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1 哈夫曼编码简史#xff08;Huffman code#xff09;
1951年#xff0c;哈夫曼和他在MIT信息论的同学需要选择是完成学期报告还是期末考试。导师Robert M. Fano给他们的学期报告的题目是#xff0c;寻找最有效的二进制编码。由于无法证明哪个已有编码是… David A. Huffman
1 哈夫曼编码简史Huffman code
1951年哈夫曼和他在MIT信息论的同学需要选择是完成学期报告还是期末考试。导师Robert M. Fano给他们的学期报告的题目是寻找最有效的二进制编码。由于无法证明哪个已有编码是最有效的哈夫曼放弃对已有编码的研究转向新的探索最终发现了基于有序频率二叉树编码的想法并很快证明了这个方法是最有效的。由于这个算法学生终于青出于蓝超过了他那曾经和信息论创立者香农共同研究过类似编码的导师。哈夫曼使用自底向上的方法构建二叉树避免了次优算法Shannon-Fano编码的最大弊端──自顶向下构建树。 1952年David A. Huffman在麻省理工攻读博士时发表了《一种构建极小多余编码的方法》一文它一般就叫做Huffman编码。A Method for the Construction of Minimum-Redundancy Codeshttps://www.ias.ac.in/article/fulltext/reso/011/02/0091-0099 Huffman在1952年根据香农Shannon在1948年和范若Fano在1949年阐述的这种编码思想提出了一种不定长编码的方法也称霍夫曼Huffman编码。霍夫曼编码的基本方法是先对图像数据扫描一遍计算出各种像素出现的概率按概率的大小指定不同长度的唯一码字由此得到一张该图像的霍夫曼码表。编码后的图像数据记录的是每个像素的码字而码字与实际像素值的对应关系记录在码表中。 2 赫夫曼编码
赫夫曼编码是可变字长编码(VLC)的一种。 Huffman于1952年提出一种编码方法该方法完全依据字符出现概率来构造异字头的平均长 度最短的码字有时称之为最佳编码一般就称Huffman编码。下面引证一个定理该定理保证了按字符出现概率分配码长可使平均码长最短。 3 源程序
using System; using System.IO; using System.Text; using System.Linq; using System.Collections; using System.Collections.Generic;
namespace Legalsoft.Truffer.Algorithm { /// summary /// 哈夫曼编码的压缩与解压缩 /// /summary public class HuffmanCompressor { private HuffmanNode oRootHuffmanNode { get; set; } null; private ListHuffmanNode oValueHuffmanNodes { get; set; } null; private ListHuffmanNode BuildBinaryTree(string Value) { ListHuffmanNode oHuffmanNodes GetInitialNodeList(); Value.ToList().ForEach(m oHuffmanNodes[m].Weight); oHuffmanNodes oHuffmanNodes .Where(m (m.Weight 0)) .OrderBy(m (m.Weight)) .ThenBy(m (m.Value)) .ToList(); oHuffmanNodes UpdateNodeParents(oHuffmanNodes); oRootHuffmanNode oHuffmanNodes[0]; oHuffmanNodes.Clear(); SortNodes(oRootHuffmanNode, oHuffmanNodes); return oHuffmanNodes; } public void Compress(string FileName) { FileInfo oFileInfo new FileInfo(FileName); if (oFileInfo.Exists true) { string sFileContents ; using (StreamReader oStreamReader new StreamReader(File.OpenRead(FileName))) { sFileContents oStreamReader.ReadToEnd(); } ListHuffmanNode oHuffmanNodes BuildBinaryTree(sFileContents); oValueHuffmanNodes oHuffmanNodes .Where(m (m.Value.HasValue true)) .OrderBy(m (m.BinaryWord)) .ToList(); Dictionarychar, string oCharToBinaryWordDictionary new Dictionarychar, string(); foreach (HuffmanNode oHuffmanNode in oValueHuffmanNodes) { oCharToBinaryWordDictionary.Add(oHuffmanNode.Value.Value, oHuffmanNode.BinaryWord); } StringBuilder oStringBuilder new StringBuilder(); Listbyte oByteList new Listbyte(); for (int i 0; i sFileContents.Length; i) { string sWord ; oStringBuilder.Append(oCharToBinaryWordDictionary[sFileContents[i]]); while (oStringBuilder.Length 8) { sWord oStringBuilder.ToString().Substring(0, 8); oStringBuilder.Remove(0, sWord.Length); } if (String.IsNullOrEmpty(sWord) false) { oByteList.Add(Convert.ToByte(sWord, 2)); } } if (oStringBuilder.Length 0) { string sWord oStringBuilder.ToString(); if (String.IsNullOrEmpty(sWord) false) { oByteList.Add(Convert.ToByte(sWord, 2)); } } string sCompressedFileName