【数据压缩】Huffman原理与代码实现

转载请注明出处：http://blog.csdn.net/luoshixian099/article/details/50374452

勿在浮沙筑高台

  Huffman算法也是一种无损压缩算法，但与上篇文章LZW压缩算法不同，Huffman需要得到每种字符出现概率的先验知识。通过计算字符序列中每种字符出现的频率，为每种字符进行唯一的编码设计，使得频率高的字符占的位数短，而频率低的字符长，来达到压缩的目的。通常可以节省20%~90%的空间，很大程度上依赖数据的特性！Huffman编码是变长编码，即每种字符对应的编码长度不唯一。

前缀码：任何一个字符的编码都不是同一字符集中另一种字符编码的前缀。Huffman编码为最优前缀码，即压缩后数据量最小。

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 Huffman算法：

  1.统计字符序列的每种字符的频率，并为每种字符建立一个节点，节点权重为其频率；

  2.初始化最小优先队列中，把上述的结点全部插入到队列中；

  3.取出优先队列的前两种符号节点，并从优先队列中删除；

  4.新建一个父节点，并把上述两个节点作为其左右孩子节点，父节点的权值为左右节点之和；

  5.如果此时优先队列为空，则退出并返回父节点的指针！否则把父节点插入到优先队列中，重复步骤3；

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  通过上述建造的Huffman树，可以看到，每种字符结点都是叶子结点，编码方法：从根节点开始向左定义编码'0',向右定义为'1',遍历到叶子结点所得到的二值码串，即为此种字符的编码值。由于字符码字为前缀码，在译码过程中，每种字符可以参照Huffman树被唯一的译码出，但是前缀码的缺点是，错误具有传播功能，当有1位码字错误，此后的译码过程很可能都不正确；

 代码实现：

优先队列采用堆排序算法

/*CSDN 勿在浮沙筑高台 http://blog.csdn.net/luoshixian099数据压缩--Huffman编码 2015年12月21日 *///main.cpp#include <iostream>#include <vector>#include "compress.h"using namespace std;void ShowCode(PNode root, vector<char> &code);//显示编码void FreeTREE(PNode root);int main(){char A[] = "EEEEEEBBBBBBBAAADDDDDCCCCCCCCC";//原始数据UINT Length = sizeof(A)-1;Priority_Q queue(A, Length); //建立优先队列-堆排序//输入每组字符的频率for (UINT i = 0; i <= queue.Heap_Size;i++){cout << (char)(queue.table[i]->key) << "  Frequency:  " << queue.table[i]->Frequency << endl;}cout << "--------------------" << endl;PNode root = Build_Huffman_Tree(queue);//构建Huffman树vector<char> code;ShowCode(root, code); //显示编码数据FreeTREE(root);return 0;}void FreeTREE(PNode root)//释放内存{if ( root!=NULL){FreeTREE(root->_left);FreeTREE(root->_right);delete root;}}void ShowCode(PNode root,vector<char> &code){   if (root!=NULL)   {   if (root->_left == NULL && root->_right == NULL)  //叶子结点   {   cout << (char)(root->key) << "  code : " ;   for (UINT i = 0; i < code.size() ; i++)   {   cout << (int)code[i];   }   cout << endl;   return;   }   code.push_back(0);   ShowCode(root->_left,code);   code[code.size()-1] = 1;   ShowCode(root->_right,code);   code.resize(code.size()-1);   }}

