#include <iostream> #include <iomanip> #include <string> #include <cstdlib> using namespace std; //定义哈夫曼树存储结构 typedef struct { char data; //存放结点数据 int weight; //记录结点权值 int parent, lchild, rchild; }HTNode, * HuffmanTree; //哈夫曼编码存储表示 typedef char** HuffmanCode; //动态分配数组储存哈夫曼编码表 //初始化 HuffmanTree InitHuffman(HuffmanTree& HT, int n) { if (n < 0) { cout << "输入初态结点数目不正确！！！" << endl; return NULL; } else { int m = 2 * n - 1; //n个叶子结点的哈夫曼树有2n-1个结点 HT = new HTNode[m + 1]; //0号单元未用，申请m+1个空间 for (int i = 1; i <= m; i++) { HT[i].parent = 0; HT[i].lchild = 0; HT[i].rchild = 0; HT[i].weight = 0; HT[i].data = '-'; } //输入初始数据，为了方便理解HT[0]不存放数据 cout << "请输入初态结点数据及相应权值（格式形式：a 3）："; for (int i = 1; i <= n; i++) { cin >> HT[i].data; cin >> HT[i].weight; } return HT; } } //打印HT void PrintState(HuffmanTree& HT, int n) { int m = 2 * n - 1; //总结点数 cout << "结点i\tdata值\tweight\tparent\tlchild\trchild" << endl; for (int i = 1; i <= m; i++) { cout << setw(3) << i << "\t"; cout << setw(4) << HT[i].data << "\t"; cout << setw(4) << HT[i].weight << "\t"; cout << setw(4) << HT[i].parent << "\t"; cout << setw(4) << HT[i].lchild << "\t"; cout << setw(4) << HT[i].rchild << "\t" << endl; } } //选择双亲域为0且两权值最小的结点，选择范围为1到i-1 int* Select(HuffmanTree& HT, int n, int* Idx) { int MIN, MinSecond; //打擂台法使权最小值和次权最小值最大（假设第一个值权值最小无法进行） MIN = MinSecond = 99999; //循环从1到n次 for (int i = 1; i <= n; i++) { //如果双亲为0（未删除结点与新生成结点），一定会执行if语句,寻找权最小值 if ((HT[i].parent == 0) && HT[i].weight < MIN) { //将最小的权值给MinSecond方便寻找次最小值 MinSecond = MIN; MIN = HT[i].weight; //记录权最小值下标 Idx[0] = i; } //否则如果满足条件寻找次最小值 else if ((HT[i].parent == 0) && HT[i].weight < MinSecond) { MinSecond = HT[i].weight; //记录权次最小值下标 Idx[1] = i; } } return Idx; } //构造哈夫曼树 void CreateHuffmanTree(HuffmanTree& HT, int n) { if (n <= 1) return; int m = 2 * n - 1; //n个叶子结点的哈夫曼树有2n-1个结点 //从n+1开始构造哈弗曼树 for (int i = n + 1; i <= m; i++) { //Idx用于存放两个返回最小权值的下标，i-1为前n个结点，后面随着i增加，n也增加 int* Idx = Idx = new int[2]; Idx = Select(HT, i - 1, Idx); int s1 = Idx[0]; //权最小值下标 int s2 = Idx[1]; //权次最小值下标 //给两权值最小的结点置双亲,使s1，s2结点不在录入Select范围 HT[s1].parent = i; HT[s2].parent = i; //给新节点i左右孩子置位s1,s2 HT[i].lchild = s1; HT[i].rchild = s2; //给新结点赋权值 HT[i].weight = HT[s1].weight + HT[s2].weight; delete[]Idx; } } //哈夫曼编码 void CreateHuffmanCode(HuffmanTree& HT, HuffmanCode& HC, int n) { HC = new char* [n + 1]; //分配字符的空间 char* TempCode = new char[n]; //分配临时编码表空间n个 TempCode[n - 1] = '\0'; //编码有叶子结点开始逆序存放，先将末尾结束符标志打上，为后序strcpy //for循环逐个逆序求叶子结点的哈夫曼编码 for (int i = 1; i <= n; i++) { int start = n - 1; //开始存放的起点指向末尾，用于后面HC拷贝是的起始地址 int NodeIdx = i; //NodeIdx最开始存放叶子结点序号 