Path.Combine(oFileInfo.Directory.FullName, String.Format({0}.compressed, oFileInfo.Name.Replace(oFileInfo.Extension, ))); if (File.Exists(sCompressedFileName) true) { File.Delete(sCompressedFileName); } using (FileStream oFileStream File.OpenWrite(sCompressedFileName)) { oFileStream.Write(oByteList.ToArray(), 0, oByteList.Count); } } } public void Decompress(string FileName) { FileInfo oFileInfo new FileInfo(FileName); if (oFileInfo.Exists true) { string sCompressedFileName String.Format({0}.compressed, oFileInfo.FullName.Replace(oFileInfo.Extension, )); byte[] oBuffer null; using (FileStream oFileStream File.OpenRead(sCompressedFileName)) { oBuffer new byte[oFileStream.Length]; oFileStream.Read(oBuffer, 0, oBuffer.Length); } HuffmanNode oZeroHuffmanNode oRootHuffmanNode; while (oZeroHuffmanNode.Left ! null) { oZeroHuffmanNode oZeroHuffmanNode.Left; } HuffmanNode oCurrentHuffmanNode null; StringBuilder oStringBuilder new StringBuilder(); for (int i 0; i oBuffer.Length; i) { string sBinaryWord ; byte oByte oBuffer[i]; if (oByte 0) { sBinaryWord oZeroHuffmanNode.BinaryWord; } else { sBinaryWord Convert.ToString(oByte, 2); } if ((sBinaryWord.Length 8) (i (oBuffer.Length - 1))) { StringBuilder oBinaryStringBuilder new StringBuilder(sBinaryWord); while (oBinaryStringBuilder.Length 8) { oBinaryStringBuilder.Insert(0, 0); } sBinaryWord oBinaryStringBuilder.ToString(); } for (int j 0; j sBinaryWord.Length; j) { char cValue sBinaryWord[j]; if (oCurrentHuffmanNode null) { oCurrentHuffmanNode oRootHuffmanNode; } if (cValue 0) { oCurrentHuffmanNode oCurrentHuffmanNode.Left; } else { oCurrentHuffmanNode oCurrentHuffmanNode.Right; } if ((oCurrentHuffmanNode.Left null) (oCurrentHuffmanNode.Right null)) { oStringBuilder.Append(oCurrentHuffmanNode.Value.Value); oCurrentHuffmanNode null; } } } string sUncompressedFileName Path.Combine(oFileInfo.Directory.FullName, String.Format({0}.uncompressed, oFileInfo.Name.Replace(oFileInfo.Extension, ))); if (File.Exists(sUncompressedFileName) true) { File.Delete(sUncompressedFileName); } using (StreamWriter oStreamWriter new StreamWriter(File.OpenWrite(sUncompressedFileName))) { oStreamWriter.Write(oStringBuilder.ToString()); } } } private static ListHuffmanNode GetInitialNodeList() { ListHuffmanNode oGetInitialNodeList new ListHuffmanNode(); for (int i Char.MinValue; i Char.MaxValue; i) { oGetInitialNodeList.Add(new HuffmanNode((char)(i))); } return oGetInitialNodeList; } private static void SortNodes(HuffmanNode Node, ListHuffmanNode Nodes) { if (Nodes.Contains(Node) false) { Nodes.Add(Node); } if (Node.Left ! null) { SortNodes(Node.Left, Nodes); } if (Node.Right ! null) { SortNodes(Node.Right, Nodes); } } private static ListHuffmanNode UpdateNodeParents(ListHuffmanNode Nodes) { while (Nodes.Count 1) { int iOperations (Nodes.Count / 2); for (int iOperation 0, i 0, j 1; iOperation iOperations; iOperation, i 2, j 2) { if (j Nodes.Count) { HuffmanNode oParentHuffmanNode new HuffmanNode(Nodes[i], Nodes[j]); Nodes.Add(oParentHuffmanNode); Nodes[i] null; Nodes[j] null; } } Nodes Nodes .Where(m (m ! null)) .OrderBy(m (m.Weight)) .ToList(); } return