设计实现一个基于哈夫曼算法的压缩软件，统计文件中各字符出现的频次，设计哈夫曼编码，实现文件的压缩及解压缩。将建立哈夫曼树、实现哈夫曼编码、哈夫曼译码都定义成子函数的形式，用c语言写出并写出详细注释

以下是基于哈夫曼算法的压缩软件的具体实现步骤：

1. 统计文件中各字符出现的频次

可以使用一个数组来记录每个字符出现的次数，遍历整个文件，对于每个读取到的字符，将其对应的计数器加一。

2. 构建哈夫曼树

首先将每个字符的出现频次作为权值，构建一个森林，每个节点为一个单独的树。接着按照权值从小到大的顺序选择两个树合并成一棵更大的树，直到最后只剩下一棵树，这棵树就是哈夫曼树。

3. 实现哈夫曼编码

从根节点出发，对于每个左子树的路径标记为 0，对于每个右子树的路径标记为 1，直到到达叶子节点，每个叶子节点对应一个字符的编码。将这些编码存储到一个编码表中，用于压缩文件时使用。

4. 实现文件压缩

首先将原始文件中的每个字符替换为其对应的哈夫曼编码，然后将编码后的文件写入到新的文件中。

5. 实现文件解压缩

对于压缩后的文件，读取其中的每个比特位，并从根节点开始，沿着哈夫曼树的路径寻找对应的字符，直到到达叶子节点。将找到的字符写入到解压缩后的文件中。

以下是具体的 C 语言实现代码：

#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;
};

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

// 创建一个哈夫曼树节点
struct MinHeapNode* createNode(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;
}

// 创建一个空的哈夫曼树堆
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;
}

// 交换两个节点的位置
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);
    }
}

// 检查堆的大小是否为 1
int isSizeOne(struct MinHeap* minHeap) {
    return (minHeap->size == 1);
}

// 抽取堆中最小的节点
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;
}

// 插入一个新的节点到堆中
void insertMinHeap(struct MinHeap* minHeap, struct MinHeapNode* minHeapNode) {
    ++minHeap->size;
    int i = minHeap->size - 1;

    while (i && minHeapNode->freq < minHeap->array[(i - 1) / 2]->freq) {
        minHeap->array[i] = minHeap->array[(i - 1) / 2];
        i = (i - 1) / 2;
    }

    minHeap->array[i] = minHeapNode;
}

// 构建哈夫曼树
struct MinHeapNode* buildHuffmanTree(char data[], int freq[], int size) {
    struct MinHeapNode *left, *right, *top;
    struct MinHeap* minHeap = createMinHeap(size);

    for (int i = 0; i < size; ++i)
        insertMinHeap(minHeap, createNode(data[i], freq[i]));

    while (!isSizeOne(minHeap)) {
        left = extractMin(minHeap);
        right = extractMin(minHeap);
        top = createNode('$', left->freq + right->freq);
        top->left = left;
        top->right = right;
        insertMinHeap(minHeap, top);
    }

    return extractMin(minHeap);
}

// 将编码写入到哈夫曼树编码表中
void storeCodes(struct MinHeapNode* root, int arr[], int top, int codes[][MAX_TREE_HT]) {
    if (root->left) {
        arr[top] = 0;
        storeCodes(root->left, arr, top + 1, codes);
    }

    if (root->right) {
        arr[top] = 1;
        storeCodes(root->right, arr, top + 1, codes);
    }

    if (!root->left && !root->right) {
        for (int i = 0; i < top; ++i)
            codes[(int) root->data][i] = arr[i];
    }
}

// 将字符串转换为比特流
void convertToBits(char* input, int* bits, int* size, int codes[][MAX_TREE_HT]) {
    int len = strlen(input);
    int bitIdx = 0;

    for (int i = 0; i < len; ++i) {
        int c = input[i];
        int j = 0;

        while (codes[c][j] != -1) {
            bits[bitIdx++] = codes[c][j++];
        }
    }

    *size = bitIdx;
}

// 将比特流转换为字符串
void convertToString(int* bits, int size, char* output, struct MinHeapNode* root) {
    struct MinHeapNode* p = root;
    int outIdx = 0;

    for (int i = 0; i < size; ++i) {
        if (bits[i] == 0)
            p = p->left;
        else
            p = p->right;

        if (!p->left && !p->right) {
            output[outIdx++] = p->data;
            p = root;
        }
    }

    output[outIdx] = '\0';
}

// 压缩文件
void compress(char* inputFile, char* outputFile) {
    FILE* fpIn = fopen(inputFile, "r");
    FILE* fpOut = fopen(outputFile, "wb");

    char data[MAX_TREE_HT], c;
    int freq[MAX_TREE_HT] = {0}, size = 0;
    int codes[MAX_TREE_HT][MAX_TREE_HT];
    int arr[MAX_TREE_HT];
    int bitSize = 0, bitIdx = 0;
    int bits[MAX_TREE_HT * MAX_TREE_HT];
    char buffer = 0;

    while ((c = fgetc(fpIn)) != EOF) {
        data[size++] = c;
        ++freq[(int) c];
    }

    struct MinHeapNode* root = buildHuffmanTree(data, freq, size);
    memset(codes, -1, sizeof(codes));
    storeCodes(root, arr, 0, codes);
    rewind(fpIn);

    while ((c = fgetc(fpIn)) != EOF) {
        int j = 0;

        while (codes[(int) c][j] != -1) {
            if (bitIdx == 8) {
                fwrite(&buffer, sizeof(buffer), 1, fpOut);
                buffer = 0;
                bitIdx = 0;
            }

            buffer <<= 1;
            buffer |= codes[(int) c][j];
            ++bitIdx;
            ++j;
        }
    }

    if (bitIdx > 0) {
        buffer <<= (8 - bitIdx);
        fwrite(&buffer, sizeof(buffer), 1, fpOut);
    }

    fclose(fpIn);
    fclose(fpOut);
}

// 解压缩文件
void decompress(char* inputFile, char* outputFile) {
    FILE* fpIn = fopen(inputFile, "rb");
    FILE* fpOut = fopen(outputFile, "w");

    char data[MAX_TREE_HT], c;
    int freq[MAX_TREE_HT] = {0}, size = 0;
    int codes[MAX_TREE_HT][MAX_TREE_HT];
    int arr[MAX_TREE_HT];
    int bitIdx = 0;
    int bits[MAX_TREE_HT * MAX_TREE_HT];
    char output[MAX_TREE_HT];
    int outIdx = 0;

    while (fread(&c, sizeof(c), 1, fpIn) != 0) {
        int i = 0;

        for (i = 7; i >= 0; --i) {
            int bit = (c >> i) & 1;
            bits[bitIdx++] = bit;

            if (bitIdx % 8 == 0) {
                convertToString(bits + outIdx, 8, output, root);
                outIdx += strlen(output);
                fwrite(output, sizeof(char), strlen(output), fpOut);
                outIdx = 0;
            }
        }
    }

    if (bitIdx % 8 != 0) {
        while (bitIdx % 8 != 0)
            bits[bitIdx++] = 0;

        convertToString(bits + outIdx, bitIdx - outIdx, output, root);
        fwrite(output, sizeof(char), strlen(output), fpOut);
    }

    fclose(fpIn);
    fclose(fpOut);
}

int main() {
    char inputFile[] = "input.txt";
    char compressedFile[] = "compressed.bin";
    char decompressedFile[] = "decompressed.txt";

    // 压缩文件
    compress(inputFile, compressedFile);

    // 解压缩文件
    decompress(compressedFile, decompressedFile);

    return 0;
}