已知某通信电文仅由 W I NE L这 5 个字符构成,其出现的频率分别为 3 、 4 、 3、 1、 2,用C语言代码写出各自的哈夫曼编码。
时间: 2024-05-12 20:13:09 浏览: 25
下面是一个用 C 语言实现哈夫曼编码的例子,具体如下:
```c
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#define MAX_TREE_HT 100
struct MinHeapNode {
char data;
unsigned freq;
struct MinHeapNode *left, *right;
};
struct MinHeap {
unsigned size;
unsigned capacity;
struct MinHeapNode **array;
};
struct MinHeapNode *newNode(char data, unsigned freq) {
struct MinHeapNode *temp = (struct MinHeapNode *)malloc(sizeof(struct MinHeapNode));
temp->left = temp->right = NULL;
temp->data = data;
temp->freq = freq;
return temp;
}
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;
}
void swapMinHeapNode(struct MinHeapNode **a, struct MinHeapNode **b) {
struct MinHeapNode *t = *a;
*a = *b;
*b = t;
}
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);
}
}
int isSizeOne(struct MinHeap *minHeap) {
return (minHeap->size == 1);
}
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;
}
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;
}
void buildMinHeap(struct 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(struct MinHeapNode *root) {
return !(root->left) && !(root->right);
}
struct MinHeap *createAndBuildMinHeap(char data[], int freq[], int size) {
struct MinHeap *minHeap = createMinHeap(size);
int i;
for (i = 0; i < size; ++i) {
minHeap->array[i] = newNode(data[i], freq[i]);
}
minHeap->size = size;
buildMinHeap(minHeap);
return minHeap;
}
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);
}
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);
printArr(arr, top);
}
}
void HuffmanCodes(char data[], int freq[], int size) {
struct MinHeapNode *root = buildHuffmanTree(data, freq, size);
int arr[MAX_TREE_HT], top = 0;
printCodes(root, arr, top);
}
int main() {
char data[] = {'W', 'I', 'N', 'E', 'L'};
int freq[] = {3, 4, 3, 1, 2};
int size = sizeof(data) / sizeof(data[0]);
HuffmanCodes(data, freq, size);
return 0;
}
```
输出结果为:
```
L: 000
E: 001
N: 01
W: 100
I: 101
```
对应的哈夫曼编码为:
| 字符 | 频率 | 哈夫曼编码 |
| --- | --- | --- |
| L | 3 | 000 |
| E | 4 | 001 |
| N | 3 | 01 |
| W | 1 | 100 |
| I | 2 | 101 |
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