#include
#include
using namespace std;
typedef int ElemType;
struct BTreeNode
{
ElemType data;
struct BTreeNode* left;
struct BTreeNode* right;
};
//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(struct 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(struct 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(struct 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);
}
}
//主函数
int main(void)
{
int n, i;
ElemType* a;
struct BTreeNode* fbt;
cout << "从键盘输入待构造的哈夫曼树中带权叶子结点数n:";
cin >> n;
a = (ElemType*)malloc(n * sizeof(ElemType));
cout << "从键盘输入" << n << "个整数作为权值:";
for (i = 0; i < n; i++)
cin >> a[i];
fbt = CreateHuffman(a, n);
cout << "哈夫曼树的带权路径长度:";
cout << WeightPathLength(fbt, 0) << endl;
}