介绍哈夫曼：

效率最高的判别树即为哈夫曼树

在计算机数据处理中，霍夫曼编码使用变长编码表对源符号（如文件中的一个字母）进行编码，其中变长编码表是通过一种评估来源符号出现机率的方法得到的，出现机率高的字母使用较短的编码，反之出现机率低的则使用较长的编码，这便使编码之后的字符串的平均长度、期望值降低，从而达到无损压缩数据的目的。

例如，在英文中，e的出现机率最高，而z的出现概率则最低。当利用霍夫曼编码对一篇英文进行压缩时，e极有可能用一个比特来表示，而z则可能花去25个比特（不是26）。用普通的表示方法时，每个英文字母均占用一个字节，即8个比特。二者相比，e使用了一般编码的1/8的长度，z则使用了3倍多。倘若我们能实现对于英文中各个字母出现概率的较准确的估算，就可以大幅度提高无损压缩的比例。

霍夫曼树又称最优二叉树，是一种带权路径长度最短的二叉树。所谓树的带权路径长度，就是树中所有的叶结点的权值乘上其到根结点的路径长度（若根结点为0层，叶结点到根结点的路径长度为叶结点的层数）。树的路径长度是从树根到每一结点的路径长度之和，记为WPL=（W1*L1+W2*L2+W3*L3+...+Wn*Ln），N个权值Wi（i=1,2,...n）构成一棵有N个叶结点的二叉树，相应的叶结点的路径长度为Li（i=1,2,...n）。可以证明霍夫曼树的WPL是最小的。

