基于哈夫曼树的数据压缩算法C语言

哈夫曼编码是一种数据压缩算法，可以将数据压缩成更小的数据量，以节省存储空间和传输带宽。下面是基于哈夫曼树的数据压缩算法的C语言实现：

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

#define MAX_TREE_HT 100
#define MAX_CHAR 256

//哈夫曼树的结构体
struct MinHeapNode {
    char data;
    int freq;
    struct MinHeapNode *left, *right;
};

struct MinHeap {
    int size;
    int capacity;
    struct MinHeapNode **array;
};

//创建一个新的哈夫曼树节点
struct MinHeapNode* newNode(char data, int freq) {
    struct MinHeapNode* node = (struct MinHeapNode*) malloc(sizeof(struct MinHeapNode));
    node->left = node->right = NULL;
    node->data = data;
    node->freq = freq;
    return node;
}

//创建一个新的最小堆
struct MinHeap* createMinHeap(int 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);
    }
}

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

//获取最小堆的最小节点
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;
}

//插入一个节点到最小堆
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;
}

//判断一个节点是否是叶子节点
int isLeaf(struct MinHeapNode* root) {
    return !(root->left) && !(root->right);
}

//创建一个最小堆，并将所有字符的频率作为节点的值
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);
}

//打印哈夫曼编码表
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");
    }
}

//压缩数据
void compress(char* input_string, char* output_string) {
    int freq[MAX_CHAR] = {0};
    int n = strlen(input_string);
    for (int i = 0; i < n; ++i)
        ++freq[input_string[i]];
    struct MinHeapNode* root = buildHuffmanTree(input_string, freq, MAX_CHAR);
    int arr[MAX_TREE_HT], top = 0;
    printCodes(root, arr, top);
    for (int i = 0; i < n; ++i) {
        int j;
        for (j = 0; j < MAX_CHAR; ++j)
            if (input_string[i] == root->data)
                break;
        int k = 0;
        while (k < top) {
            output_string[k++] = arr[j++];
        }
    }
}

int main() {
    char input_string[] = "Hello World";
    char output_string[MAX_TREE_HT];
    compress(input_string, output_string);
    printf("Compressed string: %s\n", output_string);
    return 0;
}

该算法主要包括以下步骤：

1. 创建一个哈夫曼树节点结构体，包括字符数据、字符出现频率、左子节点和右子节点。
2. 创建一个最小堆结构体，包括当前堆的大小、最大容量和哈夫曼树节点数组。
3. 实现最小堆的常用操作，包括维护最小堆性质、插入节点、获取最小节点等。
4. 构建哈夫曼树，将所有字符的频率作为节点的值，以最小堆的形式存储，并通过不断提取最小值构建哈夫曼树。
5. 打印哈夫曼编码表，遍历哈夫曼树，当遇到叶子节点时，输出该字符的编码。
6. 压缩数据，遍历输入字符串，找到对应字符的编码，并将编码存储到输出字符串中。

以上是哈夫曼编码的基本实现，实际应用中还需要考虑压缩文件头、解压缩等问题。