0. 序

• 本以为用最小堆实现个哈夫曼树是个简单的事情，结果一不小心就花了好几个小时才写完。。。实现过程中主要有三个方面的问题没注意，导致花了很多时间进行调试。
  • 一是多重指针malloc分配时要多加注意；
  • 二是指针一定要记得初始化，默认不一定为NULL；
  • 三是结构体赋值问题。
• 其余的边界问题小心就好了。。另，由于本人水平有限，如有任何问题，欢迎指出解决，谢谢大家！详细结果如下：

1. 哈夫曼树结构定义如下：

// 定义哈夫曼树结构
struct TreeNode {int weight;TreeNode* lChild;TreeNode* rChild;
};

2. 最小堆结构定义如下：

// 定义最小堆结构
struct MinHeap {TreeNode* p;    // 指向存储元素的数组int size;       // 当前元素个数int capacity;   // 最大容量
};

3. 基本操作函数如下：

• MinHeap* createMinHeap(int capacity); // 创建最小堆
• bool isFull(MinHeap* minHeap); // 判断最小堆是否已满）
• void printMinHeap(MinHeap* minHeap); // 遍历最小堆元素
• void insertMinHeap(MinHeap* minHeap, TreeNode* node); // 插入元素
• void minHeapAdjust(MinHeap* minHeap, int parent); // 最小堆调整
• void buildMinHeap(MinHeap* minHeap); // 调整法建立最小堆（n）
• bool isEmpty(MinHeap* minHeap); // 判断最小堆是否为空
• TreeNode* deleteMin(MinHeap* minHeap); // 删除最小元素并返回
• void preOrderTraverse(TreeNode* head); // 先序遍历（递归）
• TreeNode* buildHuffmanTree(MinHeap* minHeap); // 构造哈夫曼树

4. 具体代码实现如下：

#include <iostream>using namespace std;#define MinData -100000
#define SIZE 10// 定义哈夫曼树结构
struct TreeNode {int weight;TreeNode* lChild;TreeNode* rChild;
};// 定义最小堆结构
struct MinHeap {TreeNode* p;    // 指向存储元素的数组int size;       // 当前元素个数int capacity;   // 最大容量
};// 创建最小堆
MinHeap* createMinHeap(int capacity) {MinHeap* minHeap = (MinHeap*)malloc(sizeof(MinHeap));minHeap->p = (TreeNode*)malloc((capacity + 1)* sizeof(TreeNode));minHeap->size = 0;minHeap->capacity = capacity;minHeap->p[0].weight = MinData;minHeap->p[0].lChild = NULL;minHeap->p[0].rChild = NULL;return minHeap;
}// 判断最小堆是否已满
bool isFull(MinHeap* minHeap) {if (minHeap->size == minHeap->capacity) {return true;}return false;
}// 遍历最小堆元素
void printMinHeap(MinHeap* minHeap) {if (minHeap == NULL) {cout << "The min heap is not created." << endl;return;}for (int i = 0; i < minHeap->size; i++) {cout << minHeap->p[i + 1].weight << " ";}cout << endl;
}// 插入元素
void insertMinHeap(MinHeap* minHeap, TreeNode* node) {if (minHeap == NULL) {cout << "The min heap is not created." << endl;return;}if (isFull(minHeap)) {cout << "The min heap is full." << endl;return;}int i = ++(minHeap->size);for (; minHeap->p[i / 2].weight > node->weight; i /= 2) {minHeap->p[i].weight = minHeap->p[i / 2].weight;minHeap->p[i].lChild = minHeap->p[i / 2].lChild;minHeap->p[i].rChild = minHeap->p[i / 2].rChild;}minHeap->p[i].weight = node->weight;minHeap->p[i].lChild = node->lChild;minHeap->p[i].rChild = node->rChild;
}// 最小堆调整
void minHeapAdjust(MinHeap* minHeap, int parent) {int temp = minHeap->p[parent].weight;int child = 0;for (; parent * 2 <= minHeap->size; parent = child) {child = parent * 2;if (child < minHeap->size && minHeap->p[child + 1].weight < minHeap->p[child].weight) {child++;}if (temp <= minHeap->p[child].weight) {break;}else {minHeap->p[parent].weight = minHeap->p[child].weight;}}minHeap->p[parent].weight = temp;
}// 调整法建立最小堆（n）
void buildMinHeap(MinHeap* minHeap) {for (int i = minHeap->size / 2; i > 0; i--) {minHeapAdjust(minHeap, i);}
}// 判断最小堆是否为空
bool isEmpty(MinHeap* minHeap) {if (minHeap->size == 0) {return true;}return false;
}// 删除最小元素并返回
TreeNode* deleteMin(MinHeap* minHeap) {if (minHeap == NULL) {cout << "The min heap is not created." << endl;return 0;}if (isEmpty(minHeap)) {cout << "The min heap is empty." << endl;return 0;}TreeNode* minNode = (TreeNode*)malloc(sizeof(TreeNode));minNode->weight = minHeap->p[1].weight;minNode->lChild = minHeap->p[1].lChild;minNode->rChild = minHeap->p[1].rChild;int last = minHeap->p[minHeap->size--].weight;int parent = 0;int child = 0;for (parent = 1; parent * 2 <= minHeap->size; parent = child) {child = parent * 2;if (child != minHeap->size && minHeap->p[child + 1].weight < minHeap->p[child].weight) {child++;}if (last < minHeap->p[child].weight) {break;}else {minHeap->p[parent].weight = minHeap->p[child].weight;minHeap->p[parent].lChild = minHeap->p[child].lChild;minHeap->p[parent].rChild = minHeap->p[child].rChild;}}minHeap->p[parent].weight = last;minHeap->p[parent].lChild = minHeap->p[minHeap->size + 1].lChild;minHeap->p[parent].rChild = minHeap->p[minHeap->size + 1].rChild;return minNode;
}// 先序遍历（递归）
void preOrderTraverse(TreeNode* head) {if (head) {cout << head->weight << " ";preOrderTraverse(head->lChild);preOrderTraverse(head->rChild);}
}// 构造哈夫曼树
TreeNode* buildHuffmanTree(MinHeap* minHeap) {TreeNode* huffmanTreeNode = NULL;buildMinHeap(minHeap);for (int i = 0; i < minHeap->capacity - 1; i++) {huffmanTreeNode = (TreeNode*)malloc(sizeof(TreeNode));huffmanTreeNode->lChild = deleteMin(minHeap); huffmanTreeNode->rChild = deleteMin(minHeap); huffmanTreeNode->weight = huffmanTreeNode->lChild->weight + huffmanTreeNode->rChild->weight;insertMinHeap(minHeap, huffmanTreeNode);}huffmanTreeNode = deleteMin(minHeap);return huffmanTreeNode;
}int main() {MinHeap* minHeap = NULL;minHeap = createMinHeap(SIZE);for (int i = 0; i < SIZE; i++) {minHeap->p[i + 1].weight = SIZE - i;minHeap->p[i + 1].lChild = NULL;minHeap->p[i + 1].rChild = NULL;minHeap->size++;}cout << "原始数据序列：" << endl;printMinHeap(minHeap);buildMinHeap(minHeap);cout << "最小堆数据序列：" << endl;printMinHeap(minHeap);TreeNode* huffumanTree = NULL;huffumanTree = buildHuffmanTree(minHeap);cout << "哈夫曼树先序遍历序列：" << endl;preOrderTraverse(huffumanTree);cout << endl;system("pause");return 0;
}

5. 运行结果截图如下：

6. 哈夫曼树构造如下：