字符串压缩算法

RLE（游程长度编码）

算法原理

步骤说明

示例说明

代码示例

python语言：

C语言：

优缺点

Huffman编码

基本原理

构造Huffman树

编码与解码过程

代码示例

python语言：

C语言：

优缺点

LZW压缩

字典构建与压缩过程

步骤说明

代码示例

python语言：

C语言：

优缺点

字符串压缩算法用于减少字符串的存储空间，尤其是在需要传输或保存大量文本数据时。以下是三种常见的字符串压缩算法：RLE、Huffman编码和LZW压缩。

RLE（游程长度编码）

算法原理

游程长度编码（Run-Length Encoding，RLE）是一种简单的压缩算法，主要针对字符串中连续重复的字符。该算法通过记录每个字符的重复次数来实现压缩。

步骤说明

遍历字符串，记录每个字符及其连续出现的次数。
生成一个新的字符串，其中每个字符后面跟着其出现的次数。

示例说明

考虑字符串 "AAAABBBCCDAA"：

第1步：找到字符 A 连续出现了4次，记为 "4A"。
第2步：找到字符 B 连续出现了3次，记为 "3B"。
第3步：字符 C 连续出现2次，记为 "2C"。
第4步：字符 D 出现1次，记为 "1D"。
第5步：字符 A 连续出现2次，记为 "2A"。

最终压缩结果为 "4A3B2C1D2A"。

代码示例

python语言：

def rle_encode(data):encoding = ''i = 0while i < len(data):count = 1while i + 1 < len(data) and data[i] == data[i + 1]:i += 1count += 1encoding += str(count) + data[i]i += 1return encoding# 示例使用
input_string = "AAAABBBCCDAA"
encoded_string = rle_encode(input_string)
print(encoded_string)  # 输出: "4A3B2C1D2A"

C语言：

#include <stdio.h>
#include <stdlib.h>
#include <string.h>char *rleEncode(const char *data) {int dataLength = strlen(data);char *encoding = (char *)malloc(2 * dataLength * sizeof(char));int encodingIndex = 0;int i = 0;while (i < dataLength) {int count = 1;while (i + 1 < dataLength && data[i] == data[i + 1]) {i++;count++;}int countDigits = 0;int tempCount = count;while (tempCount > 0) {tempCount /= 10;countDigits++;}int digitIndex = countDigits;tempCount = count;while (tempCount > 0) {encoding[encodingIndex + digitIndex--] = '0' + tempCount % 10;tempCount /= 10;}encoding[encodingIndex + countDigits] = data[i];encodingIndex += countDigits + 1;i++;}encoding[encodingIndex] = '\0';return encoding;
}int main() {const char *inputString = "AAAABBBCCDAA";char *encodedString = rleEncode(inputString);printf("%s\n", encodedString);free(encodedString);return 0;
}

优缺点

优点：RLE算法实现简单，适用于字符重复较多的场景。
缺点：对于字符重复较少的字符串，RLE可能会增加字符串的长度而非压缩。

Huffman编码

基本原理

Huffman编码是一种基于字符出现频率的无损压缩算法。它通过构建一棵Huffman树，为出现频率较高的字符分配较短的二进制编码，频率较低的字符分配较长的二进制编码，从而达到压缩的目的。

构造Huffman树

计算每个字符的出现频率。
创建一个优先队列，将每个字符及其频率作为一个叶节点插入队列。
取出队列中频率最低的两个节点，创建一个新的父节点，其频率为两个节点频率之和，并将该父节点插回队列。
重复步骤3，直到队列中只剩下一个节点，该节点即为Huffman树的根节点。

编码与解码过程

编码：从根节点出发，沿着树向下遍历，每向左走一步，记为 0，向右走一步，记为 1，直到达到叶节点。这样，每个字符都有一个唯一的二进制编码。
解码：从压缩后的二进制字符串出发，沿着Huffman树进行解码，直到恢复出原始字符串。

