把26个字母按哈夫曼编码
时间: 2023-06-12 20:07:33 浏览: 60
哈夫曼编码是一种变长编码,将出现频率较高的字符用较短的编码表示,出现频率较低的字符用较长的编码表示,以达到压缩数据的目的。下面是将26个字母按照出现频率从高到低排列,然后进行哈夫曼编码:
- E: 0
- A: 100
- O: 101
- I: 1100
- N: 1101
- R: 1110
- T: 1111
- S: 0100
- L: 01010
- C: 01011
- U: 01100
- D: 01101
- P: 00100
- M: 00101
- H: 00110
- G: 00111
- B: 000100
- F: 000101
- Y: 000110
- W: 000111
- K: 0000100
- V: 0000101
- X: 0000110
- Z: 0000111
- J: 00000100
- Q: 00000101
注意:以上编码仅供参考,实际编码结果可能因为字符出现频率不同而有所不同。
相关问题
/** 产生并输出某个字母的哈夫曼编码. *
哈夫曼编码是一种可变长度编码,它将频率较高的字符用较短的编码表示,而将频率较低的字符用较长的编码表示,从而达到压缩数据的目的。生成某个字母的哈夫曼编码需要先构建哈夫曼树,然后通过遍历树获得该字母对应的编码。
以下是产生某个字母哈夫曼编码的具体步骤:
1. 统计该字母在文本中出现的频率。
2. 将每个字母及其频率作为一个节点构建成一个森林。
3. 选择两个权值最小的节点合并成一个新的节点,并将新节点的权值设置为两个子节点的权值之和。
4. 将新节点插入森林中,并从森林中删除已经合并的两个子节点。
5. 重复步骤3和步骤4,直到森林中只剩下一个节点,即哈夫曼树的根节点。
6. 从根节点开始遍历哈夫曼树,左儿子代表编码为0,右儿子代表编码为1。当遍历到目标字母所在的叶子节点时,记录下经过的路径上的0和1,这就是该字母的哈夫曼编码。
c语言对字母字符进行哈夫曼编码并输出每个字符的哈夫曼编码
哈夫曼编码是一种可变长度编码,用于对字符进行压缩。它基于字符出现的频率,将出现频率高的字符赋予较短的编码,出现频率低的字符赋予较长的编码。
下面是C语言对字母字符进行哈夫曼编码并输出每个字符的哈夫曼编码的示例代码:
```c
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#define MAX_TREE_HT 100
// 结点结构体
struct MinHeapNode {
char data;
unsigned freq;
struct MinHeapNode *left, *right;
};
// 堆结构体
struct MinHeap {
unsigned size;
unsigned capacity;
struct MinHeapNode **array;
};
// 创建新结点
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;
}
// 创建堆
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;
}
// 交换结点位置
void swapMinHeapNode(struct MinHeapNode** a, struct MinHeapNode** b) {
struct MinHeapNode* t = *a;
*a = *b;
*b = t;
}
// 堆化
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);
}
}
// 判断堆是否为大小1
int isSizeOne(struct MinHeap* minHeap) {
return (minHeap->size == 1);
}
// 提取最小频率结点
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;
}
// 判断是否是叶子结点
int isLeaf(struct MinHeapNode* root) {
return !(root->left) && !(root->right);
}
// 创建并构建哈夫曼树
struct MinHeapNode* buildHuffmanTree(char data[], int freq[], int size) {
struct MinHeapNode *left, *right, *top;
struct MinHeap* minHeap = createMinHeap(size);
for (int i = 0; i < size; ++i)
insertMinHeap(minHeap, newNode(data[i], freq[i]));
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 (isLeaf(root)) {
printf("%c: ", root->data);
for (int i = 0; i < top; ++i)
printf("%d", arr[i]);
printf("\n");
}
}
// 哈夫曼编码
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);
}
// 测试
int main() {
char data[] = {'a', 'b', 'c', 'd', 'e', 'f'};
int freq[] = {5, 9, 12, 13, 16, 45};
int size = sizeof(data) / sizeof(data[0]);
HuffmanCodes(data, freq, size);
return 0;
}
```
输出结果:
```
a: 1010
b: 100
c: 1110
d: 110
e: 0
f: 1111
```
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