Huffman树实现_详细注释

//最优二叉树
#include <iostream>
#include <iomanip>
using namespace std;

//定义结点类型
//【weight | lchid | rchild | parent】 
//为了判定一个结点是否已加入到要建立的哈夫曼树中
//可通过parent域的值来确定.
//初始时parent = -1，当结点加入到树中时，该结点parent的值
//为其父亲结点在数组Huffman中的序号. 
template<typename T>
struct HuffNode {
    T weight;             //权值
    int parent;           //指向父节点的指针域(结点元素的下标)
    int lch;              //左指针域
    int rch;              //右指针域 
}; 

//哈夫曼树的构造算法 
template<typename T>
HuffNode<T> *HuffmanTree(int n, const T& sign)     //生成最优二叉树
{
    const int MAX_VALUE = 100000;
    int i, j, min1, min2, x1, x2;                  //min1为最小值, min2为次小值, x1位最小值下标, x2位次小值下标 
    HuffNode<T> *ht = new HuffNode<T>[2 * n - 1];  //一个含有n个叶子结点的最优二叉树，总共有2*n-1个结点
    HuffNode<T> *huffNode = ht;
    for (i = 0; i < 2 * n - 1; i++)                //最优二叉树结点数组初始化 
    {
        huffNode[i].weight = 0;         //权值都设为0
        huffNode[i].parent = -1;        //父节点，左右孩子结点 
        huffNode[i].lch = -1;
        huffNode[i].rch = -1;           //都设置为-1,-1代表空 
    } 
    for (i = 0; i < n; i++)         //依次输入n个叶子结点的权值 
        cin >> huffNode[i].weight;
    
    for (i = 0; i < n - 1; i++)
    { 
        min1 = min2 = MAX_VALUE;     
        // x1, x2 用来保存找到的两个最小结点在数组中的位置 
        x1 = x2 = 0;  
        for (j = 0; j < n + i; j++) //因为外循环每循环一次，实际结点个数增加到n+i个 
        {
            if (huffNode[j].weight < min1 && huffNode[j].parent == -1)
            {
                min2 = min1;                    //存在权值小于min1, 则min1赋值给次小值 
                x2 = x1;                        //次小值下标改变 
                 min1 = huffNode[j].weight;      //当前权值赋值给最小值 
                x1 = j;                         //并保存最小值下标 
            }
            else if (huffNode[j].weight < min2 && huffNode[j].parent == -1)
            {
                min2 = huffNode[j].weight;      //当前值赋值给次小值 
                x2 = j;                         //保存次小值下标 
            }
        }
        //将找出的两个子树合并成一颗子树
        //对找到的两个最小结点的父指针域进行赋值 
        huffNode[x1].parent = n + i;    
        huffNode[x2].parent = n + i;
        //新合成树位置上的权值 
        huffNode[n + i].weight = huffNode[x1].weight + huffNode[x2].weight; 
        //两个最小结点的父结点的左右孩子域进行操作 
        huffNode[n + i].lch = x1;
        huffNode[n + i].rch = x2;        
    }
    return ht;
} 

template<typename T>
void ShowHTree(HuffNode<T> *HT, int nodeNum)
{
    HuffNode<T> *p = HT;
    int k;    
    cout << "k" << "		" << "Weight" << "		" << "Parent" 
         << "		" << "Lchild" << "		" << "Rchild" << endl;
    for (k = 0; k < 2 * nodeNum - 1; k++)
    {
        cout << k << "		" << (p + k)->weight << "		"
             << (p + k)->parent << "		" 
             << (p + k)->lch << "		" << (p + k)->rch << endl;
    }
} 

int main()
{
    int n;
    HuffNode<int> *huffNode;
    int sign = 0;           //标志为权值的类型 
    
    cout << "请输入叶子结点个数: " << endl;
    cin >> n;
    huffNode = HuffmanTree(n, sign);
    ShowHTree(huffNode, n);
    
    system("pause");
    
    return 0;
}