最小堆实现哈夫曼树构造

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。

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：