#include<stdio.h>
#include<stdlib.h>
typedef int ElemType;
struct BTreeNode
{
ElemType data;
struct BTreeNode* left;
struct BTreeNode* right;
};
//1、输出二叉树，可在前序遍历的基础上修改。采用广义表格式，元素类型为int
void PrintBTree_int(struct BTreeNode* BT)
{
if (BT != NULL)
{
printf("%d", BT->data); //输出根结点的值
if (BT->left != NULL || BT->right != NULL)
{
printf("(");
PrintBTree_int(BT->left); //输出左子树
if (BT->right != NULL)
printf(",");
PrintBTree_int(BT->right); //输出右子树
printf(")");
}
}
}
//2、根据数组 a 中 n 个权值建立一棵哈夫曼树，返回树根指针
struct BTreeNode* CreateHuffman(ElemType a[], int n)
{
int i, j;
struct BTreeNode **b, *q;
b = (BTreeNode**)malloc(n*sizeof(BTreeNode));
for (i = 0; i < n; i++) //初始化b指针数组，使每个指针元素指向a数组中对应的元素结点
{
b[i] = (BTreeNode*)malloc(sizeof(BTreeNode));
b[i]->data = a[i];
b[i]->left = b[i]->right = NULL;
}
for (i = 1; i < n; i++)//进行 n-1 次循环建立哈夫曼树
{
//k1表示森林中具有最小权值的树根结点的下标，k2为次最小的下标
int k1 = -1, k2;
for (j = 0; j < n; j++)//让k1初始指向森林中第一棵树，k2指向第二棵
{
if (b[j] != NULL && k1 == -1)
{
k1 = j;
continue;
}
if (b[j] != NULL)
{
k2 = j;
break;
}
}
for (j = k2; j < n; j++)//从当前森林中求出最小权值树和次最小
{
if (b[j] != NULL)
{
if (b[j]->data < b[k1]->data)
{
k2 = k1;
k1 = j;
}
else if (b[j]->data < b[k2]->data)
k2 = j;
}
}
//由最小权值树和次最小权值树建立一棵新树，q指向树根结点
q = (BTreeNode*)malloc(sizeof(BTreeNode));
q->data = b[k1]->data + b[k2]->data;
q->left = b[k1];
q->right = b[k2];
b[k1] = q;//将指向新树的指针赋给b指针数组中k1位置
b[k2] = NULL;//k2位置为空
}
free(b); //删除动态建立的数组b
return q; //返回整个哈夫曼树的树根指针
}
//3、求哈夫曼树的带权路径长度
ElemType WeightPathLength(struct BTreeNode* FBT, int len)//len初始为0
{
if (FBT == NULL) //空树返回0
return 0;
else
{
if (FBT->left == NULL && FBT->right == NULL)//访问到叶子结点
return FBT->data * len;
else //访问到非叶子结点，进行递归调用，返回左右子树的带权路径长度之和，len递增
return WeightPathLength(FBT->left, len + 1) + WeightPathLength(FBT->right, len + 1);
}
}
//4、哈夫曼编码（可以根据哈夫曼树带权路径长度的算法基础上进行修改）
void HuffManCoding(struct BTreeNode* FBT, int len)//len初始值为0
{
static int a[10];//定义静态数组a，保存每个叶子的编码，数组长度至少是树深度减一
if (FBT != NULL)//访问到叶子结点时输出其保存在数组a中的0和1序列编码
{
if (FBT->left == NULL && FBT->right == NULL)
{
int i;
printf("结点权值为%d的编码：", FBT->data);
for (i = 0; i < len; i++)
printf("%d", a[i]);
printf("\n");
}
else//访问到非叶子结点时分别向左右子树递归调用，并把分支上的0、1编码保存到数组a
{ //的对应元素中，向下深入一层时len值增1
a[len] = 0;
HuffManCoding(FBT->left, len + 1);
a[len] = 1;
HuffManCoding(FBT->right, len + 1);
}
}
}
//主函数
int main()
{
int n, i;
ElemType* a;
struct BTreeNode* fbt;
printf("从键盘输入待构造的哈夫曼树中带权叶子结点数n：");
while (1)
{
scanf("%d", &n);
if (n > 1)
break;
else
printf("重输n值：");
}
a = (ElemType*)malloc(n*sizeof(ElemType));
printf("从键盘输入%d个整数作为权值：", n);
for (i = 0; i < n; i++)
scanf(" %d", &a[i]);
fbt = CreateHuffman(a, n);
printf("广义表形式的哈夫曼树：");
PrintBTree_int(fbt);
printf("\n");
printf("哈夫曼树的带权路径长度：");
printf("%d\n", WeightPathLength(fbt, 0));
printf("树中每个叶子结点的哈夫曼编码：\n");
HuffManCoding(fbt, 0);
}
