用C语言利用Huffman树和Huffman编码实现一个无损数据压缩程序

好的，这是一个非常有趣的问题。实现一个基于Huffman树和Huffman编码的无损数据压缩程序，可以分为以下几个步骤：

1. 统计每个字符出现的频率，构建Huffman树

首先，需要对待压缩的数据进行遍历，统计每个字符出现的频率。然后，使用这些频率构建Huffman树。这个过程可以使用堆来实现，具体实现可以参考哈夫曼编码的构造算法。

2. 生成Huffman编码表

构建好Huffman树之后，可以根据Huffman树的特性，生成每个字符对应的Huffman编码。具体实现可以使用递归的方式，在遍历Huffman树的过程中生成Huffman编码表。

3. 将数据进行压缩

有了Huffman编码表之后，就可以对待压缩的数据进行压缩了。具体实现可以将数据中的每个字符替换成对应的Huffman编码，然后将所有的编码拼接在一起，形成一个二进制字符串。

4. 将压缩后的数据写入文件

最后，将压缩后的二进制字符串写入文件中即可。

这里提供一份参考代码，仅供参考：

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#define MAX_CHAR_NUM 256
#define MAX_BIT_NUM 1000000

typedef struct TreeNode {
    unsigned char data; // 存储字符
    int freq;           // 存储字符出现的频率
    struct TreeNode *left;
    struct TreeNode *right;
} TreeNode;

typedef struct Heap {
    int size;
    TreeNode *data[MAX_CHAR_NUM*2];
} Heap;

typedef struct HuffmanCode {
    unsigned char data;
    char code[MAX_BIT_NUM];
} HuffmanCode;

void swap(TreeNode **a, TreeNode **b) {
    TreeNode *temp = *a;
    *a = *b;
    *b = temp;
}

void minHeapify(Heap *heap, int index) {
    int left = index * 2, right = index * 2 + 1, smallest = index;
    if (left <= heap->size && heap->data[left]->freq < heap->data[smallest]->freq)
        smallest = left;
    if (right <= heap->size && heap->data[right]->freq < heap->data[smallest]->freq)
        smallest = right;
    if (smallest != index) {
        swap(&heap->data[index], &heap->data[smallest]);
        minHeapify(heap, smallest);
    }
}

void buildMinHeap(Heap *heap) {
    int i;
    for (i = heap->size / 2; i >= 1; i--)
        minHeapify(heap, i);
}

TreeNode *createTreeNode(unsigned char data, int freq) {
    TreeNode *newNode = (TreeNode*) malloc(sizeof(TreeNode));
    newNode->data = data;
    newNode->freq = freq;
    newNode->left = NULL;
    newNode->right = NULL;
    return newNode;
}

Heap *createHeap() {
    Heap *newHeap = (Heap*) malloc(sizeof(Heap));
    newHeap->size = 0;
    return newHeap;
}

void insertHeap(Heap *heap, TreeNode *node) {
    heap->size++;
    heap->data[heap->size] = node;
    int i = heap->size;
    while (i > 1 && heap->data[i]->freq < heap->data[i/2]->freq) {
        swap(&heap->data[i], &heap->data[i/2]);
        i = i / 2;
    }
}

TreeNode *deleteMin(Heap *heap) {
    TreeNode *minNode = heap->data[1];
    heap->data[1] = heap->data[heap->size];
    heap->size--;
    minHeapify(heap, 1);
    return minNode;
}

TreeNode *buildHuffmanTree(int freq[]) {
    int i;
    Heap *heap = createHeap();
    for (i = 0; i < MAX_CHAR_NUM; i++)
        if (freq[i] > 0)
            insertHeap(heap, createTreeNode(i, freq[i]));
    buildMinHeap(heap);
    while (heap->size > 1) {
        TreeNode *left = deleteMin(heap);
        TreeNode *right = deleteMin(heap);
        TreeNode *parent = createTreeNode('$', left->freq + right->freq);
        parent->left = left;
        parent->right = right;
        insertHeap(heap, parent);
    }
    return deleteMin(heap);
}

void generateHuffmanCode(TreeNode *root, char code[], int depth, HuffmanCode huffmanCodes[]) {
    if (root->left == NULL && root->right == NULL) {
        huffmanCodes[root->data].data = root->data;
        strcpy(huffmanCodes[root->data].code, code);
        return;
    }
    code[depth] = '0';
    generateHuffmanCode(root->left, code, depth+1, huffmanCodes);
    code[depth] = '1';
    generateHuffmanCode(root->right, code, depth+1, huffmanCodes);
}

void compressFile(char *inputFile, char *outputFile, HuffmanCode huffmanCodes[]) {
    FILE *fin = fopen(inputFile, "rb");
    FILE *fout = fopen(outputFile, "wb");
    int freq[MAX_CHAR_NUM], i;
    memset(freq, 0, sizeof(freq));
    unsigned char c;
    while (fread(&c, 1, 1, fin) > 0)
        freq[c]++;
    fseek(fin, 0, SEEK_SET);
    TreeNode *root = buildHuffmanTree(freq);
    char code[MAX_BIT_NUM];
    generateHuffmanCode(root, code, 0, huffmanCodes);
    int bitCount = 0;
    char buffer = 0;
    while (fread(&c, 1, 1, fin) > 0) {
        for (i = 0; i < strlen(huffmanCodes[c].code); i++) {
            buffer = buffer << 1;
            if (huffmanCodes[c].code[i] == '1')
                buffer |= 1;
            bitCount++;
            if (bitCount == 8) {
                fwrite(&buffer, 1, 1, fout);
                bitCount = 0;
                buffer = 0;
            }
        }
    }
    if (bitCount > 0) {
        buffer = buffer << (8 - bitCount);
        fwrite(&buffer, 1, 1, fout);
    }
    fclose(fin);
    fclose(fout);
}

void decompressFile(char *inputFile, char *outputFile, TreeNode *root) {
    FILE *fin = fopen(inputFile, "rb");
    FILE *fout = fopen(outputFile, "wb");
    unsigned char c;
    TreeNode *p = root;
    while (fread(&c, 1, 1, fin) > 0) {
        int i;
        for (i = 7; i >= 0; i--) {
            if ((c & (1 << i)) == 0)
                p = p->left;
            else
                p = p->right;
            if (p->left == NULL && p->right == NULL) {
                fwrite(&p->data, 1, 1, fout);
                p = root;
            }
        }
    }
    fclose(fin);
    fclose(fout);
}

int main() {
    char inputFile[] = "input.txt";
    char compressedFile[] = "compressed.bin";
    char decompressedFile[] = "decompressed.txt";
    HuffmanCode huffmanCodes[MAX_CHAR_NUM];
    memset(huffmanCodes, 0, sizeof(huffmanCodes));
    compressFile(inputFile, compressedFile, huffmanCodes);
    TreeNode *root = buildHuffmanTree(NULL);
    decompressFile(compressedFile, decompressedFile, root);
    return 0;
}

这份代码使用了堆来构建Huffman树，使用了递归的方式来生成Huffman编码表，并且实现了对文件进行压缩和解压缩的功能。需要注意的是，对于一个字符集大小为N的情况，Huffman树的构建时间复杂度为O(NlogN)，压缩和解压缩的时间复杂度也为O(NlogN)。