int ParentsIdx = HT[i].parent; //Parents指向其双亲结点序号 //若有双亲则由下到上进行编码，编码的字符，从序号1开始 while (ParentsIdx) { start--; //在一维数组末尾，strat先指向最后 //若双亲结点的左结点序号为NodeIdx，将0打入一维临时数组中，否则打入1 if (HT[ParentsIdx].lchild == NodeIdx) TempCode[start] = '0'; else TempCode[start] = '1'; //结点的序号更新，进入上一层 NodeIdx = ParentsIdx; ParentsIdx = HT[NodeIdx].parent; } //临时一维数组存放编码成功，开始用HC顺序存放字符编码 HC[i] = new char[n - start]; //为序号为i的字符分配编码空间 strcpy_s(HC[i], n - start, &TempCode[start]); //编码字符串拷贝strcpy报错因为没有指定长度 } //打印哈夫曼编码 cout << "---字符对应编码----" << endl; for (int i = 1; i <= n; i++) { cout << HT[i].data << "\t\t" << HC[i] << endl; } delete []TempCode; } //输入字符打印哈夫曼编码 void PrintCode(HuffmanTree & HT, HuffmanCode & HC, int n) { char *str =new char[100]; //存储需要解码的字符 int flag = 0; //flag用于检查输入是否错误 cout << "请输入需要编码的字符："; cin >> str; //匹配字符并打印相应的哈夫曼编码 cout << "输入的字符哈夫曼编码为："; for (int j = 0; j < strlen(str); j++) { flag = 0; for (int i = 1; i <= n; i++) { //匹配成功打印编码 if (HT[i].data == str[j]) { cout << HC[i] ; flag = 1; //匹配成功 } } //如果有匹配失败的情况，则跳出循环 if (flag == 0) { cout << "\n第" << j+1 << "字符输入错误!" ; break; } } putchar(10); delete []str; //释放str空间 } //哈夫曼解码并打印 void HuffmanDecode(HuffmanTree& HT, int n) { char* str = new char[1024]; cout << "请输入二进制编码："; cin >> str; int flag = 0; //用于检查二进制编码是否输入错误 cout << "解码对应字符为："; //遍历二进制编码 for (int i = 0; i < strlen(str);) { int Root = 2 * n - 1; //Root为根结点序号 //当结点的左右孩子不为空时进入循环，由根结点进入 while (HT[Root].lchild && HT[Root].rchild) { if (str[i] == '0') Root = HT[Root].lchild; else if (str[i] == '1') Root = HT[Root].rchild; else { cout << "输入的二级制编码有误！" << endl; flag = 1; break; } i++; //相后读取二进制编码，i值更新 } //如果找到错误跳出循环 if (flag) break; //打印编码对应字符 cout << HT[Root].data; } delete []str; } int main() { int n; cout << "请输入哈夫曼树初态结点数："; cin >> n; //初始化哈夫曼树 HuffmanTree HT = InitHuffman(HT, n); //打印HT初态 cout << "--------------------HT初态--------------------" << endl; PrintState(HT, n); //构造哈夫曼树 CreateHuffmanTree(HT, n); //打印HT终态 cout << "--------------------HT终态--------------------" << endl; PrintState(HT, n); HuffmanCode HC; //哈夫曼编码-由下而上 CreateHuffmanCode(HT, HC, n); //打印字符对应编码 PrintCode(HT, HC, n); //哈夫曼解码并打印-由上而下 HuffmanDecode(HT, n); return 0; }
//由于编译器版本原因strcpy出现不安全原因，导致无法运行，后使用strcpy_s给予拷贝长度得到解决；把“==”写成“=”导致报错；
/*
输入字符串统计字符个数（权值）
int CreateWeightArray(char* str, int* Array) {
//初始化权值数组，128为str[i]的最大数值
for (int i = 0; i < 128; i++)
{
Array[i] = 0;
}
int length = 0;
//利用下标记录位权
for (int i = 0; str[i]; i++)
{
Array[str[i]]++; //值加1，下标即字符
}
//统计字符串去重后的长度
for (int i = 0; i < 128; i++)
{
if (Array[i] != 0)
{
length++;
}
}
return length;
}
*/