重温经典之赫夫曼(Huffman)编码

 

先看看赫夫曼树
假设有n个权值{w1,w2,…，wn}，构造一个有n个叶子结点的二叉树，每个叶子结点权值为wi,则其中带权路径长度WPL最小的二叉树称作赫夫曼树或最优二叉树。
 
赫夫曼树的构造，赫夫曼最早给出了带有一般规律的算法，俗称赫夫曼算法。如下：
（1）根据给定的n个权值{w1,w2,…，wn}构造n棵二叉树的集合F={T1,T2,…，Tn}，其中Ti中只有一个权值为wi的根结点，左右子树为空。
（2）在F中选取两棵根结点的权值为最小的数作为左、右子树以构造一棵新的二叉树，且置新的二叉树的根结点的权值为左、右子树上根结点的权值之和。
（3）在F中删除这两棵树，同时将新得到的二叉树加入到F中。
（4）重复（2）和（3）直到F中只含一棵树为止，这棵树就是赫夫曼树。

 

例如下图便是赫夫曼树的构造过程。其中，根节点上标注的是所赋的权值。

 

 

设计一棵赫夫曼树，由此得到的二进制前缀编码就是赫夫曼编码。那么什么是前缀编码呢？所谓前缀编码，就是若要设计长短不等的编码，则必须是任意一个字符的编码都不是另一个字符编码的前缀。所以我们可以利用二叉树来设计二进制的前缀编码。

 

假设需要传送的字符为：A B A C C D A。如下图就是一个前缀编码的示例。

 

说了这么多理论，总该实践一下了，下面是赫夫曼编码的具体实现代码:

#include <stdio.h>#include <string.h>#include <malloc.h>#include <assert.h>#define NUM 256typedef struct{int weight;int parent, lchild, rchild;}HTNode, *HuffmanTree;/******* Choose two smallest from 0 to n in T *************/void Select(HuffmanTree T, int len, int *s1, int *s2){int i = 0;while (T[i++].parent != -1);*s1 = i-1;while (T[i++].parent != -1);*s2 = i-1;if (T[*s1].weight>T[*s2].weight) {i = *s1;*s1 = *s2;*s2 = i;}for (i=0; i<=len; i++) {if(T[i].parent == -1) {if (T[*s1].weight > T[i].weight) {*s2 = *s1;*s1 = i;}else if (T[*s2].weight >T[i].weight && i != *s1)*s2 = i;}}return;}void show_binary(char ch){char i;for (i = 0; i < 8; i++) { if (ch&0x80)printf("1");else printf("0");if (i == 3)printf(",");ch <<= 1;}printf(" ");}void HuffmanCoding(FILE *psrc, FILE *pdst, FILE *pdeciphering){int i;char ch;int m = 2*NUM-1;int size = m*sizeof(HTNode);HuffmanTree HT = (HuffmanTree)malloc(size);assert(HT);memset(HT, -1, size);for (i=0; i<NUM; i++)HT[i].weight = 0;while ((ch=fgetc(psrc)) != EOF) {(HT[ch].weight)++;}rewind(psrc);/******************printf the Huffman weight****int j;for(j=0; j<NUM; j++) {printf("%c:%d\t", j, HT[j].weight);}**********************************************/int s1, s2;for (i=NUM; i<m; i++) {Select(HT, i-1, &s1, &s2);HT[s1].parent = i; HT[s2].parent = i;HT[i].lchild = s1; HT[i].rchild = s2;HT[i].weight = HT[s1].weight + HT[s2].weight;}/*******************printf the HuffmanTree*********int j;for (j=0; j<m; j++)printf("%d:w%d p%d l%d r%d\t\t", j, HT[j].weight, HT[j].parent, HT[j].lchild, HT[j].rchild);**************************************************/char **HC = (char**)malloc(NUM*sizeof(char*));char* cd = (char*)malloc(NUM*sizeof(char));cd[NUM-1] = '\0';int start,c,f;for (i=0; i<NUM; i++) {start = NUM-1;for (c=i,f=HT[i].parent; f!=-1; c=f,f=HT[f].parent) {if (HT[f].lchild==c) cd[--start] ='0';else cd[--start] ='1';}HC[i] = (char *)malloc((NUM-start)*sizeof(char));strcpy(HC[i], &cd[start]);}/************printf the Huffmancode******************************int j;for (j=0; j<NUM; j++) {printf("%c:%s\t", j, HC[j]);}****************************************************************/char buff[100] = {0};char k = 0, j = 0;while ((ch=fgetc(psrc)) != EOF) {i = -1; while (HC[ch][++i] != '\0') {buff[j] <<= 1;k++;if (HC[ch][i] == '1')buff[j] |= 0x01;if ((k %= 8) == 0)j++;if (j == 100) {j =0;fwrite(buff, 1, 100, pdst);}}}buff[j] <<= (8-k);fwrite(buff, 1, j + 1, pdst);/*****************************************************printf("\ndata write to %s\n", dstfile);for (i=0; i<=j; i++)show_binary(buff[i]);***************************************************/rewind(pdst);fflush(pdst);c = 510;while (!feof(pdst)) {j = fread(buff, 1, 100, pdst);/********************************************printf("\nfrom read:\n");for (i=0; i<j; i++)show_binary(buff[i]);*******************************************/for (i=0; i<j; i++) {for (k=0; k<8; k++) {if (buff[i]&0x80)c = HT[c].rchild;else c = HT[c].lchild;if (HT[c].lchild == -1) {fputc((char)c, pdeciphering);c = 510;}buff[i] <<= 1;}}}/**************free the memery and return*******************/for(i=0; i<NUM; i++) {free(HC[i]);}free(cd);free(HC);free(HT);HT = NULL;fclose(pdst);fclose(psrc);fclose(pdeciphering);return;}int main(void){char srcfile[100], dstfile[100],deciphering[100];printf("Input source file:");scanf("%s", srcfile);printf("Input dest file:");scanf("%s", dstfile);printf("Input deciphering file:");scanf("%s", deciphering);FILE *psrc = fopen(srcfile, "r");FILE *pdst = fopen(dstfile, "w+");FILE *pdeciphering = fopen(deciphering, "w");if (psrc == NULL || pdst == NULL || pdeciphering == NULL) {printf("file opened failed\n");return -1;} else HuffmanCoding(psrc, pdst, pdeciphering);return 0;}