本节主要来自书本《大话数据结构》,挺容易看懂的。

另附Huffman编码代码,代码来自:

cnblogs.com/kubixueshen

1 //haffman 树的结构
  2 typedef struct
  3 {
  4     //叶子结点权值
  5     unsigned int weight;
  6     //指向双亲,和孩子结点的指针
  7     unsigned int parent;
  8     unsigned int lChild;
  9     unsigned int rChild;
 10 } Node, *HuffmanTree;
 11 
 12 //动态分配数组,存储哈夫曼编码
 13 typedef char *HuffmanCode;
 14 
 15 //选择两个parent为0,且weight最小的结点s1和s2的方法实现
 16 //n 为叶子结点的总数,s1和 s2两个指针参数指向要选取出来的两个权值最小的结点
 17 void select(HuffmanTree *huffmanTree, int n, int *s1, int *s2)
 18 {
 19     //标记 i
 20     int i = 0;
 21     //记录最小权值
 22     int min;
 23     //遍历全部结点,找出单节点
 24     for(i = 1; i <= n; i++)
 25     {
 26         //如果此结点的父亲没有,那么把结点号赋值给 min,跳出循环
 27         if((*huffmanTree)[i].parent == 0)
 28         {
 29             min = i;
 30             break;
 31         }
 32     }
 33     //继续遍历全部结点,找出权值最小的单节点
 34     for(i = 1; i <= n; i++)
 35     {
 36         //如果此结点的父亲为空,则进入 if
 37         if((*huffmanTree)[i].parent == 0)
 38         {
 39             //如果此结点的权值比 min 结点的权值小,那么更新 min 结点,否则就是最开始的 min
 40             if((*huffmanTree)[i].weight < (*huffmanTree)[min].weight)
 41             {
 42                min = i;
 43             }
 44         }
 45     }
 46     //找到了最小权值的结点,s1指向
 47     *s1 = min;
 48     //遍历全部结点
 49     for(i = 1; i <= n; i++)
 50     {
 51         //找出下一个单节点,且没有被 s1指向,那么i 赋值给 min,跳出循环
 52         if((*huffmanTree)[i].parent == 0 && i != (*s1))
 53         {
 54             min = i;
 55             break;
 56         }
 57     }
 58     //继续遍历全部结点,找到权值最小的那一个
 59     for(i = 1; i <= n; i++)
 60     {
 61         if((*huffmanTree)[i].parent == 0 && i != (*s1))
 62         {
 63             //如果此结点的权值比 min 结点的权值小,那么更新 min 结点,否则就是最开始的 min
 64             if((*huffmanTree)[i].weight < (*huffmanTree)[min].weight)
 65             {
 66                min = i;
 67             }
 68         }
 69     }
 70     //s2指针指向第二个权值最小的叶子结点
 71     *s2 = min;
 72 }
 73 
 74 //创建哈夫曼树并求哈夫曼编码的算法如下,w数组存放已知的n个权值
 75 void createHuffmanTree(HuffmanTree *huffmanTree, int w[], int n)
 76 {
 77     //m 为哈夫曼树总共的结点数,n 为叶子结点数
 78     int m = 2 * n - 1;
 79     //s1 和 s2 为两个当前结点里,要选取的最小权值的结点
 80     int s1;
 81     int s2;
 82     //标记
 83     int i;
 84     // 创建哈夫曼树的结点所需的空间,m+1,代表其中包含一个头结点
 85     *huffmanTree = (HuffmanTree)malloc((m + 1) * sizeof(Node));
 86     //1--n号存放叶子结点,初始化叶子结点,结构数组来初始化每个叶子结点,初始的时候看做一个个单个结点的二叉树
 87     for(i = 1; i <= n; i++)
 88     {
 89        
 90         //其中叶子结点的权值是 w【n】数组来保存
 91         (*huffmanTree)[i].weight = w[i];
 92         //初始化叶子结点(单个结点二叉树)的孩子和双亲,单个结点,也就是没有孩子和双亲,==0
 93         (*huffmanTree)[i].lChild = 0;
 94         (*huffmanTree)[i].parent = 0;
 95         (*huffmanTree)[i].rChild = 0;
 96     }// end of for
 97     //非叶子结点的初始化
 98     for(i = n + 1; i <= m; i++)
 99     {
100         (*huffmanTree)[i].weight = 0;
101         (*huffmanTree)[i].lChild = 0;
102         (*huffmanTree)[i].parent = 0;
