用c语言哈夫曼编码和译码

以下是使用C语言实现哈夫曼编码和译码的示例代码，其中包含注释说明：

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

#define MAX_TREE_HT 100

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

// 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* temp = (struct MinHeapNode*)malloc(sizeof(struct MinHeapNode));
    temp->left = temp->right = NULL;
    temp->data = data;
    temp->freq = freq;
    return temp;
}

// 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;
}

// 维护最小堆的性质
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);
    }
}

// 判断堆是否只有一个节点
int isSizeOne(struct MinHeap* minHeap) {
    return (minHeap->size == 1);
}

// 从堆中取出最小的节点
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;
}

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

// 创建一个新的哈夫曼树
struct MinHeap* createAndBuildMinHeap(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 - 1) / 2; i >= 0; --i)
        minHeapify(minHeap, i);
    return minHeap;
}

// 构建哈夫曼树
struct MinHeapNode* buildHuffmanTree(char data[], int freq[], int size) {
    struct MinHeapNode *left, *right, *top;
    struct MinHeap* minHeap = createAndBuildMinHeap(data, freq, size);
    while (!isSizeOne(minHeap)) {
        left = extractMin(minHeap);
        right = extractMin(minHeap);
        top = newNode('$', left->freq + right->freq);
        top->left = left;
        top->right = right;
        insertMinHeap(minHeap, top);
    }
    return extractMin(minHeap);
}

// 打印哈夫曼编码
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* root = buildHuffmanTree(data, freq, size);
    int arr[MAX_TREE_HT], top = 0;
    printCodes(root, arr, top);
}

// 哈夫曼译码主函数
void decodeHuffman(struct MinHeapNode* root, char* s) {
    struct MinHeapNode* curr = root;
    while (*s) {
        if (*s == '0')
            curr = curr->left;
        else
            curr = curr->right;
        if (isLeaf(curr)) {
            printf("%c", curr->data);
            curr = root;
        }
        ++s;
    }
}

// 计算信源熵
float calculateEntropy(int freq[], int size) {
    float entropy = 0.0;
    int total = 0;
    for (int i = 0; i < size; ++i)
        total += freq[i];
    for (int i = 0; i < size; ++i) {
        float p = (float)freq[i] / total;
        entropy -= p * log2(p);
    }
    return entropy;
}

// 计算平均编码长度
float calculateAvgCodeLength(int freq[], int size, int codes[][MAX_TREE_HT]) {
    float avgCodeLength = 0.0;
    int total = 0;
    for (int i = 0; i < size; ++i)
        total += freq[i];
    for (int i = 0; i < size; ++i) {
        float p = (float)freq[i] / total;
        int len = strlen((char*)codes[i]);
        avgCodeLength += p * len;
    }
    return avgCodeLength;
}

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]);
    printf("Huffman Codes:\n");
    HuffmanCodes(data, freq, size);
    printf("\n");
    char str[] = "101010000111110101011100";
    printf("Decoded Huffman data: ");
    decodeHuffman(buildHuffmanTree(data, freq, size), str);
    printf("\n");
    printf("Entropy: %f\n", calculateEntropy(freq, size));
    int codes[size][MAX_TREE_HT];
    for (int i = 0; i < size; ++i)
        memset(codes[i], 0, sizeof(codes[i]));
    int arr[MAX_TREE_HT], top = 0;
    printCodes(buildHuffmanTree(data, freq, size), arr, top);
    printf("Average Code Length: %f\n", calculateAvgCodeLength(freq, size, codes));
    return 0;
}