数据结构-二叉树（Huffman算法）-优快云博客

本文介绍了一种基于哈夫曼算法实现最优二叉树的方法，并通过C语言具体实现了哈夫曼树及其编码过程。该实现利用了结构体、数组等数据结构来构造哈夫曼树，并最终打印出每个叶子节点对应的哈夫曼编码。

huffman算法即最优二叉树的实现：（其中用到的堆栈算法在前面的文章中以列出）Code

  1 // Huffman.cpp : 定义控制台应用程序的入口点。
  2 //
  3
  4 #include "stdafx.h"
  5 #include "stack.h"
  6 #include <stdlib.h>
  7 #define MAXINT 2147483647
  8 #define MAXNODE 100
  9
10 struct HtNode
11 {
12     int ww;
13     int parent, llink, rlink;
14 };
15
16 struct HtTree
17 {
18     struct HtNode ht[MAXNODE];
19     int root;
20     int count;
21 };
22
23 typedef struct HtTree * PHtTree;
24
25 PHtTree huffman(int m, int * w)
26 /* 构造具有m 个叶子节点的哈夫曼树*/
27 {
28     PHtTree pht;
29     int i, j, x1, x2, m1, m2;
30     pht = (PHtTree)malloc(sizeof(struct HtTree));
31     if(pht == NULL)
32     {
33         printf("Out of space!!\n");
34         return pht;
35     }
36     pht->count = m;
37     for(i = 0; i < 2 * m - 1; i++)
38     {
39         pht->ht[i].llink = -1;
40         pht->ht[i].rlink = -1;
41         pht->ht[i].parent = -1;
42         if(i < m)
43             pht->ht[i].ww = w[i];
44         else
45             pht->ht[i].ww = -1;
46     }
47
48     for(i = 0; i < m - 1; i++)
49     {
50         m1 = MAXINT, m2 = MAXINT;
51         x1 = -1; x2 = -1;
52         for(j = 0; j < m + i; j++)
53         {
54             if(pht->ht[j].ww < m1 && pht->ht[j].parent == -1)
55             {
56                 m2 = m1;
57                 x2 = x1;
58                 m1 = pht->ht[j].ww;
59                 x1 = j;
60             }
61             else
62             {
63                 if(pht->ht[j].ww < m2 && pht->ht[j].parent == -1)
64                 {
65                     m2 = pht->ht[j].ww;
66                     x2 = j;
67                 }
68             }
69         }
70         pht->ht[x1].parent = m + i; /*构造一个内部节点*/
71         pht->ht[x2].parent = m + i;
72         pht->ht[m + i].ww = m1 + m2;
73         pht->ht[m + i].llink = x1;
74         pht->ht[m + i].rlink = x2;
75         pht->root = m + i;
76     }
77     return pht;
78 }
79
80 void printThreeEncode(PHtTree tree)
81 {
82     PSeqStack pastack = createEmptyStack_seq();
83     int j;
84     for(int i = 0; i < tree->count; i++)
85     {
86         printf("Eoncode for W %d is: ",tree->ht[i].ww );
87         j = i;
88         HtNode node = tree->ht[i];
89         do
90         {
91             if(tree->ht[node.parent].llink == j )
92             {
93                 push_seq(pastack,0);
94             }
95             else
96             {
97                 push_seq(pastack,1);
98             }
99             j = node.parent;
100             node = tree->ht[j];
101         }
102         while(j != tree->root);
103         int code;
104         while(!isEmptyStack_seq(pastack))
105         {
106             code = top_seq(pastack);
107             pop_seq(pastack);
108             printf(" %d ", code);
109         }
110         printf("\n");
111
112     }
113 }
114
115 int _tmain(int argc, _TCHAR* argv[])
116 {
117     int w[] = {2,3,5,7,11,13,17,19,23,29,31,37,41};
118     printThreeEncode(huffman(13,w));
119     return 0;
120 }

121

运行结果为：

Eoncode for W 2 is: 1 0 1 1 1 1 0

Eoncode for W 3 is: 1 0 1 1 1 1 1

Eoncode for W 5 is: 1 0 1 1 1 0

Eoncode for W 7 is: 1 0 1 1 0

Eoncode for W 11 is: 0 1 0 0

Eoncode for W 13 is: 0 1 0 1

Eoncode for W 17 is: 1 0 1 0

Eoncode for W 19 is: 0 0 0

Eoncode for W 23 is: 0 0 1

Eoncode for W 29 is: 0 1 1