103         (*huffmanTree)[i].rChild = 0;
104     }
105     
106     printf("\n HuffmanTree: \n");
107     //创建非叶子结点,建哈夫曼树
108     for(i = n + 1; i <= m; i++)
109     {
110         //在(*huffmanTree)[1]~(*huffmanTree)[i-1]的范围内选择两个parent为0
111         //且weight最小的结点,其序号分别赋值给s1、s2
112         select(huffmanTree, i-1, &s1, &s2);
113         //选出的两个权值最小的叶子结点,组成一个新的二叉树,根为 i 结点
114         (*huffmanTree)[s1].parent = i;
115         (*huffmanTree)[s2].parent = i;
116         (*huffmanTree)[i].lChild = s1;
117         (*huffmanTree)[i].rChild = s2;
118         //新的结点 i 的权值
119         (*huffmanTree)[i].weight = (*huffmanTree)[s1].weight + (*huffmanTree)[s2].weight;
120         
121         printf("%d (%d, %d)\n", (*huffmanTree)[i].weight, (*huffmanTree)[s1].weight, (*huffmanTree)[s2].weight);
122     }
123     
124     printf("\n");
125 }
126 
127 //哈夫曼树建立完毕,从 n 个叶子结点到根,逆向求每个叶子结点对应的哈夫曼编码
128 void creatHuffmanCode(HuffmanTree *huffmanTree, HuffmanCode *huffmanCode, int n)
129 {
130     //指示biaoji
131     int i;
132     //编码的起始指针
133     int start;
134     //指向当前结点的父节点
135     int p;
136     //遍历 n 个叶子结点的指示标记 c
137     unsigned int c;
138     //分配n个编码的头指针
139     huffmanCode=(HuffmanCode *)malloc((n+1) * sizeof(char *));
140     //分配求当前编码的工作空间
141     char *cd = (char *)malloc(n * sizeof(char));
142     //从右向左逐位存放编码,首先存放编码结束符
143     cd[n-1] = '\0';
144     //求n个叶子结点对应的哈夫曼编码
145     for(i = 1; i <= n; i++)
146     {
147         //初始化编码起始指针
148         start = n - 1;
149         //从叶子到根结点求编码
150         for(c = i, p = (*huffmanTree)[i].parent; p != 0; c = p, p = (*huffmanTree)[p].parent)
151         {
152             if( (*huffmanTree)[p].lChild == c)
153             {
154                 //从右到左的顺序编码入数组内
155                  cd[--start] = '0';  //左分支标0
156             }
157             else
158             {
159                 cd[--start] = '1';  //右分支标1
160             }
161         }// end of for
162         //为第i个编码分配空间
163         huffmanCode[i] = (char *)malloc((n - start) * sizeof(char));
164         
165         strcpy(huffmanCode[i], &cd[start]);
166     }
167     
168     free(cd);
169     //打印编码序列
170     for(i = 1; i <= n; i++)
171     {
172          printf("HuffmanCode of %3d is %s\n", (*huffmanTree)[i].weight, huffmanCode[i]);
173     }
174     
175     printf("\n");
176 }
177 
178 int main(void)
179 {
180     HuffmanTree HT;
181     HuffmanCode HC;
182     int *w,i,n,wei,m;
183     
184     printf("\nn = " );
185     
186     scanf("%d",&n);
187     
188     w=(int *)malloc((n+1)*sizeof(int));
189     
190     printf("\ninput the %d element's weight:\n",n);
191     
192     for(i=1; i<=n; i++)
193     {
194         printf("%d: ",i);
195         fflush(stdin);
196         scanf("%d",&wei);
197         w[i]=wei;
198     }
199     
200     createHuffmanTree(&HT, w, n);
201     creatHuffmanCode(&HT,&HC,n);
202     
203     return 0;
204 }