根据哈夫曼编码的原理,编写一个程序,在用户输入结点权值的基础上求赫夫曼编码,并能把给定的编码进行译码。
(1)初始化:从键盘输入一字符串(或读入一文件),统计出现的字符和每个字符出现的频率,将字符出现的频率作为结点的权值,建立哈夫曼树。对各个字符进行哈夫曼编码,最后打印输出字符及每个字符对应的哈夫曼编码。
(2)编码:利用已建好的哈夫曼树对“输入串”进行哈夫曼编码,最后打印输入串对应的哈夫曼编码(写入文件)。 √
(3)计算压缩比(选作)
(4)译码:利用已建好的哈夫曼树对给定的一串代码进行译码,并打印输出得到的字符串。(选作)
测试数据:对字符串{casbcatbsatbat}进行编码;对电文“1101000”译码。字符集D={ ?},出现频率为w={?}
//运行环境 VS2015
#include "stdafx.h"
#include "malloc.h"
#include<stdio.h>
#include<string.h>
typedef struct HTNode
{
unsigned int weight;
char parent;
unsigned int lchild, //count
rchild;
}HTNode;
typedef char * *HC;
int Found(char c, HTNode ht[],int index)
{
for (int i=1;i<index;i++)
{
if (c == ht[i].parent)return i;
}
return 0;
}
void Select(HTNode ht[], int i, int&s1, int&s2) {
int j, k = 1;
while (ht[k].parent != 0)
k++;
s1 = k;
for (j = 1; j <= i; ++j) // Select the first least of ht[].weight
if (ht[j].parent == 0 && ht[j].weight<ht[s1].weight)
s1 = j;
k = 1;
while ((ht[k].parent != 0 || k == s1))
k++;
s2 = k;
for (j = 1; j <= i; ++j) // Select the second least of ht[].weight
if (ht[j].parent == 0 && ht[j].weight<ht[s2].weight&&j != s1)
s2 = j;
}
int Aver(int n)
{
int i = 0;
int m = 1;
for (;m < n;i ++)
{
m *= 2;
}
return i;
}
#pragma warning(disable:4996)
void main()
{
char st[101]; //字符种类字符串
char ch[101]; //输入的所有字符字符串
int num = 0;
float haver=0; //赫夫曼编码平均字符编码长度
HTNode *ht=(HTNode*)malloc(101*sizeof(HTNode));
ht[0].lchild = 0;ht[0].parent = 1;
while (char c = getchar())
{
if (c == '\n')break;
ch[num] = c;
num++;
int temp = Found(c, ht, ht[0].parent);
if (!temp)
{
ht[ht[0].parent].lchild = 1;
ht[ht[0].parent].parent = c;
st[ht[0].parent] = c;
ht[0].parent++;
}
else
{
ht[temp].lchild++;
}
ht[0].lchild++;
}
ch[num] = '\0';
for (int i = 1;i < ht[0].parent;i++)
{
ht[i].weight = (int)(((float)ht[i].lchild / (float)ht[0].lchild)*100);
}
int n = ht[0].parent - 1; //字母种类总数
int m = 2 * n - 1;
for (int i = 1;i <= n;i++)ht[i] = { ht[i].weight,0,0,0 };
for (int i = n + 1;i <= m;i++)ht[i] = { 0,0,0,0 };
for (int i = n + 1;i <= m;++i)
{
int s1, s2;
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;
}
HC hc = (HC)malloc((n + 1) * sizeof(char*));
char *cd = (char*)malloc(n * sizeof(char));
cd[n - 1] = '\0';
for (int i = 1;i <= n;++i)
{
int start = n - 1;
int c;char f;
for (c = i, f = ht[i].parent;f != 0;c = f, f = ht[f].parent)
{
if (ht[f].lchild == c) cd[--start] = '0';
else cd[--start] = '1';
}
hc[i] = (char*)malloc((n - start) * sizeof(char));
strcpy(hc[i], &cd[start]);
haver += (float)(ht[i].weight *strlen(hc[i])) / 100;
}
free(cd);
FILE *fp;
fp = fopen("d:\\code.txt", "w");
for (num = 0;ch[num] != '\0';num++) //遍历输入的字符
{
for (int j = 1;j <= n;j++) //遍历编码表
{
if (ch[num] == st[j])
{
fprintf(fp, "%s",hc[j]);
printf("%s", hc[j]);
break;
}
}
}
fclose(fp);
putchar('\n');
printf("********译码表*********\n");
for (int i = 1;i<=n;i++)
{
printf("%c:%s\n", st[i],hc[i]);
}
printf("***********************\n");
printf("赫夫曼编码平均码长=%0.2f\n", haver);
printf("等长编码平均码长=%d\n", Aver(n));
printf("赫夫曼编码的压缩率为%%%0.1lf\n",100.00-haver/(float)Aver(n)*100);
printf("*********译码器********\n");
printf("请输入要翻译的编码\n");
char buffer[101]; //缓冲数组
int index = 0;
while (char c = getchar())
{
if (c == '\n')break;
buffer[index] = c; //将c存入缓冲
index++;
buffer[index] = '\0';
for (int i = 1;i<=n;i++) //遍历密钥表列
{
bool found = true;
for (int j = 0;hc[i][j] != '\0';j++) //遍历密钥表行
{
if (buffer[j] != hc[i][j])
{
found = false;
break;
}
}
if (found)
{
printf("%c", st[i]);
index = 0;
break;
}
}
}
}