(数据结构)哈夫曼编码实现（C语言）

(数据结构)哈夫曼编码实现（C语言）

哈夫曼的编码:从一堆数组当中取出来最小的两个值，按照左下右大的进行绘制，将两个权值之和，放入队列当中，然后再进行取出两个小的，以此类推，直到全部结束，在根据图根节点，到叶子节点，每一个分支来得出编码，向左0，向右1，即可得到一个结果。

#include 
#include 

// 定义哈夫曼树结点的结构
struct Node {
    int frequency;
    char data;
    struct Node* left;
    struct Node* right;
};

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

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

// 创建最小堆
struct MinHeap* createMinHeap(int capacity) {
    struct MinHeap* minHeap = (struct MinHeap*)malloc(sizeof(struct MinHeap));
    minHeap->size = 0;
    minHeap->capacity = capacity;
    minHeap->array = (struct Node**)malloc(capacity * sizeof(struct Node*));
    return minHeap;
}

// 交换两个结点的位置
void swapNode(struct Node** a, struct Node** b) {
    struct Node* temp = *a;
    *a = *b;
    *b = temp;
}

// 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]->frequency < minHeap->array[smallest]->frequency) {
        smallest = left;
    }

    if (right < minHeap->size && minHeap->array[right]->frequency < minHeap->array[smallest]->frequency) {
        smallest = right;
    }

    if (smallest != idx) {
        swapNode(&minHeap->array[smallest], &minHeap->array[idx]);
        minHeapify(minHeap, smallest);
    }
}

// 检查最小堆是否只有一个元素
int isSizeOne(struct MinHeap* minHeap) {
    return minHeap->size == 1;
}

// 检查结点是否是叶子结点
int isLeaf(struct Node* root) {
    return !(root->left) && !(root->right);
}

// 从最小堆中提取最小值（即频率最小的结点）
struct Node* extractMin(struct MinHeap* minHeap) {
    struct Node* temp = minHeap->array[0];
    minHeap->array[0] = minHeap->array[minHeap->size - 1];
    --minHeap->size;
    minHeapify(minHeap, 0);
    return temp;
}

// 将结点插入最小堆
void insertMinHeap(struct MinHeap* minHeap, struct Node* node) {
    ++minHeap->size;
    int i = minHeap->size - 1;

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

    minHeap->array[i] = node;
}

// 构建哈夫曼树
struct Node* buildHuffmanTree(char data[], int frequency[], int size) {
    struct Node *left, *right, *top;
    // 创建一个最小堆并初始化
    struct MinHeap* minHeap = createMinHeap(size);

    // 向最小堆中插入结点
    for (int i = 0; i < size; i++) {
        insertMinHeap(minHeap, newNode(frequency[i], data[i]));
    }

    // 构建哈夫曼树
    while (!isSizeOne(minHeap)) {
        // 从最小堆中取出最小的两个结点作为左子树和右子树
        left = extractMin(minHeap);
        right = extractMin(minHeap);

        // 创建一个新的结点作为父结点
        top = newNode(left->frequency + right->frequency, '-');
        top->left = left;
        top->right = right;

        // 将父结点插入最小堆中
        insertMinHeap(minHeap, top);
    }

    // 最后剩下的结点就是哈夫曼树的根结点
    return extractMin(minHeap);
}

// 打印哈夫曼编码
void printHuffmanCodes(struct Node* root, int arr[], int top) {
    // 叶子结点是存有字符的结点
    if (root->left) {
        arr[top] = 0;
        printHuffmanCodes(root->left, arr, top + 1);
    }

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

    // 如果是叶子结点（没有左右子结点），则打印编码
    if (!root->left && !root->right) {
        printf("%c: ", root->data);
        for (int i = 0; i < top; i++) {
            printf("%d", arr[i]);
        }
        printf("\n");
    }
}

int main() {
    char data[] = { 'a', 'b', 'c', 'd', 'e' };
    int frequency[] = { 5, 9, 12, 13, 16 };
    int size = sizeof(data) / sizeof(data[0]);

    struct Node* root = buildHuffmanTree(data, frequency, size);

    int arr[100], top = 0;
    printHuffmanCodes(root, arr, top);

    return 0;
}