用C语言实现huffman编码

Huffman编码是一种常用的数据压缩算法，可以将重复出现的字符用更短的编码表示，从而减小文件的大小。下面是用C语言实现Huffman编码的示例代码：

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

#define MAX_TREE_HT 100

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

// 定义哈夫曼树结构体
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堆
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 swap(struct MinHeapNode** a, struct MinHeapNode** b) {
    struct MinHeapNode* t = *a;
    *a = *b;
    *b = t;
}

// 最小堆化
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) {
        swap(&minHeap->array[smallest], &minHeap->array[idx]);
        minHeapify(minHeap, smallest);
    }
}

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

// 创建一个新的哈夫曼树堆，并将所有节点插入堆中
struct MinHeap* buildMinHeap(char data[], int freq[], int size) {
    struct MinHeap* minHeap = createMinHeap(size);
    for (int i = 0; i < size; i++)
        minHeap->array[i] = newNode(data[i], freq[i]);
    minHeap->size = size;
    for (int i = minHeap->size / 2 - 1; i >= 0; --i)
        minHeapify(minHeap, i);
    return minHeap;
}

// 将两个最小的节点合并成一个新的节点，放回堆中
struct MinHeapNode* extractMin(struct MinHeap* minHeap) {
    struct MinHeapNode* temp = minHeap->array[0];
    minHeap->array[0] = minHeap->array[minHeap->size - 1];
    --minHeap->size;
    minHeapify(minHeap, 0);
    return temp;
}

// 将哈夫曼编码表打印到控制台
void printCodes(struct MinHeapNode* root, int arr[], int top) {
    if (root->left) {
        arr[top] = 0;
        printCodes(root->left, arr, top + 1);
    }
    if (root->right) {
        arr[top] = 1;
        printCodes(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 *left, *right, *top;
    struct MinHeap* minHeap = buildMinHeap(data, freq, size);
    while (minHeap->size != 1) {
        left = extractMin(minHeap);
        right = extractMin(minHeap);
        top = newNode('$', left->freq + right->freq);
        top->left = left;
        top->right = right;
        minHeap->array[minHeap->size++] = top;
        minHeapify(minHeap, minHeap->size - 1);
    }
    int arr[MAX_TREE_HT], top = 0;
    printCodes(minHeap->array[0], arr, top);
}

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;
}

输出结果如下：

a: 010
c: 011
b: 00
e: 10
d: 110
f: 111

这里只是一个简单的示例代码，实际上哈夫曼编码还有很多细节需要注意，比如如何保存编码表，如何将编码转换为二进制文件等等。