Huffman 编码的编程与实现C语言

Huffman 编码是一种基于字符频率的压缩算法，将出现频率高的字符用较短的编码表示，出现频率低的字符用较长的编码表示，从而实现数据压缩。以下是 Huffman 编码的 C 语言实现：

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

#define MAX_TREE_HT 100

// Huffman树节点
struct MinHeapNode {
    char data;
    unsigned freq;
    struct MinHeapNode *left, *right;
};

// 建立一个最小堆
struct MinHeap {
    unsigned size;
    unsigned capacity;
    struct MinHeapNode** array;
};

// 创建一个节点
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;
}

// 创建一个最小堆
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
void swapMinHeapNode(struct MinHeapNode** a, struct MinHeapNode** b) {
    struct MinHeapNode* t = *a;
    *a = *b;
    *b = t;
}

// 最小堆的向下调整
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;
}

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

// 创建一个最小堆并构建Huffman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;

    while (!isSizeOne(minHeap)) {
        struct MinHeapNode* left = extractMin(minHeap);
        struct MinHeapNode* right = extractMin(minHeap);

        struct MinHeapNode* top =
            newNode('$', left->freq + right->freq);

        top->left = left;
        top->right = right;

        insertMinHeap(minHeap, top);
    }
    return minHeap;
}

// 递归地打印Huffman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");
    }
}

// Huffman编码
void HuffmanCodes(char data[], int freq[], int size) {
    struct MinHeapNode* root = createAndBuildMinHeap(data, freq, size);
    int arr[MAX_TREE_HT], top = 0;
    printCodes(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;
}

以上代码中，我们定义了 Huffman 树节点，最小堆和对应的操作。在主函数中，我们定义了一些字符和它们出现的频率，然后调用 HuffmanCodes 函数来生成对应的 Huffman 编码。在函数内部，我们首先创建一个包含所有字符节点的最小堆，然后构建 Huffman 树，并使用 printCodes 函数递归地计算每个字符的编码并打印出来。