Nodes; } } public class HuffmanNode { private string sBinaryWord { get; set; } ; private bool bIsLeftNode { get; set; } false; private bool bIsRightNode { get; set; } false; private HuffmanNode oLeft { get; set; } null; private HuffmanNode oParent { get; set; } null; private HuffmanNode oRight { get; set; } null; private char? cValue { get; set; } ; private int iWeight { get; set; } 0; public HuffmanNode() { } public HuffmanNode(char Value) { cValue Value; } public HuffmanNode(HuffmanNode Left, HuffmanNode Right) { oLeft Left; oLeft.oParent this; oLeft.bIsLeftNode true; oRight Right; oRight.oParent this; oRight.bIsRightNode true; iWeight (oLeft.Weight oRight.Weight); } public string BinaryWord { get { string sReturnValue ; if (String.IsNullOrEmpty(sBinaryWord) true) { StringBuilder oStringBuilder new StringBuilder(); HuffmanNode oHuffmanNode this; while (oHuffmanNode ! null) { if (oHuffmanNode.bIsLeftNode true) { oStringBuilder.Insert(0, 0); } if (oHuffmanNode.bIsRightNode true) { oStringBuilder.Insert(0, 1); } oHuffmanNode oHuffmanNode.oParent; } sReturnValue oStringBuilder.ToString(); sBinaryWord sReturnValue; } else { sReturnValue sBinaryWord; } return sReturnValue; } } public HuffmanNode Left { get { return oLeft; } } public HuffmanNode Parent { get { return oParent; } } public HuffmanNode Right { get { return oRight; } } public char? Value { get { return cValue; } } public int Weight { get { return iWeight; } set { iWeight value; } } public static int BinaryStringToInt32(string Value) { int iBinaryStringToInt32 0; for (int i (Value.Length - 1), j 0; i 0; i--, j) { iBinaryStringToInt32 ((Value[j] 0 ? 0 : 1) * (int)(Math.Pow(2, i))); } return iBinaryStringToInt32; } public override string ToString() { StringBuilder sb new StringBuilder(); if (cValue.HasValue true) { sb.AppendFormat({0} ({1}) - {2} ({3}), cValue.Value, iWeight, BinaryWord, BinaryStringToInt32(BinaryWord)); } else { if ((oLeft ! null) (oRight ! null)) { if ((oLeft.Value.HasValue true) (oRight.Value.HasValue true)) { sb.AppendFormat({0} {1} ({2}), oLeft.Value, oRight.Value, iWeight); } else { sb.AppendFormat({0}, {1} - ({2}), oLeft, oRight, iWeight); } } else { sb.Append(iWeight); } } return sb.ToString(); } } } 4 源代码
using System;
using System.IO;
using System.Text;
using System.Linq;
using System.Collections;
using System.Collections.Generic;namespace Legalsoft.Truffer.Algorithm
{/// summary/// 哈夫曼编码的压缩与解压缩/// /summarypublic class HuffmanCompressor{private HuffmanNode oRootHuffmanNode { get; set; } null;private ListHuffmanNode oValueHuffmanNodes { get; set; } null;private ListHuffmanNode BuildBinaryTree(string Value){ListHuffmanNode oHuffmanNodes GetInitialNodeList();Value.ToList().ForEach(m oHuffmanNodes[m].Weight);oHuffmanNodes oHuffmanNodes.Where(m (m.Weight 0)).OrderBy(m (m.Weight)).ThenBy(m (m.Value)).ToList();oHuffmanNodes UpdateNodeParents(oHuffmanNodes);oRootHuffmanNode oHuffmanNodes[0];oHuffmanNodes.Clear();SortNodes(oRootHuffmanNode, oHuffmanNodes);return oHuffmanNodes;}public void Compress(string FileName){FileInfo oFileInfo new FileInfo(FileName);if (oFileInfo.Exists