文件压缩与解压

姓名：范天祚

1 程序说明

1.1数据结构

哈夫曼树

1.2函数功能说明

printfPercent界面

compress()读取文件内容并加以压缩，将压缩内容写入另一个文档

uncompress()解压缩文件，并将解压后的内容写入新文件

1.3 程序编写的思路及流程

压缩：统计字符出现次数、将节点按出现次数排序、构造哈夫曼树、设置字符编码、读文件字符、按设置好的编码替换字符、写入存储文件

解压：读取文件各参数、转换成二进制码、按码求对应字符、写入存储文件

#define _CRT_SECURE_NO_WARNINGS
#include <stdlib.h>
#include <stdio.h>
#include <string.h>struct head
{int b;						  //字符long count;                   //文件中该字符出现的次数long parent, lch, rch;        //make a treechar bits[256];               //the huffuman code
};struct head header[512], tmp;  //节点树void printfPercent(int per)
{int i = 0;printf("|");for(i = 0; i < 10; i++){if(i < per/10)printf(">");elseprintf("-");}printf("|已完成%d%%\n",per);
}//函数：compress()
//作用：读取文件内容并加以压缩
//将压缩内容写入另一个文档
int compress(const char *filename,const char *outputfile)
{char buf[512];unsigned char c;long i, j, m, n, f;long min1, pt1, flength;FILE *ifp, *ofp;int per = 10;ifp = fopen(filename, "rb");                  //打开原始文件if (ifp == NULL){printf("打开文件失败:%s\n",filename);return 0;                             //如果打开失败，则输出错误信息}ofp = fopen(outputfile,"wb");                 //打开压缩后存储信息的文件if (ofp == NULL){printf("打开文件失败:%s\n",outputfile);return 0;}flength = 0;while (!feof(ifp)){fread(&c, 1, 1, ifp);header[c].count ++;                       //读文件，统计字符出现次数flength ++;                               //记录文件的字符总数}flength --;header[c].count --;for (i = 0; i < 512; i ++)                    //HUFFMAN算法中初始节点的设置{if (header[i].count != 0)header[i].b = (unsigned char) i;elseheader[i].b = -1;header[i].parent = -1;header[i].lch = header[i].rch = -1;}for (i = 0; i < 256; i ++)                    //将节点按出现次数排序{for (j = i + 1; j < 256; j ++){if (header[i].count < header[j].count){tmp = header[i];header[i] = header[j];header[j] = tmp;}}}for (i = 0; i < 256; i ++)                    //统计不同字符的数量{if (header[i].count == 0)break;}n = i;m = 2 * n - 1;for (i = n; i < m; i ++){min1 = 999999999;for (j = 0; j < i; j ++){if (header[j].parent != -1) continue;if (min1 > header[j].count){pt1 = j;min1 = header[j].count;continue;}}header[i].count = header[pt1].count;header[pt1].parent = i;header[i].lch = pt1;min1 = 999999999;for (j = 0; j < i; j ++){if (header[j].parent != -1) continue;if (min1 > header[j].count){pt1 = j;min1 = header[j].count;continue;}}header[i].count += header[pt1].count;header[i].rch = pt1;header[pt1].parent = i;}for (i = 0; i < n; i ++)                        //构造HUFFMAN树，设置字符的编码{f = i;header[i].bits[0] = 0;while (header[f].parent != -1){j = f;f = header[f].parent;if (header[f].lch == j){j = strlen(header[i].bits);memmove(header[i].bits + 1, header[i].bits, j + 1);header[i].bits[0] = '0';}else{j = strlen(header[i].bits);memmove(header[i].bits + 1, header[i].bits, j + 1);header[i].bits[0] = '1';}}}//下面的就是读原文件的每一个字符，按照设置好的编码替换文件中的字符fseek(ifp, 0, SEEK_SET);                                                //将指针定在文件起始位置fseek(ofp, 8, SEEK_SET);                                //以8位二进制数为单位进行读取buf[0] = 0;f = 0;pt1 = 8;printf("读取将要压缩的文件:%s\n",filename);printf("当前文件有:%d字符\n",flength);printf("正在压缩\n");while (!feof(ifp)){c = fgetc(ifp);f ++;for (i = 0; i < n; i ++){if (c == header[i].b) break;}strcat(buf, header[i].bits);j = strlen(buf);c = 0;while (j >= 8)                                             //当剩余字符数量不小于8个时{for (i = 0; i < 8; i ++)                               //按照八位二进制数转化成十进制ASCII码写入文件一次进行压缩{if (buf[i] == '1') c = (c << 1) | 1;else c = c << 1;}fwrite(&c, 1, 1, ofp);pt1 ++;strcpy(buf, buf + 8);j = strlen(buf);}if(100 * f/flength > per){printfPercent(per);per += 10;}if (f == flength)break;}printfPercent(100);if (j > 0)                                                      //当剩余字符数量少于8个时{strcat(buf, "00000000");for (i = 0; i < 8; i ++){if (buf[i] == '1') c = (c << 1) | 1;else c = c << 1;                                        //对不足的位数进行补零}fwrite(&c, 1, 1, ofp);pt1 ++;}fseek(ofp, 0, SEEK_SET);                                        //将编码信息写入存储文件fwrite(&flength,1,sizeof(flength),ofp);fwrite(&pt1, sizeof(long), 1, ofp);fseek(ofp, pt1, SEEK_SET);fwrite(&n, sizeof(long), 1, ofp);for (i = 0; i < n; i ++){tmp = header[i];fwrite(&(header[i].b), 1, 1, ofp);pt1++;c = strlen(header[i].bits);fwrite(&c, 1, 1, ofp);pt1++;j = strlen(header[i].bits);if (j % 8 != 0)                                             //当位数不满8时，对该数进行补零操作{for (f = j % 8; f < 8; f ++)strcat(header[i].bits, "0");}while (header[i].bits[0] != 0){c = 0;for (j = 0; j < 8; j ++){if (header[i].bits[j] == '1') c = (c << 1) | 1;else c = c << 1;}strcpy(header[i].bits, header[i].bits + 8);fwrite(&c, 1, 1, ofp);                                            //将所得的编码信息写入文件pt1++;}header[i] = tmp;}fclose(ifp);fclose(ofp);                                                              //关闭文件printf("压缩后文件为:%s\n",outputfile);printf("压缩后文件有:%d字符\n",pt1 + 4);return 1;                                       //返回压缩成功信息
}//函数：uncompress()
//作用：解压缩文件，并将解压后的内容写入新文件
int uncompress(const char *filename,const char *outputfile)
{char buf[255], bx[255];unsigned char c;char out_filename[512];long i, j, m, n, f, p, l;long flength;int per = 10;int len = 0;FILE *ifp, *ofp;char c_name[512] = {0};ifp = fopen(filename, "rb");                                              //打开文件if (ifp == NULL){return 0;     //若打开失败，则输出错误信息}//读取原文件长if(outputfile)strcpy(out_filename,outputfile);elsestrcpy(out_filename,c_name);ofp = fopen(out_filename, "wb");                                            //打开文件if (ofp == NULL){return 0;}fseek(ifp,0,SEEK_END);len = ftell(ifp);fseek(ifp,0,SEEK_SET);printf("将要读取解压的文件:%s\n",filename);printf("当前文件有:%d字符\n",len);printf("正在解压\n");fread(&flength, sizeof(long), 1, ifp);                                    //读取原文件长fread(&f, sizeof(long), 1, ifp);fseek(ifp, f, SEEK_SET);fread(&n, sizeof(long), 1, ifp);                                          //读取原文件各参数for (i = 0; i < n; i ++)                                                  //读取压缩文件内容并转换成二进制码{fread(&header[i].b, 1, 1, ifp);fread(&c, 1, 1, ifp);p = (long) c;header[i].count = p;header[i].bits[0] = 0;if (p % 8 > 0) m = p / 8 + 1;else m = p / 8;for (j = 0; j < m; j ++){fread(&c, 1 , 1 , ifp);f = c;_itoa(f, buf, 2);f = strlen(buf);for (l = 8; l > f; l --){strcat(header[i].bits, "0");                                  //位数不足，执行补零操作}strcat(header[i].bits, buf);}header[i].bits[p] = 0;}for (i = 0; i < n; i ++){for (j = i + 1; j < n; j ++){if (strlen(header[i].bits) > strlen(header[j].bits)){tmp = header[i];header[i] = header[j];header[j] = tmp;}}}p = strlen(header[n-1].bits);fseek(ifp, 8, SEEK_SET);m = 0;bx[0] = 0;while (1){while (strlen(bx) < (unsigned int)p){fread(&c, 1, 1, ifp);f = c;_itoa(f, buf, 2);f = strlen(buf);for (l = 8; l > f; l --){strcat(bx, "0");}strcat(bx, buf);}for (i = 0; i < n; i ++){if (memcmp(header[i].bits, bx, header[i].count) == 0) break;}strcpy(bx, bx + header[i].count);c = header[i].b;fwrite(&c, 1, 1, ofp);m ++;if(100 *  m/flength > per){printfPercent(per);per += 10;}if (m == flength) break;}printfPercent(100);fclose(ifp);fclose(ofp);printf("解压后文件为:%s\n",out_filename);printf("解压后文件有:%d字符\n",flength);return 1;                   //输出成功信息
}int main(int argc,const char *argv[])
{memset(&header,0,sizeof(header));memset(&tmp,0,sizeof(tmp));compress("测试文档.txt","测试文档.txt.zip");uncompress("测试文档.txt.zip","测试文档.txt 解压后.txt");system("pause");return 0;
}