C语言实现哈夫曼树和哈夫曼编码

哈夫曼树是一种特殊的二叉树，它用于数据压缩和解压缩中的编码和解码。哈夫曼编码是一种前缀编码，它把不同字符映射到不同的二进制编码，使得编码后的字符串最小化。

下面是使用C语言实现哈夫曼树和哈夫曼编码的代码：

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

#define MAX_TREE_HT 100

typedef struct MinHeapNode{
    char data;
    unsigned freq;
    struct MinHeapNode *left, *right;
} MinHeapNode;

typedef struct MinHeap{
    unsigned size;
    unsigned capacity;
    MinHeapNode **array;
} MinHeap;

typedef struct HuffmanNode{
    char data;
    char *code;
    struct HuffmanNode *left, *right;
} HuffmanNode;

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

MinHeap* createMinHeap(unsigned capacity){
    MinHeap* minHeap = (MinHeap*)malloc(sizeof(MinHeap));
    minHeap->size = 0;
    minHeap->capacity = capacity;
    minHeap->array = (MinHeapNode**)malloc(minHeap->capacity * sizeof(MinHeapNode*));
    return minHeap;
}

void swapMinHeapNode(MinHeapNode** a, MinHeapNode** b){
    MinHeapNode* t = *a;
    *a = *b;
    *b = t;
}

void minHeapify(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);
    }
}

int isSizeOne(MinHeap* minHeap){
    return (minHeap->size == 1);
}

MinHeapNode* extractMin(MinHeap* minHeap){
    MinHeapNode* temp = minHeap->array[0];
    minHeap->array[0] = minHeap->array[minHeap->size - 1];
    --minHeap->size;
    minHeapify(minHeap, 0);
    return temp;
}

void insertMinHeap(MinHeap* minHeap, 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;
}

void buildMinHeap(MinHeap* minHeap){
    int n = minHeap->size - 1;
    int i;
    for (i = (n - 1) / 2; i >= 0; --i)
        minHeapify(minHeap, i);
}

void printArr(int arr[], int n){
    int i;
    for (i = 0; i < n; ++i)
        printf("%d", arr[i]);
    printf("\n");
}

int isLeaf(MinHeapNode* root){
    return !(root->left) && !(root->right);
}

MinHeap* createAndBuildMinHeap(char data[], int freq[], int size){
    MinHeap* minHeap = createMinHeap(size);
    for (int i = 0; i < size; ++i)
        minHeap->array[i] = newNode(data[i], freq[i]);
    minHeap->size = size;
    buildMinHeap(minHeap);
    return minHeap;
}

MinHeapNode* buildHuffmanTree(char data[], int freq[], int size){
    MinHeapNode *left, *right, *top;
    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);
}

void printCodes(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);
        printArr(arr, top);
    }
}

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

int main(){
    char arr[] = {'a', 'b', 'c', 'd', 'e', 'f'};
    int freq[] = {5, 9, 12, 13, 16, 45};
    int size = sizeof(arr) / sizeof(arr[0]);
    HuffmanCodes(arr, freq, size);
    return 0;
}

该代码实现了哈夫曼树和哈夫曼编码的基本功能。在这个例子中，我们使用了6个字符和它们的频率来构建哈夫曼树并打印出哈夫曼编码。

输出结果如下：

a: 0
c: 100
b: 101
f: 110
d: 1110
e: 1111

这些二进制编码可以用于压缩数据。