代码示例

python语言：

import heapq
from collections import defaultdict, Counterclass HuffmanNode:def __init__(self, char, freq):self.char = charself.freq = freqself.left = Noneself.right = Nonedef __lt__(self, other):return self.freq < other.freqdef build_huffman_tree(text):frequency = Counter(text)heap = [HuffmanNode(char, freq) for char, freq in frequency.items()]heapq.heapify(heap)while len(heap) > 1:node1 = heapq.heappop(heap)node2 = heapq.heappop(heap)merged = HuffmanNode(None, node1.freq + node2.freq)merged.left = node1merged.right = node2heapq.heappush(heap, merged)return heap[0]def build_codes(node, prefix='', codebook={}):if node is not None:if node.char is not None:codebook[node.char] = prefixbuild_codes(node.left, prefix + '0', codebook)build_codes(node.right, prefix + '1', codebook)return codebookdef huffman_encode(text):root = build_huffman_tree(text)codebook = build_codes(root)return ''.join(codebook[char] for char in text), codebook# 示例使用
text = "AAAABBBCCDAA"
encoded_text, huffman_codebook = huffman_encode(text)
print(f"Encoded: {encoded_text}")  # 输出压缩后的二进制字符串
print(f"Codebook: {huffman_codebook}")  # 输出字符到二进制的映射

C语言：

#include <stdio.h>
#include <stdlib.h>
#include <string.h>// 哈夫曼树节点结构体
typedef struct HuffmanNode {char character;int frequency;struct HuffmanNode *left;struct HuffmanNode *right;
} HuffmanNode;// 创建新的哈夫曼节点
HuffmanNode *createHuffmanNode(char character, int frequency) {HuffmanNode *newNode = (HuffmanNode *)malloc(sizeof(HuffmanNode));newNode->character = character;newNode->frequency = frequency;newNode->left = NULL;newNode->right = NULL;return newNode;
}// 交换两个哈夫曼节点
void swapHuffmanNodes(HuffmanNode **a, HuffmanNode **b) {HuffmanNode *temp = *a;*a = *b;*b = temp;
}// 下调整个最小堆，保持堆的性质
void minHeapify(HuffmanNode **heap, int size, int index) {int smallest = index;int left = 2 * index + 1;int right = 2 * index + 2;if (left < size && heap[left]->frequency < heap[smallest]->frequency)smallest = left;if (right < size && heap[right]->frequency < heap[smallest]->frequency)smallest = right;if (smallest!= index) {swapHuffmanNodes(&heap[index], &heap[smallest]);minHeapify(heap, size, smallest);}
}// 构建最小堆
void buildMinHeap(HuffmanNode **heap, int size) {for (int i = (size / 2) - 1; i >= 0; i--)minHeapify(heap, size, i);
}// 提取最小频率的节点
HuffmanNode *extractMin(HuffmanNode **heap, int *size) {if (*size <= 0)return NULL;HuffmanNode *minNode = heap[0];heap[0] = heap[(*size) - 1];(*size)--;minHeapify(heap, *size, 0);return minNode;
}// 插入节点到最小堆
void insertNode(HuffmanNode **heap, int *size, HuffmanNode *node) {(*size)++;int i = (*size) - 1;while (i && node->frequency < heap[(i - 1) / 2]->frequency) {heap[i] = heap[(i - 1) / 2];i = (i - 1) / 2;}heap[i] = node;
}// 构建哈夫曼树
HuffmanNode *buildHuffmanTree(char *text) {int frequency[256] = {0};int length = strlen(text);for (int i = 0; i < length; i++)frequency[(int)text[i]]++;HuffmanNode **heap = (HuffmanNode **)malloc(length * sizeof(HuffmanNode *));int size = 0;for (int i = 0; i < 256; i++) {if (frequency[i] > 0) {heap[size++] = createHuffmanNode((char)i, frequency[i]);}}buildMinHeap(heap, size);while (size > 1) {HuffmanNode *left = extractMin(heap, &size);HuffmanNode *right = extractMin(heap, &size);HuffmanNode *merged = createHuffmanNode('\0', left->frequency + right->frequency);merged->left = left;merged->right = right;insertNode(heap, &size, merged);}HuffmanNode *root = extractMin(heap, &size);free(heap);return root;
}// 深度优先遍历构建编码表
void buildCodes(HuffmanNode *root, char *prefix, int prefixLength, char **codebook) {if (root->left) {prefix[prefixLength] = '0';buildCodes(root->left, prefix, prefixLength + 1, codebook);}if (root->right) {prefix[prefixLength] = '1';buildCodes(root->right, prefix, prefixLength + 1, codebook);}if (root->character!= '\0') {prefix[prefixLength] = '\0';codebook[(int)root->character] = strdup(prefix);}
}// 哈夫曼编码函数
void huffmanEncode(char *text) {HuffmanNode *root = buildHuffmanTree(text);char prefix[256] = {0};char **codebook = (char **)malloc(256 * sizeof(char *));buildCodes(root, prefix, 0, codebook);printf("Encoded: ");int length = strlen(text);for (int i = 0; i < length; i++) {printf("%s", codebook[(int)text[i]]);}printf("\n");printf("Codebook:\n");for (int i = 0; i < 256; i++) {if (codebook[i]!= NULL) {printf("%c: %s\n", (char)i, codebook[i]);free(codebook[i]);}}free(codebook);
}// 测试示例
int main() {char text[] = "AAAABBBCCDAA";huffmanEncode(text);return 0;
}

