

Character character = new Character(leafNode.getChars().charAt(0));

String codeword = "";

Node currentNode = leafNode;

do {

if (currentNode.isLeftChild()) {

codeword = "0" + codeword;

} else {

codeword = "1" + codeword;

}

currentNode = currentNode.parent;

} while (currentNode.parent != null);

codewords.put(character, codeword);

}

return codewords;

}

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。代码如下:

public static String decode(String binaryStr,

Map statistics) {

if (binaryStr == null || binaryStr.equals("")) {

return "";

}

char[] binaryCharArray = binaryStr.toCharArray();

LinkedList binaryList = new LinkedList();

int size = binaryCharArray.length;

for (int i = 0; i < size; i++) {

binaryList.addLast(new Character(binaryCharArray[i]));

}

List leafNodes = new ArrayList();

Tree tree = buildTree(statistics, leafNodes);

StringBuffer buffer = new StringBuffer();

while (binaryList.size() > 0) {

Node node = tree.root;

do {

Character c = binaryList.removeFirst();

if (c.charValue() == '0') {

node = node.leftNode;

} else {

node = node.rightNode;

}

} while (!node.isLeaf());

buffer.append(node.chars);

}

return buffer.toString();

}

测试以及比较

以下测试Huffman编码的正确性(先编码，后解码，包括中文)，以及Huffman编码与常见的字符编码的二进制字符串比较。代码如下:

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";

Map statistics = statistics(oriStr.toCharArray());

String encodedBinariStr = encode(oriStr, statistics);

String decodedStr = decode(encodedBinariStr, statistics);

System.out.println("Original sstring: " + oriStr);

System.out.println("Huffman encoed binary string: " + encodedBinariStr);

System.out.println("decoded string from binariy string: " + decodedStr);

System.out.println("binary string of UTF-8: "

+ getStringOfByte(oriStr, Charset.forName("UTF-8")));

System.out.println("binary string of UTF-16: "

+ getStringOfByte(oriStr, Charset.forName("UTF-16")));

System.out.println("binary string of US-ASCII: "

+ getStringOfByte(oriStr, Charset.forName("US-ASCII")));

System.out.println("binary string of GB2312: "

+ getStringOfByte(oriStr, Charset.forName("GB2312")));

}

public static String getStringOfByte(String str, Charset charset) {

if (str == null || str.equals("")) {

return "";

}

byte[] byteArray = str.getBytes(charset);

int size = byteArray.length;

StringBuffer buffer = new Shttp://tringBuffer();

for (int i = 0; i < size; i++) {

byte temp = byteArray[i];

buffer.append(getStringOfByte(temp));

}

return buffer.toString();

}

public static String getStringOfByte(byte b) {

StringBufzpBDAfer buffer = new StringBuffer();

for (int i = 7; i >= 0; i--) {

byte temp = (byte) ((b >> i) & 0x1);

buffer.append(String.valueOf(temp));

}

return buffer.toString();

}

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