C++ 哈夫曼树（HuffmanTree）

如何建立哈夫曼树的，网上搜索一堆，这里就不写了，直接给代码。

1.哈夫曼树结点类：HuffmanNode.h

#ifndef HuffmanNode_h
#define HuffmanNode_h

template 
struct HuffmanNode {
    T weight; // 存储权值
    HuffmanNode *leftChild, *rightChild, *parent; // 左、右孩子和父结点
};

#endif /* HuffmanNode_h */

2.哈夫曼树最小堆：HuffmanMinHeap.h

#ifndef HuffmanMinHeap_h
#define HuffmanMinHeap_h

#include "HuffmanNode.h"
#include 
using namespace std;

const int DefaultSize = 100;

template 
class MinHeap {
public:
    MinHeap(); // 构造函数
    ~MinHeap(); // 析构函数
    void Insert(HuffmanNode *current); // 插入
    HuffmanNode *getMin(); // 获取最小结点
private:
    HuffmanNode *heap; // 动态数组存储最小堆
    int CurrentSize; // 目前最小堆的结点数
    void ShiftUp(int start); // 向上调整
    void ShiftDown(int start, int m); // 下滑
};

// 构造函数
template 
MinHeap::MinHeap() {
    heap = new HuffmanNode[DefaultSize]; // 创建堆空间
    CurrentSize = 0;
}

// 析构函数
template 
MinHeap::~MinHeap() {
    delete []heap; // 释放空间
}

// 插入
template 
void MinHeap::Insert(HuffmanNode *current) {
    if(CurrentSize == DefaultSize) {
        cout << "堆已满" << endl;
        return;
    }
    // 把current的数据复制到“数组末尾”
    heap[CurrentSize] = *current;
    // 向上调整堆
    ShiftUp(CurrentSize);
    CurrentSize++;
}

// 获取最小结点并在堆中删除该结点
template 
HuffmanNode *MinHeap::getMin() {
    if(CurrentSize == 0) {
        cout << "堆已空!" << endl;
        return NULL;
    }
    HuffmanNode *newNode = new HuffmanNode();
    if(newNode == NULL) {
        cerr << "存储空间分配失败！" << endl;
        exit(1);
    }
    *newNode = heap[0]; // 将最小结点的数据复制给newNode
    heap[0] = heap[CurrentSize-1]; // 用最后一个元素填补
    CurrentSize--;
    ShiftDown(0, CurrentSize-1); // 从0位置开始向下调整
    return newNode;
}

// 向上调整
template 
void MinHeap::ShiftUp(int start) {
    // 从start开始，直到0或者当前值大于双亲结点的值时，调整堆
    int j = start, i = (j-1)/2; // i是j的双亲
    
    HuffmanNode temp = heap[j];
    while(j > 0) {
        if(heap[i].weight <= temp.weight)
            break;
        else {
            heap[j] = heap[i];
            j = i;
            i = (j - 1) / 2;
        }
    }
    heap[j] = temp;
}

// 向下调整
template 
void MinHeap::ShiftDown(int start, int m) {
    int i = start, j = 2 * i + 1; // j是i的左子女
    
    HuffmanNode temp = heap[i];
    while(j <= m) {
        if(j < m && heap[j].weight > heap[j+1].weight)
            j++; // 选两个子女中较小者
        if(temp.weight <= heap[j].weight)
            break;
        else {
            heap[i] = heap[j];
            i = j;
            j = 2 * j + 1;
        }
    }
    heap[i] = temp;
}


#endif /* HuffmanMinHeap_h */

3.哈夫曼树实现：HuffmanTree.h

#ifndef HuffmanTree_h
#define HuffmanTree_h


#include "HuffmanMinHeap.h"
#include "HuffmanNode.h"

template 
class HuffmanTree {
public:
    HuffmanTree(); // 构造函数
    ~HuffmanTree(); // 析构函数
    void Create(T w[], int n); // 创建哈夫曼树
    void Merge(HuffmanNode *first, HuffmanNode *second, HuffmanNode *parent); // 合并
    void PreOrder(); // 前序遍历Huffman树
private:
    HuffmanNode *root; // 根结点
    void Destroy(HuffmanNode *current); // 销毁哈夫曼树
    void PreOrder(HuffmanNode *current); // 前序遍历Huffman树
};

// 构造函数
template 
HuffmanTree::HuffmanTree() {
    root = NULL;
}

// 析构函数
template 
HuffmanTree::~HuffmanTree() {
    Destroy(root); // 销毁哈夫曼树
}

// 销毁哈夫曼树
template 
void HuffmanTree::Destroy(HuffmanNode *current) {
    if(current != NULL) { // 不为空
        Destroy(current->leftChild); // 递归销毁左子树
        Destroy(current->rightChild); // 递归销毁右子树
        delete current; // 释放空间
        current = NULL;
    }
}

// 创建哈夫曼树
template 
void HuffmanTree::Create(T w[], int n) {
    int i;
    MinHeap hp; // 使用最小堆存放森林
    HuffmanNode *first, *second, *parent = NULL;
    HuffmanNode*work = new HuffmanNode();
    
    if(work == NULL) {
        cerr << "存储空间分配失败！" << endl;
        exit(1);
    }
    for(i = 0; i < n; i++) {
        work->weight = w[i];
        work->leftChild = work->rightChild = work->parent = NULL;
        hp.Insert(work); // 插入到最小堆中
    }
    for(i=0; i < n-1; i++) { // 做n-1趟，形成Huffman树
        first = hp.getMin(); // 获取权值最小的树
        second = hp.getMin(); // 获取权值次小的树
        parent = new HuffmanNode();
        if(parent == NULL) {
            cerr << "存储空间分配失败！" << endl;
            exit(1);
        }
        Merge(first, second, parent); // 合并
        hp.Insert(parent); // 重新插入到最小堆中
    }
    root = parent; // 根结点
}
// 合并
template 
void HuffmanTree::Merge(HuffmanNode *first, HuffmanNode *second, HuffmanNode *parent) {
    parent->leftChild = first; // 左子树
    parent->rightChild = second; // 右子树
    parent->weight = first->weight + second->weight; // 父结点权值
    first->parent = second->parent = parent; // 父指针
}

// 前序遍历Huffman树
template 
void HuffmanTree::PreOrder() {
    PreOrder(root);
}

// 前序遍历Huffman树
template 
void HuffmanTree::PreOrder(HuffmanNode *current) {
    if(current != NULL) {
        cout << current->weight << " "; // 访问当前结点数据
        PreOrder(current->leftChild); // 递归遍历左子树
        PreOrder(current->rightChild); // 递归遍历右子树
    }
}
#endif /* HuffmanTree_h */

4.测试：main.cpp

#include "HuffmanTree.h"

int main(int argc, const char * argv[]) {
    int arr[] = {7, 5, 2, 4};
    int len = sizeof(arr) / sizeof(arr[0]); // 数组长度
    HuffmanTree tree; // Huffman树的对象
    
    tree.Create(arr, len); // 创建Huffman树
    tree.PreOrder(); // 前序遍历Huffman树
    return 0;
}

测试结果：