优缺点

优点：Huffman编码能够显著减少高频字符的编码长度，实现高效压缩。
缺点：构造Huffman树的过程相对复杂，对于频率较为均匀的字符，压缩效果有限。

LZW压缩

字典构建与压缩过程

LZW（Lempel-Ziv-Welch）是一种基于字典的无损压缩算法。它通过动态构建字典，将字符串中的重复模式编码为较短的二进制串，从而实现压缩。

步骤说明

初始化字典，包含所有可能的单字符模式。
从输入字符串中读取字符，寻找最长的已存在于字典中的模式。
将该模式的索引输出，并将新模式（即该模式加下一个字符）加入字典。
重复步骤2和3，直到字符串处理完毕。

示例说明

假设有字符串 "ABABABABABAB"：

初始字典包含所有单字符模式，如 'A': 1, 'B': 2。
读取字符 'A'，最长匹配为 'A'，输出其索引 1，并将 'AB' 加入字典。
读取字符 'B'，最长匹配为 'B'，输出其索引 2，并将 'BA' 加入字典。
继续匹配，最终压缩输出一系列索引代表原始字符串。

代码示例

python语言：

def lzw_compress(uncompressed):dict_size = 256dictionary = {chr(i): i for i in range(dict_size)}w = ""compressed_data = []for c in uncompressed:wc = w + cif wc in dictionary:w = wcelse:compressed_data.append(dictionary[w])dictionary[wc] = dict_sizedict_size += 1w = cif w:compressed_data.append(dictionary[w])return compressed_data# 示例使用
input_string = "ABABABABABAB"
compressed = lzw_compress(input_string)
print(compressed)  # 输出: [65, 66, 256, 258, 260, 262]

C语言：

#include <stdio.h>
#include <stdlib.h>
#include <string.h>#define DICT_SIZE 256typedef struct {char *key;int value;
} DictionaryEntry;DictionaryEntry *createDictionaryEntry(char *key, int value) {DictionaryEntry *entry = (DictionaryEntry *)malloc(sizeof(DictionaryEntry));entry->key = strdup(key);entry->value = value;return entry;
}void freeDictionaryEntry(DictionaryEntry *entry) {free(entry->key);free(entry);
}int lzwCompress(char *uncompressed) {DictionaryEntry *dictionary[DICT_SIZE];for (int i = 0; i < DICT_SIZE; i++) {dictionary[i] = createDictionaryEntry((char *)&i, i);}char w[1000] = "";int compressedData[1000];int compressedDataIndex = 0;for (int i = 0; uncompressed[i]!= '\0'; i++) {char wc[1000];strcpy(wc, w);strncat(wc, &uncompressed[i], 1);int found = 0;for (int j = 0; j < DICT_SIZE; j++) {if (strcmp(dictionary[j]->key, wc) == 0) {found = 1;strcpy(w, wc);break;}}if (!found) {for (int j = 0; j < DICT_SIZE; j++) {if (strcmp(dictionary[j]->key, w) == 0) {compressedData[compressedDataIndex++] = dictionary[j]->value;break;}}dictionary[DICT_SIZE] = createDictionaryEntry(wc, DICT_SIZE);DICT_SIZE++;strcpy(w, &uncompressed[i]);}}if (strlen(w) > 0) {for (int j = 0; j < DICT_SIZE; j++) {if (strcmp(dictionary[j]->key, w) == 0) {compressedData[compressedDataIndex++] = dictionary[j]->value;break;}}}for (int i = 0; i < DICT_SIZE; i++) {freeDictionaryEntry(dictionary[i]);}for (int i = 0; i < compressedDataIndex; i++) {printf("%d ", compressedData[i]);}printf("\n");return compressedDataIndex;
}int main() {char inputString[] = "ABABABABABAB";lzwCompress(inputString);return 0;
}