true){string sFileContents ;using (StreamReader oStreamReader new StreamReader(File.OpenRead(FileName))){sFileContents oStreamReader.ReadToEnd();}ListHuffmanNode oHuffmanNodes BuildBinaryTree(sFileContents);oValueHuffmanNodes oHuffmanNodes.Where(m (m.Value.HasValue true)).OrderBy(m (m.BinaryWord)).ToList();Dictionarychar, string oCharToBinaryWordDictionary new Dictionarychar, string();foreach (HuffmanNode oHuffmanNode in oValueHuffmanNodes){oCharToBinaryWordDictionary.Add(oHuffmanNode.Value.Value, oHuffmanNode.BinaryWord);}StringBuilder oStringBuilder new StringBuilder();Listbyte oByteList new Listbyte();for (int i 0; i sFileContents.Length; i){string sWord ;oStringBuilder.Append(oCharToBinaryWordDictionary[sFileContents[i]]);while (oStringBuilder.Length 8){sWord oStringBuilder.ToString().Substring(0, 8);oStringBuilder.Remove(0, sWord.Length);}if (String.IsNullOrEmpty(sWord) false){oByteList.Add(Convert.ToByte(sWord, 2));}}if (oStringBuilder.Length 0){string sWord oStringBuilder.ToString();if (String.IsNullOrEmpty(sWord) false){oByteList.Add(Convert.ToByte(sWord, 2));}}string sCompressedFileName Path.Combine(oFileInfo.Directory.FullName, String.Format({0}.compressed, oFileInfo.Name.Replace(oFileInfo.Extension, )));if (File.Exists(sCompressedFileName) true){File.Delete(sCompressedFileName);}using (FileStream oFileStream File.OpenWrite(sCompressedFileName)){oFileStream.Write(oByteList.ToArray(), 0, oByteList.Count);}}}public void Decompress(string FileName){FileInfo oFileInfo new FileInfo(FileName);if (oFileInfo.Exists true){string sCompressedFileName String.Format({0}.compressed, oFileInfo.FullName.Replace(oFileInfo.Extension, ));byte[] oBuffer null;using (FileStream oFileStream File.OpenRead(sCompressedFileName)){oBuffer new byte[oFileStream.Length];oFileStream.Read(oBuffer, 0, oBuffer.Length);}HuffmanNode oZeroHuffmanNode oRootHuffmanNode;while (oZeroHuffmanNode.Left ! null){oZeroHuffmanNode oZeroHuffmanNode.Left;}HuffmanNode oCurrentHuffmanNode null;StringBuilder oStringBuilder new StringBuilder();for (int i 0; i oBuffer.Length; i){string sBinaryWord ;byte oByte oBuffer[i];if (oByte 0){sBinaryWord oZeroHuffmanNode.BinaryWord;}else{sBinaryWord Convert.ToString(oByte, 2);}if ((sBinaryWord.Length 8) (i (oBuffer.Length - 1))){StringBuilder oBinaryStringBuilder new StringBuilder(sBinaryWord);while (oBinaryStringBuilder.Length 8){oBinaryStringBuilder.Insert(0, 0);}sBinaryWord oBinaryStringBuilder.ToString();}for (int j 0; j sBinaryWord.Length; j){char cValue sBinaryWord[j];if (oCurrentHuffmanNode null){oCurrentHuffmanNode oRootHuffmanNode;}if (cValue 0){oCurrentHuffmanNode oCurrentHuffmanNode.Left;}else{oCurrentHuffmanNode oCurrentHuffmanNode.Right;}if ((oCurrentHuffmanNode.Left null) (oCurrentHuffmanNode.Right null)){oStringBuilder.Append(oCurrentHuffmanNode.Value.Value);oCurrentHuffmanNode null;}}}string sUncompressedFileName Path.Combine(oFileInfo.Directory.FullName, String.Format({0}.uncompressed, oFileInfo.Name.Replace(oFileInfo.Extension, )));if (File.Exists(sUncompressedFileName) true){File.Delete(sUncompressedFileName);}using (StreamWriter