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<Node> {private String chars = "";private int frequence = 0;private Node parent;private Node leftNode;private Node rightNode;@Overridepublic 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 != null && 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<Character,Integer>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<Character, Integer> statistics(char[] charArray) {Map<Character, Integer> map = new HashMap<Character, Integer>();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<Character, Integer> statistics,List<Node> leafs) {Character[] keys = statistics.keySet().toArray(new Character[0]);PriorityQueue<Node> priorityQueue = new PriorityQueue<Node>();for (Character character : keys) {Node node = new Node();node.chars = character.toString();node.frequence = statistics.get(character);priorityQueue.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<Character, Integer> statistics) {if (originalStr == null || originalStr.equals("")) {return "";}char[] charArray = originalStr.toCharArray();List<Node> leafNodes = new ArrayList<Node>();buildTree(statistics, leafNodes);Map<Character, String> 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<Character, String> buildEncodingInfo(List<Node> leafNodes) {Map<Character, String> codewords = new HashMap<Character, String>();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<Character, Integer> statistics) {if (binaryStr == null || binaryStr.equals("")) {return "";}char[] binaryCharArray = binaryStr.toCharArray();LinkedList<Character> binaryList = new LinkedList<Character>();int size = binaryCharArray.length;for (int i = 0; i < size; i++) {binaryList.addLast(new Character(binaryCharArray[i]));}List<Node> leafNodes = new ArrayList<Node>();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<Character, Integer> 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 StringBuffer();for (int i = 0; i < size; i++) {byte temp = byteArray[i];buffer.append(getStringOfByte(temp));}return buffer.toString();}public static String getStringOfByte(byte b) {StringBuffer buffer = new StringBuffer();for (int i = 7; i >= 0; i--) {byte temp = (byte) ((b >> i) & 0x1);buffer.append(String.valueOf(temp));}return buffer.toString();}

参考链接

维基百科-霍夫曼编码
维基百科-字母频率