赫夫曼树与赫夫曼编码

赫夫曼树，又称最优二叉树。它的最优体现在每个结点的权值与它的路径长度的乘积之和最小。具体定义参考博客：https://blog.csdn.net/heart_love/article/details/50901943赫夫曼树的构造原理非常简单，每次在当前的树中找到节点权值最小的两个节点分别作为左右子树，他们双亲的权值就是这两个左右孩子的权值之和。循环构造，直到生成一棵树。赫夫曼编码就是在赫夫曼树的基础上，左边编码为0，右边为1，构成的二进制码值。

#include <stdio.h>
#include <string.h>

#define MAXVALUE      10000

typedef struct
{
char data;
int weight;
int parent;
int lchild;
int rchild;
int flag;
}HuffNode;

typedef struct
{
char code[10];
int start;
}HuffCode;

HuffNode H[9];
HuffCode HC[5];                            //当有n个结点需要构造赫夫曼树时，总共需要2*n-1个节点

int select (HuffNode *H, int n)           //选出当前树中的最小值
{
int min = MAXVALUE, i, j;
for(i = 0; i <= n; i++)
{
if(H[i].weight < min && H[i].flag == -1)
{
min = H[i].weight;
j = i;
}
}
H[j].flag = 1;
return j;
}

void HuffTreeInit (HuffNode *H, int n)
{
int i;
for(i = 0; i < n; i++)
{
H[i].data = getchar();
scanf("%d", &(H[i].weight));
getchar();
H[i].flag = -1;
H[i].lchild = -1;
H[i].parent = -1;
H[i].rchild = -1;
}
for(; i < 2*n-1; i++)
{
H[i].flag = -1;
H[i].lchild = -1;
H[i].parent = -1;
H[i].rchild = -1;
}
}

void CreatHuffTree (HuffNode *H, int n)
{
int i, l, r;
for(i = n; i < 2*n-1; i++)
{
l = select(H, i-1);                     //分别选出当前树中的最小的俩个权值，构造成二叉树
r = select(H, i-1);
H[l].parent = i;
H[r].parent = i;
H[i].weight = H[l].weight+H[r].weight;
H[i].lchild = l;
H[i].rchild = r;
}
}

void PrintHuffTree (HuffNode *H, int n)         //将构造好的赫夫曼树（最优二叉树）层序遍历
{
HuffNode list[2*n-1];
int in, out;
in = out = 0;
list[in++] = H[2*n-2];
while(in > out)
{
printf("%d\n", list[out].weight);
if(list[out].lchild != -1)
{
list[in++] = H[list[out].lchild];
list[in++] = H[list[out].rchild];

}
out++;
}
}

void CreatHuffCode (HuffNode *H, HuffCode *HC, int n)    //赫夫曼编码，从每个节点开始，向上编码
{
int i, c, f;
HuffCode d;
for(i = 0; i < n; i++)
{
d.start = n+1;
c = i;
f = H[c].parent;
while(f != -1)                                    //一直编码，知道结点为根节点
{
if(H[f].lchild == c)
{
d.code[--d.start] = '0';
}
else
{
d.code[--d.start] = '1';
}
c = f;
f = H[c].parent;
}
HC[i] = d;
}
}

void PrintHuffCode (HuffNode *H, HuffCode *HC, int n)
{
int i, j;
for(i = 0; i < n; i++)
{
printf("data:%c   ", H[i].data);
for(j = HC[i].start; j < n+1; j++)
{
printf("%c", HC[i].code[j]);
}
printf("\n");
}
}

int main ()
{
HuffTreeInit(H, 5);
CreatHuffTree(H, 5);
CreatHuffCode (H, HC, 5) ;
PrintHuffCode(H, HC, 5);
//    PrintHuffTree(H, 5);
return 0;
}

参考博客：https://blog.csdn.net/sinat_28826891/article/details/79802739                 https://blog.csdn.net/zhao19961027/article/details/53025670