文件的哈夫曼编码与解码

张林

2021-12-19 (Updated: 2022-11-25)

面试 › 数据结构与算法

数据结构与算法

编码过程中，踩了一些小坑，做下记录：

1.全局变量count与std:count矛盾，建议用其他变量名。
2.内存泄漏问题注意空间要开够指针不可越界 main函数内开辟的栈空间大小一般为8MB 若要开辟较大的数组请去main函数之外
3.编译器错误推荐大家使用教新的较稳定的编译器
4.文件操作打开后记得关闭否则会占用系统资源
5.申请完空间，要记得释放，养成习惯。释放函数不可张冠李戴(留心编译器的Warning)。malloc/free,new/delete要配对使用。具体原因可参考这篇文章

编码要求及任务：

准备一个字符文件，要求：

统计该文件中各种字符的频率
对各字符进行 Huffman编码，显示每个字符的编码
以及将该文件翻译成 Huffman编码文件
再将 Huffman编码文件翻译成源文件
显示每个字符以一个字节进行二进制编码后的编码文件

实现步骤可分为：

统计被编码文件中个字符出现的频数，即统计权重
根据权重，构造哈夫曼树，进行哈夫曼编码
读取文件进行二进制编码
读取文件，将每个字符匹配哈夫曼编码，写入新文件，即完成编码
读取编码文件，根据哈夫曼编码进行解码，并写入新文件
对比二进制编码和哈夫曼编码后的文件字节大小，并计算压缩率

首先，准备一个源文件

这里我准备了一首小诗，写入文件，并将其命名为poem.txt

If I could save time in a bottle
the first thing that I'd like to do
is to save every day until eternity passes away
just to spend them with you
if I could make days last forever
if words could make wishes come true
I'd save every day like a treasure and then
again I would spend them with you

构建哈夫曼节点

// 定义哈夫曼树节点
typedef struct {
	int weight;
	int parent;
	int l_child;
	int r_child;
	char data;
} HTNode, * HuffmanTree;
typedef char** HuffmanCode;

频数统计

//统计该文件中各种字符的频率
void frequencyRecord(HuffmanTree& HT) {
	HuffmanTree TEMP;
	TEMP = new HTNode[130];
	for (int i = 0; i < 130; ++i) {
		TEMP[i].weight = 0;
	}
	ifstream originFile("poem.txt");
	originFile.seekg(0);
	if (!originFile) {
		cout << "Can't find the file!" << endl;
	} else {
		char _data;
		cin.unsetf(ios::skipws);
		while (!originFile.eof()) {
			if (originFile.get(_data)) {
				TEMP[_data].data = _data;
				TEMP[_data].weight++;
			}
		}
		originFile.close();
	}
	for (int i = 0; i < 130; ++i) {
		if (TEMP[i].weight != 0) {
			N++;
		}
	}
	HT = new HTNode[2 * N];
	int k = 1;
	for (int i = 0; i < 130; ++i) {
		if (TEMP[i].weight != 0) {
			HT[k++] = TEMP[i];
		}
	}
}

哈夫曼编码

//对各字符进行 Huffman编码，显示每个字符的编码
void HuffmanCoding(HuffmanTree& HT, HuffmanCode& HC) {
	int m = 2 * N - 1;
	for (int i = 1; i <= N; ++i) {
		HT[i].parent = 0;
		HT[i].l_child = 0;
		HT[i].r_child = 0;
	}
	for (int i = N + 1; i <= m; ++i) {
		HT[i].weight = 0;
		HT[i].parent = 0;
		HT[i].l_child = 0;
		HT[i].r_child = 0;
		HT[i].data = '#';
	}
	int child1, child2;
	for (int i = N + 1; i <= m; i++) {
		select(HT, i - 1, child1, child2);
		HT[child1].parent = i;
		HT[child2].parent = i;
		HT[i].l_child = child1;
		HT[i].r_child = child2;
		HT[i].weight = HT[child1].weight + HT[child2].weight;
	}
	HC = new char* [N + 1];
	char* cd = new char[N];
	cd[N - 1] = '\0';
	int start, c, f;
	for (int i = 1; i <= N; i++) {
		start = N - 1;
		for (c = i, f = HT[i].parent; f != 0; c = f, f = HT[f].parent) {
			if (HT[f].l_child == c) cd[--start] = '0';
			else cd[--start] = '1';
		}
		HC[i] = new char[N - start];
		strcpy(HC[i], &cd[start]);
	}
	delete[] cd;
	for (int i = 1; i <= N; i++) {
		if (HT[i].data == '\n') {
			cout << "回车" << " " << HC[i] << endl;
		} else if (HT[i].data == ' ') {
			cout << "空格" << " " << HC[i] << endl;
		} else {
			cout << HT[i].data << " " << HC[i] << endl;;
		}
	}
}

其中，寻找最小的两个叶子节点功能函数为

//找出最小的两个叶子节点
void select(HuffmanTree HT, int num, int& child1, int& child2) {
	child1 = child2 = 0;
	int w1 = 0, w2 = 0;
	//Start finding...
	for (int i = 1; i <= num; ++i) {
		if (HT[i].parent == 0) {
			if (child1 == 0) {
				child1 = i;
				w1 = HT[i].weight;
				continue;
			}
			if (child2 == 0) {
				child2 = i;
				w2 = HT[i].weight;
				continue;
			}
			if (w1 > w2 && w1 > HT[i].weight) {
				child1 = i;
				w1 = HT[i].weight;
				continue;
			}
			if (w2 > w1 && w2 > HT[i].weight) {
				child2 = i;
				w2 = HT[i].weight;
				continue;
			}
		}
	}
	// 使得w1永远小于w2
	int temp;
	if (w1 > w2) {
		temp = child1;
		child1 = child2;
		child2 = temp;
	}
}

编码并写入文件

//将该文件翻译成 Huffman编码文件
void zip(HuffmanTree& HT, HuffmanCode& HC, vector<string>& code) {
	ofstream codeFile("codefile.txt");
	ifstream originFile("poem.txt");
	if (!codeFile) {
		cout << "Can't find the file!" << endl;
	} else {
		char _data;
		cin.unsetf(ios::skipws);
		while (!originFile.eof()) {
			if (originFile.get(_data)) {
				for (int i = 1; i <= N; ++i) {
					if (HT[i].data == _data) {
						codeFile << HC[i];
						code.push_back(HC[i]);
					}
				}
			}
		}
	}
	codeFile.close();
}

打开编码文件，进行解码

//再将 Huffman编码文件翻译成源文件
void unzip(HuffmanTree& HT, HuffmanCode& HC, vector<string>& code) {
	ofstream decodeFile("decodefile.txt");
	if (!decodeFile) {
		cout << "Can't find the file!" << endl;
	} else {
		vector<string>::iterator v = code.begin();
		while (v != code.end()) {
			for (int i = 1; i <= N; ++i) {
				if (HC[i] == *v) {
					decodeFile << HT[i].data;
				}
			}
			v++;
		}
	}
	decodeFile.close();
}

二进制编码

//显示每个字符以一个字节进行二进制编码后的编码文件
void binaryCode() {
	ofstream binaryFile("binaryfile.txt");
	ifstream originFile("poem.txt");
	originFile.seekg(0);
	if (!originFile) {
		cout << "Can't find the file!" << endl;
	} else {
		char _data;
		cin.unsetf(ios::skipws);
		while (!originFile.eof()) {
			if (originFile.get(_data)) {
				bitset<8> data(_data);
				binaryFile << data;
			}
		}
		originFile.close();
	}
}