赫夫曼编码

说明：本程序是依据严蔚敏的数据结构（C语言版）上的代码实现的，书上的伪代码有两处有小问题。

#pragma once
#include<stdio.h>
#include<tchar.h>
#include<stdlib.h>
#define MAX 100
typedef struct{ //节点
int weight;
int parent, lchild, rchild;
}HTNode, *HuffmanTree;
typedef char **HuffmanCode; //字符串数组，用于存储叶子节点的编码
void SelectMinNode(HuffmanTree &HT, int m, int &i1, int &i2) //找出权值最小的两个节点对应的数组下标
{
HuffmanTree p = HT;
int s1, s2;
s1 = s2 = MAX;
i1 = i2 = 1;
for(int i=1; i<=m; i++)
{
if(!(p+i)->parent)
{
if((p+i)->weight < s1)
{
i2 = i;
s1 = (p+i)->weight ;
}
}
}
for(int i=1; i<=m; i++)
{
if(!(p+i)->parent && i!=i2)
{
if((p+i)->weight < s2)
{
i1 = i;
s2 = (p+i)->weight ;
}
}
}
}
void StrCopy(char *p, char *q, int start) //从字符数组中第start个字符开始复制
{
char *c1, *c2;
c1 = p;
while(q[start] != '\0')
{
*c1 = q[start];
c1++;
start++;
}
*c1 = q[start];//别忘了将‘\n’复制过来
}
void HuffmanCoding(HuffmanTree &HT, HuffmanCode &HC, int *w, int n)
{ //HT赫夫曼树节点数组，HC存储赫夫曼编码，*w 节点权值数组的首地址，n节点个数int i, i1, i2, m;
HuffmanTree p;
if(n<=1) return;
m = 2 * n -1; //n个叶子节点的赫夫曼树的节点总数为2n-1，可以结合树的度为n-1自己证明。

HT = (HuffmanTree)malloc((m+1)*sizeof(HTNode)); //数组首元素不使用，故多分配一个空间p = HT + 1;
for(i=1;i<=n;++i,++p,++w) //n个叶子节点初始化
{
p->weight = *w;
p->lchild = 0;
p->rchild = 0;
p->parent = 0;
}
for(;i<=m;++i,++p) //非叶子节点初始化
{
p->weight = 0;
p->lchild = 0;
p->rchild = 0;
p->parent = 0;
}
for(i=n+1;i<=m;++i) //对非叶子节点重新计算
{
SelectMinNode(HT, i-1, i1, i2);
HT[i1].parent = i;
HT[i2].parent = i;
HT[i].lchild = i1;
HT[i].rchild = i2;
HT[i].weight = HT[i1].weight + HT[i2].weight ;
}
///从叶子节点到根节点求赫夫曼编码
char* cd;
int start, c, f;
HC = (HuffmanCode)malloc((n+1)*sizeof(char*));//分配字符指针数组，同样多分配一个
cd = (char*)malloc(n*sizeof(char)); //零时变量，用于存储当前叶子节点的赫夫曼编码
cd[n-1] = '\0';
for(int i=1; i<=n; i++)
{
start = n-1;
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));
StrCopy(HC[i], cd, start); //将存储的编码copy给HC的第i个数组
}
free(cd);
}
void PrintHuffmanCode(HuffmanTree HT, HuffmanCode HC, int n) //打印各节点的赫夫曼编码{
HuffmanCode p;
for(int i=1; i<=n; i++)
{
p = HC;
printf("The weight %d HuffmanCode is: ", HT[i]);
while(*p[i]!='\0')
{
printf("%c",*p[i]);
p[i]++;
}
printf("\n");
}
}
void main()
{
int n = 8;
HuffmanTree HT;
HuffmanCode HC;
int a[8] = {5, 29, 7, 8, 14, 23, 3, 11};
HuffmanCoding(HT, HC, a, n);
PrintHuffmanCode(HT, HC, n);
system("pause");
}。