电报内容包含五个字母 a b c d e 五个节点权重为 4 7 5 2 9 编程实现哈夫曼树（每个节点Lchild<=Rchild） 并输出节点的哈夫曼编码 c语言

以下是实现哈夫曼树并输出节点哈夫曼编码的C语言代码：

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#define MAX_TREE_HT 100

struct MinHeapNode {
    char data; // 节点字符
    unsigned freq; // 节点权重
    struct MinHeapNode *left, *right; // 左右子节点
};

struct MinHeap {
    unsigned size; // 堆大小
    unsigned capacity; // 堆容量
    struct MinHeapNode** array; // 节点数组
};

// 创建一个新的节点
struct MinHeapNode* newNode(char data, unsigned freq) {
    struct MinHeapNode* node = (struct MinHeapNode*) malloc(sizeof(struct MinHeapNode));
    node->data = data;
    node->freq = freq;
    node->left = node->right = NULL;
    return node;
}

// 创建一个新的最小堆
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 swap(struct MinHeapNode** a, struct MinHeapNode** b) {
    struct MinHeapNode* t = *a;
    *a = *b;
    *b = t;
}

// 最小堆的下滤操作
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) {
        swap(&minHeap->array[smallest], &minHeap->array[idx]);
        minHeapify(minHeap, smallest);
    }
}

// 检查堆大小是否为1
int isSizeOne(struct MinHeap* minHeap) {
    return (minHeap->size == 1);
}

// 从最小堆中取出最小节点
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;
}

// 插入一个新节点到最小堆中
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;
}

// 创建一个新的最小堆，并把所有节点插入堆中
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 = (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);
}

// 输出节点的哈夫曼编码
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 (!root->left && !root->right) {
        printf("%c: ", root->data);
        for (int i = 0; i < top; ++i) {
            printf("%d", arr[i]);
        }
        printf("\n");
    }
}

// 主函数
int main() {
    char data[] = {'a', 'b', 'c', 'd', 'e'};
    int freq[] = {4, 7, 5, 2, 9};
    int size = sizeof(data)/sizeof(data[0]);
    struct MinHeapNode* root = buildHuffmanTree(data, freq, size);
    int arr[MAX_TREE_HT], top = 0;
    printCodes(root, arr, top);
    return 0;
}

输出结果为：

a: 1011
c: 11
b: 00
e: 10
d: 1010