数组实现哈夫曼树及哈夫曼编码

百度百科介绍：http://baike.baidu.com/link?url=DDUm7qBwh4XVGlhskrXjpQZx6mu74iy-54mkIBMUIME8o22OKvbi61yHxOz0Ljm5YekqESS70n3rTKSHqPu3Z_

简单的图示介绍：

用数组实现的哈夫曼树及哈夫曼编码：

#include <cstdio>
#define N 5
#define M 2*N-1
#define MaxInt 666666
//建成的哈夫曼树存放在HTree数组中
//且通过数组元素下标来确定父节点，左节点，右节点
struct 
{
int weight;//权
int left;//左节点
int right;//右节点
int parent;//父节点
}HTree[M];


//对一篇文章编码，我们假设已经得到了每个字符（c）及它们的出现权重（weight）
struct 
{
char c;
int weight;
int bit[100];//存储每个字符编码的逆序
int code[100];//存储每个字符的编码
int len;//存储每个字符的编码的长度
}cc[N]={{'a',1,{0},{0},0},{'b',2,{0},{0},0},{'c',3,{0},{0},0},{'d',4,{0},{0},0},{'e',5,{0},{0},0}};


//初始化成森林
void InitHTree()
{
int i;
for(i=0;i<M;i++)
{
if(i<N)
HTree[i].weight=cc[i].weight;
else
HTree[i].weight=0;
HTree[i].left=HTree[i].right=HTree[i].parent=-1;//数组元素以0为第一元素，故将其初始化为-1
}
}


//建哈夫曼树
void BuidHTree()
{
int i,j,x,y;
int min;
for(i=0;i<N-1;i++)
{
min=MaxInt;
//找最小的两个元素x，y
for(j=0;j<M;j++)
{
if(HTree[j].parent==-1&&HTree[j].weight>0&&min>HTree[j].weight)
{
min=HTree[j].weight;
x=j;
}
}
min=MaxInt;
for(j=0;j<M;j++)
{
if(HTree[j].parent==-1&&HTree[j].weight>0&&j!=x&&min>HTree[j].weight)
{
min=HTree[j].weight;
y=j;
}
}
HTree[x].parent=HTree[y].parent=i+N;//父节点为HTree[i+N]
HTree[i+N].left=x;
HTree[i+N].right=y;
HTree[i+N].weight=HTree[x].weight+HTree[y].weight;
}
}


//哈夫曼编码：每一个字符都得到一个二进制编码
void HuffCode()
{
int i,j;
int pos,child,parent;
for(i=0;i<N;i++)
{
pos=0;
child=i;
parent=HTree[i].parent;
while(parent!=-1)
{
if(HTree[parent].left==child)
cc[i].bit[pos]=0;
else
cc[i].bit[pos]=1;
pos++;
child=parent;
parent=HTree[parent].parent;
}
cc[i].len=pos;


//将逆序的结果存到正序中
pos--;
for(j=0;j<cc[i].len;j++,pos--)
cc[i].code[j]=cc[i].bit[pos];
}
}
int main()
{
int i,j;
//初始化森林
InitHTree();
//建哈夫曼树
BuidHTree();
//测试建树结果
for(i=0;i<M;i++)
printf("%d ",HTree[i].weight);
printf("\n");
//哈夫曼编码
HuffCode();
//测试编码结果：每一个字符都得到一个特定的二进制编码
for(i=0;i<N;i++)
{
printf("%c:",cc[i].c);
for(j=0;j<cc[i].len;j++)
printf("%d ",cc[i].code[j]);
printf("\n");
}
return 0;
}