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詳解Huffman編碼算法之Java實(shí)現(xiàn)

更新時(shí)間：2016年12月15日 09:17:36 作者：kimy

Huffman編碼是一種編碼方式,常用于無損壓縮。本文只介紹用Java語言來實(shí)現(xiàn)該編碼方式的算法和數(shù)據(jù)結(jié)構(gòu)。有興趣的可以了解一下。

Huffman編碼介紹

Huffman編碼處理的是字符以及字符對(duì)應(yīng)的二進(jìn)制的編碼配對(duì)問題，分為編碼和解碼，目的是壓縮字符對(duì)應(yīng)的二進(jìn)制數(shù)據(jù)長(zhǎng)度。我們知道字符存貯和傳輸?shù)臅r(shí)候都是二進(jìn)制的(計(jì)算機(jī)只認(rèn)識(shí)0/1)，那么就有字符與二進(jìn)制之間的mapping關(guān)系。字符屬于字符集(Charset), 字符需要通過編碼(encode)為二進(jìn)制進(jìn)行存貯和傳輸，顯示的時(shí)候需要解碼(decode)回字符，字符集與編碼方法是一對(duì)多關(guān)系(Unicode可以用UTF-8,UTF-16等編碼)。理解了字符集，編碼以及解碼，滿天飛的亂碼問題也就游刃而解了。以英文字母小寫a為例, ASCII編碼中，十進(jìn)制為97，二進(jìn)制為01100001。ASCII的每一個(gè)字符都用8個(gè)Bit(1Byte)編碼，假如有1000個(gè)字符要傳輸，那么就要傳輸8000個(gè)Bit。問題來了，英文中字母e的使用頻率為12.702%，而z為0.074%，前者是后者的100多倍，但是確使用相同位數(shù)的二進(jìn)制?？梢宰龅酶?，方法就是可變長(zhǎng)度編碼，指導(dǎo)原則就是頻率高的用較短的位數(shù)編碼，頻率低的用較長(zhǎng)位數(shù)編碼。Huffman編碼算法就是處理這樣的問題。

Huffman編碼Java實(shí)現(xiàn)

Huffman編碼算法主要用到的數(shù)據(jù)結(jié)構(gòu)是完全二叉樹(full binary tree)和優(yōu)先級(jí)隊(duì)列。后者用的是Java.util.PriorityQueue，前者自己實(shí)現(xiàn)(都為內(nèi)部類)，代碼如下:

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; 
    } 
  }

統(tǒng)計(jì)數(shù)據(jù)

既然要按頻率來安排編碼表，那么首先當(dāng)然得獲得頻率的統(tǒng)計(jì)信息。我實(shí)現(xiàn)了一個(gè)方法處理這樣的問題。如果已經(jīng)有統(tǒng)計(jì)信息，那么轉(zhuǎn)為Map<Character,Integer>即可。如果你得到的信息是百分比，乘以100或1000，或10000。總是可以轉(zhuǎn)為整數(shù)。比如12.702%乘以1000為12702，Huffman編碼只關(guān)心大小問題。統(tǒng)計(jì)方法實(shí)現(xiàn)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; 
  }

構(gòu)建樹

構(gòu)建樹是Huffman編碼算法的核心步驟。思想是把所有的字符掛到一顆完全二叉樹的葉子節(jié)點(diǎn)，任何一個(gè)非頁子節(jié)點(diǎn)的左節(jié)點(diǎn)出現(xiàn)頻率不大于右節(jié)點(diǎn)。算法為把統(tǒng)計(jì)信息轉(zhuǎn)為Node存放到一個(gè)優(yōu)先級(jí)隊(duì)列里面，每一次從隊(duì)列里面彈出兩個(gè)最小頻率的節(jié)點(diǎn)，構(gòu)建一個(gè)新的父Node(非葉子節(jié)點(diǎn)), 字符內(nèi)容剛彈出來的兩個(gè)節(jié)點(diǎn)字符內(nèi)容之和，頻率也是它們的和，最開始的彈出來的作為左子節(jié)點(diǎn)，后面一個(gè)作為右子節(jié)點(diǎn)，并且把剛構(gòu)建的父節(jié)點(diǎn)放到隊(duì)列里面。重復(fù)以上的動(dòng)作N-1次，N為不同字符的個(gè)數(shù)(每一次隊(duì)列里面?zhèn)€數(shù)減1)。結(jié)束以上步驟，隊(duì)列里面剩一個(gè)節(jié)點(diǎn)，彈出作為樹的根節(jié)點(diǎn)。代碼如下:

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; 
  }

編碼

某個(gè)字符對(duì)應(yīng)的編碼為，從該字符所在的葉子節(jié)點(diǎn)向上搜索，如果該字符節(jié)點(diǎn)是父節(jié)點(diǎn)的左節(jié)點(diǎn)，編碼字符之前加0，反之如果是右節(jié)點(diǎn)，加1，直到根節(jié)點(diǎn)。只要獲取了字符和二進(jìn)制碼之間的mapping關(guān)系，編碼就非常簡(jiǎn)單。代碼如下:

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; 
  }

解碼

因?yàn)镠uffman編碼算法能夠保證任何的二進(jìn)制碼都不會(huì)是另外一個(gè)碼的前綴，解碼非常簡(jiǎn)單，依次取出二進(jìn)制的每一位，從樹根向下搜索，1向右，0向左，到了葉子節(jié)點(diǎn)(命中)，退回根節(jié)點(diǎn)繼續(xù)重復(fù)以上動(dòng)作。代碼如下:

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(); 
  }

測(cè)試以及比較

以下測(cè)試Huffman編碼的正確性(先編碼，后解碼，包括中文)，以及Huffman編碼與常見的字符編碼的二進(jìn)制字符串比較。代碼如下:

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. 中華崛起"; 
    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(); 
  }

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