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;
@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 != 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();
}