哈夫曼编码

#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;

//Huffman树的节点类
typedef struct Node
{
    char value;               //结点的字符值   
    int weight;               //结点字符出现的频度
    Node *lchild, *rchild;     //结点的左右孩子
}Node;

//自定义排序规则，即以vector中node结点weight值升序排序
bool ComNode(Node *p, Node *q)
{
    return p->weight<q->weight;
}

//构造Huffman树，返回根结点指针
Node* BuildHuffmanTree(vector<Node*> vctNode)
{
    while (vctNode.size()>1)                            //vctNode森林中树个数大于1时循环进行合并
    {
        sort(vctNode.begin(), vctNode.end(), ComNode);   //依频度高低对森林中的树进行升序排序

        Node *first = vctNode[0];    //取排完序后vctNode森林中频度最小的树根
        Node *second = vctNode[1];   //取排完序后vctNode森林中频度第二小的树根
        Node *merge = new Node;      //合并上面两个树
        merge->weight = first->weight + second->weight;
        merge->lchild = first;
        merge->rchild = second;

        vector<Node*>::iterator iter;
        iter = vctNode.erase(vctNode.begin(), vctNode.begin() + 2);    //从vctNode森林中删除上诉频度最小的两个节点first和second
        vctNode.push_back(merge);                                 //向vctNode森林中添加合并后的merge树
    }
    return vctNode[0];            //返回构造好的根节点
}

//用回溯法来打印编码
void PrintHuffman(Node *node, vector<int> vctchar)
{
    if (node->lchild == NULL && node->rchild == NULL)
    {//若走到叶子节点，则迭代打印vctchar中存的编码
        cout << node->value << ": ";
        for (vector<int>::iterator iter = vctchar.begin(); iter != vctchar.end(); iter++)
            cout << *iter;
        cout << endl;
        return;
    }
    else
    {
        vctchar.push_back(1);     //遇到左子树时给vctchar中加一个1
        PrintHuffman(node->lchild, vctchar);
        vctchar.pop_back();       //回溯，删除刚刚加进去的1
        vctchar.push_back(0);     //遇到左子树时给vctchar中加一个0
        PrintHuffman(node->rchild, vctchar);
        vctchar.pop_back();       //回溯，删除刚刚加进去的0

    }
}

int main()
{
    cout << "************ Huffman编码问题 ***************" << endl;
    cout << "请输入要编码的字符,并以空格隔开（个数任意）：" << endl;
    vector<Node*> vctNode;        //存放Node结点的vector容器vctNode
    char ch;                      //临时存放控制台输入的字符
    while ((ch = getchar()) != '
')
    {
        if (ch == ' ')continue;      //遇到空格时跳过，即没输入一个字符空一格空格
        Node *temp = new Node;
        temp->value = ch;
        temp->lchild = temp->rchild = NULL;
        vctNode.push_back(temp);  //将新的节点插入到容器vctNode中
    }

    cout << endl << "请输入每个字符对应的频度，并以空格隔开：" << endl;
    for (int i = 0; i<vctNode.size(); i++)
        cin >> vctNode[i]->weight;

    Node *root = BuildHuffmanTree(vctNode);   //构造Huffman树，将返回的树根赋给root
    vector<int> vctchar;
    cout << endl << "对应的Huffman编码如下：" << endl;
    PrintHuffman(root, vctchar);

    system("pause");
}