oStreamWriter new StreamWriter(File.OpenWrite(sUncompressedFileName))){oStreamWriter.Write(oStringBuilder.ToString());}}}private static ListHuffmanNode GetInitialNodeList(){ListHuffmanNode oGetInitialNodeList new ListHuffmanNode();for (int i Char.MinValue; i Char.MaxValue; i){oGetInitialNodeList.Add(new HuffmanNode((char)(i)));}return oGetInitialNodeList;}private static void SortNodes(HuffmanNode Node, ListHuffmanNode Nodes){if (Nodes.Contains(Node) false){Nodes.Add(Node);}if (Node.Left ! null){SortNodes(Node.Left, Nodes);}if (Node.Right ! null){SortNodes(Node.Right, Nodes);}}private static ListHuffmanNode UpdateNodeParents(ListHuffmanNode Nodes){while (Nodes.Count 1){int iOperations (Nodes.Count / 2);for (int iOperation 0, i 0, j 1; iOperation iOperations; iOperation, i 2, j 2){if (j Nodes.Count){HuffmanNode oParentHuffmanNode new HuffmanNode(Nodes[i], Nodes[j]);Nodes.Add(oParentHuffmanNode);Nodes[i] null;Nodes[j] null;}}Nodes Nodes.Where(m (m ! null)).OrderBy(m (m.Weight)).ToList();}return Nodes;}}public class HuffmanNode{private string sBinaryWord { get; set; } ;private bool bIsLeftNode { get; set; } false;private bool bIsRightNode { get; set; } false;private HuffmanNode oLeft { get; set; } null;private HuffmanNode oParent { get; set; } null;private HuffmanNode oRight { get; set; } null;private char? cValue { get; set; } ;private int iWeight { get; set; } 0;public HuffmanNode(){}public HuffmanNode(char Value){cValue Value;}public HuffmanNode(HuffmanNode Left, HuffmanNode Right){oLeft Left;oLeft.oParent this;oLeft.bIsLeftNode true;oRight Right;oRight.oParent this;oRight.bIsRightNode true;iWeight (oLeft.Weight oRight.Weight);}public string BinaryWord{get{string sReturnValue ;if (String.IsNullOrEmpty(sBinaryWord) true){StringBuilder oStringBuilder new StringBuilder();HuffmanNode oHuffmanNode this;while (oHuffmanNode ! null){if (oHuffmanNode.bIsLeftNode true){oStringBuilder.Insert(0, 0);}if (oHuffmanNode.bIsRightNode true){oStringBuilder.Insert(0, 1);}oHuffmanNode oHuffmanNode.oParent;}sReturnValue oStringBuilder.ToString();sBinaryWord sReturnValue;}else{sReturnValue sBinaryWord;}return sReturnValue;}}public HuffmanNode Left{get{return oLeft;}}public HuffmanNode Parent{get{return oParent;}}public HuffmanNode Right{get{return oRight;}}public char? Value{get{return cValue;}}public int Weight{get{return iWeight;}set{iWeight value;}}public static int BinaryStringToInt32(string Value){int iBinaryStringToInt32 0;for (int i (Value.Length - 1), j 0; i 0; i--, j){iBinaryStringToInt32 ((Value[j] 0 ? 0 : 1) * (int)(Math.Pow(2, i)));}return iBinaryStringToInt32;}public override string ToString(){StringBuilder sb new StringBuilder();if (cValue.HasValue true){sb.AppendFormat({0} ({1}) - {2} ({3}), cValue.Value, iWeight, BinaryWord, BinaryStringToInt32(BinaryWord));}else{if ((oLeft ! null) (oRight ! null)){if ((oLeft.Value.HasValue true) (oRight.Value.HasValue true)){sb.AppendFormat({0} {1} ({2}), oLeft.Value, oRight.Value, iWeight);}else{sb.AppendFormat({0}, {1} - ({2}), oLeft, oRight, iWeight);}}else{sb.Append(iWeight);}}return sb.ToString();}}
}