/*compress.cpp*/#include "compress.h"Priority_Q::Priority_Q(char *A,int Length) //统计各种字符的频率{for (int i = 0; i < 256; i++){table[i] = new Node;}Heap_Size = 0;for (int i = 0; i < Length; i++)  //统计字符频率{bool Flag = true;for (int j = 0; j < Heap_Size; j++){           if ( table[j]->key == *(A+i) )           {   table[j]->Frequency = table[j]->Frequency + 1;   Flag = false;   break;           }}if (Flag)  //加入新的字符{table[Heap_Size]->key = *(A + i);table[Heap_Size]->Frequency = table[Heap_Size]->Frequency + 1;Heap_Size++;}}Heap_Size--;Build_Min_Heap(Heap_Size); //建立优先队列}void Priority_Q::Build_Min_Heap(UINT Length)//建立优先队列{for (int i = (int)(Length / 2); i >= 0; i--){Min_Heapify(i);}}void Priority_Q::Min_Heapify(UINT i){UINT Smaller = i;UINT Left = 2 * i + 1;UINT Right = 2 * i + 2;if (Left <= Heap_Size && table[Left]->Frequency < table[i]->Frequency)  //判断是否小于其孩子的值{Smaller = Left;}if (Right <= Heap_Size && table[Right]->Frequency < table[Smaller]->Frequency){Smaller = Right;}if (Smaller != i)                      //如果小于，就与其中最大的孩子调换位置{Swap(i, Smaller);Min_Heapify(Smaller);}}void Priority_Q::Swap(int x, int y) //交换两个元素的数据{PNode temp = table[x];table[x] = table[y];table[y] = temp;}PNode CopyNode(PNode _src, PNode _dst)//拷贝数据{_dst->Frequency = _src->Frequency;_dst->key = _src->key;_dst->_left = _src->_left;_dst->_right = _src->_right;return _dst;}PNode Priority_Q::Extract_Min()  //输出队列最前结点{if (Heap_Size == EMPTY)return NULL;if (Heap_Size == 0){Heap_Size = EMPTY;return table[0];}if (Heap_Size >= 0)                 {Swap(Heap_Size, 0);Heap_Size--;Min_Heapify(0);}return table[Heap_Size+1];}void Priority_Q::Insert(PNode pnode)//优先队列的插入{Heap_Size++;CopyNode(pnode, table[Heap_Size]);delete pnode;UINT i = Heap_Size;while ( i > 0 && table[Parent(i)]->Frequency > table[i]->Frequency ){Swap(i, Parent(i));i = Parent(i);}}Priority_Q::~Priority_Q(){for (int i = 0; i < 256; i++){delete table[i];}}PNode Build_Huffman_Tree(Priority_Q &queue) //建立Huffman树{PNode parent=NULL,left=NULL,right=NULL;while (queue.Heap_Size != EMPTY){left = new Node;right = new Node;parent = new Node;CopyNode(queue.Extract_Min(), left); //取出两个元素CopyNode(queue.Extract_Min(), right);//复制左右节点数据parent->Frequency = right->Frequency + left->Frequency;//建立父节点parent->_left = left;parent->_right = right;if (queue.Heap_Size == EMPTY)break;queue.Insert(parent);  //再插入回优先队列}return parent;}

/*compress.h*/#ifndef COMPRESS#define COMPRESS#include <vector>#define UINT unsigned int #define UCHAR unsigned char #define EMPTY 0xFFFFFFFF#define Parent(i) (UINT)(((i) - 1) / 2)typedef struct Node   //结点{Node::Node():key(EMPTY), Frequency(0),_left(NULL),_right(NULL){}UINT key;UINT Frequency;struct Node * _left;struct Node * _right;}Node,*PNode;class Priority_Q  //优先队列{public:Priority_Q(char *A, int Length);~Priority_Q();void Insert(PNode pnode); //插入PNode Extract_Min();  //取出元素UINT Heap_Size;  //队列的长度PNode table[256];  //建立256种结点private:void Build_Min_Heap(UINT Length); //建立队列void Swap(int x, int y);   //交换两个元素void Min_Heapify(UINT i); //维护优先队列的性质};PNode Build_Huffman_Tree(Priority_Q &queue);//构建优先队列#endif // COMPRESS

参考：

    http://wenku.baidu.com/view/04a8a13b580216fc700afd2e.html

    http://blog.csdn.net/abcjennifer/article/details/8020695