C#資料結構-赫夫曼樹

溫暖如太陽發表於2020-12-19
C#資料結構

什麼是赫夫曼樹？

赫夫曼樹(Huffman Tree)是指給定N個權值作為N個葉子結點，構造一棵二叉樹，若該樹的帶權路徑長度達到最小。哈夫曼樹（也稱為最優二叉樹）是帶權路徑長度最短的樹，權值較大的結點離根較近。

 1 　　 public class HNode<T>
 2     {
 3         public HNode()
 4         {
 5             data = default(T);
 6             weight = 0;
 7             leftNode = null;
 8             rightNode = null;
 9         }
10 
11         public HNode(T val)
12         {
13             data = val;
14             weight = 0;
15             leftNode = null;
16             rightNode = null;
17         }
18 
19         /// <summary>
20         /// 權重
21         /// </summary>
22         public int weight { get; set; }
23 
24         /// <summary>
25         /// 內容
26         /// </summary>
27         public T data { get; set; }
28 
29         /// <summary>
30         /// 左樹
31         /// </summary>
32         public HNode<T> leftNode { get; set; }
33 
34         /// <summary>
35         /// 右樹
36         /// </summary>
37         public HNode<T> rightNode { get; set; }
38     }

 

 1 　　 /// <summary>
 2     /// 赫夫曼樹
 3     /// </summary>
 4     /// <typeparam name="T"></typeparam>
 5     public class HTree<T>
 6     {
 7         /// <summary>
 8         /// 樹的頭結點
 9         /// </summary>
10         public HNode<T> head { get; set; }
11 
12         /// <summary>
13         /// 建構函式
14         /// </summary>
15         /// <param name="val"></param>
16         public HTree(T val)
17         {
18             head = new HNode<T>(val);
19         }
20 
21         public HTree()
22         {
23             head = new HNode<T>();
24         }
25         /// <summary>
26         /// 構建樹結構
27         /// </summary>
28         /// <param name="list"></param>
29         public void build(List<T> list)
30         {
31             //判斷是否能構建樹結構
32             if (list == null || list.Count <2)
33                 throw new ArgumentOutOfRangeException("params error");
34             //分組統計
35             List<HNode<T>> nodes = new List<HNode<T>>();
36             nodes.AddRange(from m in list group m by m into g 
37                            select new HNode<T> { data = g.Key,weight = g.Count()});
38             //排序
39             nodes = nodes.OrderBy(i => i.weight).ToList();
40 
41             for (int i =1; i< nodes.Count; i++)
42             {
43                 HNode<T> parentNode = new HNode<T>();
44                 if (i == 1)
45                 {
46                     //先取最小的兩個節點
47                     parentNode.leftNode = nodes[0];
48                     parentNode.rightNode = nodes[1];
49                     parentNode.weight = nodes[0].weight + nodes[1].weight;
50                 }
51                 else
52                 {
53                     //依次取節點構建樹
54                     if (head.weight >= nodes[i].weight)
55                     {
56                         parentNode.leftNode = head;
57                         parentNode.rightNode = nodes[i];
58                     }
59                     else
60                     {
61                         parentNode.rightNode = head;
62                         parentNode.leftNode = nodes[i];
63                     }
64                     parentNode.weight = head.weight + nodes[i].weight;
65                 }
66                 head = parentNode;
67             }
68         }
69 
70         /// <summary>
71         /// 先序遍歷
72         /// </summary>
73         /// <param name="index"></param>
74         public void PreorderTraversal(HNode<T> node)
75         {
76             //遞迴的終止條件
77             if (head == null)
78             {
79                 Console.WriteLine("當前樹為空");
80                 return;
81             }
82             if (node != null)
83             {
84                 if(node.data != null)
85                 Console.WriteLine($"{node.data} {node.weight}");
86                 PreorderTraversal(node.leftNode);
87                 PreorderTraversal(node.rightNode);
88             }
89         }
90     }

測試程式碼：

1 List<string> list = new List<string>() { "A","B", "B", "C", "C", "C", "D", "D", "D", "D", "E", "E", "E", "E", "E" };
2 HTree<string> tree = new HTree<string>();
3 tree.build(list);
4 tree.PreorderTraversal(tree.head);

列印結果：

A 1
B 2
C 3
D 4
E 5

用這個例子現在我們看下構建的二叉樹結構：

 

 

 

 

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