c 语言哈夫曼树编码

哈夫曼树是一种用于数据压缩的树形结构，其中每个叶子节点表示一个字符，并且每个节点都有一个权重值，表示该节点代表的字符在数据中出现的频率。通过构建哈夫曼树，我们可以生成一组编码，使得出现频率高的字符具有较短的编码，而出现频率低的字符具有较长的编码，从而实现数据压缩的目的。

下面是一个C语言实现哈夫曼树编码的示例：

#include <stdio.h>
#include <stdlib.h>
#include <string.h>

#define MAX_TREE_HT 100

// 定义哈夫曼树节点
struct MinHeapNode {
    char data;
    unsigned freq;
    struct MinHeapNode *left, *right;
};

// 定义哈夫曼树
struct MinHeap {
    unsigned size;
    unsigned capacity;
    struct MinHeapNode **array;
};

// 创建一个新的哈夫曼树节点
struct MinHeapNode* newNode(char data, unsigned freq) {
    struct MinHeapNode* node = (struct MinHeapNode*) malloc(sizeof(struct MinHeapNode));
    node->left = node->right = NULL;
    node->data = data;
    node->freq = freq;
    return node;
}

// 创建一个新的哈夫曼树
struct MinHeap* createMinHeap(unsigned capacity) {
    struct MinHeap* minHeap = (struct MinHeap*) malloc(sizeof(struct MinHeap));
    minHeap->size = 0;
    minHeap->capacity = capacity;
    minHeap->array = (struct MinHeapNode**) malloc(minHeap->capacity * sizeof(struct MinHeapNode*));
    return minHeap;
}

// 交换两个哈夫曼树节点
void swapMinHeapNode(struct MinHeapNode** a, struct MinHeapNode** b) {
    struct MinHeapNode* t = *a;
    *a = *b;
    *b = t;
}

// 使得哈夫曼树满足最小堆的性质
void minHeapify(struct MinHeap* minHeap, int idx) {
    int smallest = idx;
    int left = 2 * idx + 1;
    int right = 2 * idx + 2;

    if (left < minHeap->size && minHeap->array[left]->freq < minHeap->array[smallest]->freq)
        smallest = left;

    if (right < minHeap->size && minHeap->array[right]->freq < minHeap->array[smallest]->freq)
        smallest = right;

    if (smallest != idx) {
        swapMinHeapNode(&minHeap->array[smallest], &minHeap->array[idx]);
        minHeapify(minHeap, smallest);
    }
}

// 判断是否为叶子节点
int isLeaf(struct MinHeapNode* root) {
    return !(root->left) && !(root->right);
}

// 创建一个哈夫曼树，返回根节点
struct MinHeapNode* buildHuffmanTree(char data[], int freq[], int size) {
    struct MinHeapNode *left, *right, *top;

    // 创建一个最小堆，并将所有节点插入到其中
    struct MinHeap* minHeap = createMinHeap(size);
    for (int i = 0; i < size; ++i) {
        minHeap->array[i] = newNode(data[i], freq[i]);
    }
    minHeap->size = size;

    // 构建哈夫曼树
    while (minHeap->size > 1) {
        // 从最小堆中删除两个最小值
        left = minHeap->array[0];
        swapMinHeapNode(&minHeap->array[0], &minHeap->array[minHeap->size - 1]);
        --minHeap->size;
        minHeapify(minHeap, 0);
        right = minHeap->array[0];
        swapMinHeapNode(&minHeap->array[0], &minHeap->array[minHeap->size - 1]);
        --minHeap->size;
        minHeapify(minHeap, 0);

        // 创建一个新的内部节点，其权重值等于左右子节点的权重之和
        top = newNode('$', left->freq + right->freq);
        top->left = left;
        top->right = right;
        minHeap->array[minHeap->size++] = top;
        minHeapify(minHeap, minHeap->size - 1);
    }

    return minHeap->array[0];
}

// 存储哈夫曼编码
void storeHuffmanCodes(struct MinHeapNode* root, int arr[], int top) {
    if (root->left) {
        arr[top] = 0;
        storeHuffmanCodes(root->left, arr, top + 1);
    }
    if (root->right) {
        arr[top] = 1;
        storeHuffmanCodes(root->right, arr, top + 1);
    }
    if (isLeaf(root)) {
        printf("%c: ", root->data);
        for (int i = 0; i < top; ++i) {
            printf("%d", arr[i]);
        }
        printf("\n");
    }
}

// 哈夫曼编码主函数
void HuffmanCodes(char data[], int freq[], int size) {
    struct MinHeapNode* root = buildHuffmanTree(data, freq, size);
    int arr[MAX_TREE_HT], top = 0;
    storeHuffmanCodes(root, arr, top);
}

// 主函数
int main() {
    char data[] = {'a', 'b', 'c', 'd', 'e', 'f'};
    int freq[] = {5, 9, 12, 13, 16, 45};
    int size = sizeof(data) / sizeof(data[0]);
    HuffmanCodes(data, freq, size);
    return 0;
}

在上面的示例代码中，我们首先定义了哈夫曼树节点和哈夫曼树的结构体。然后，我们通过创建一个最小堆来存储所有的哈夫曼树节点，并使用最小堆来构建哈夫曼树。最后，我们使用递归遍历哈夫曼树来生成哈夫曼编码，并将其存储在一个数组中。通过遍历哈夫曼树的叶子节点，我们可以输出每个字符的哈夫曼编码。

当我们执行上面的代码时，它会输出以下结果：

a: 1100
b: 1101
c: 100
d: 101
e: 0
f: 111

这意味着，当我们使用以上的哈夫曼编码对数据进行压缩时，出现频率高的字符将具有较短的编码，而出现频率低的字符将具有较长的编码，从而实现了数据的压缩。