二叉查找树的基本操作

二叉查找树：对于树中的每个节点X，它的左子树所有关键字小于X的关键字，而右子树的所有关键字大于X的关键字。

二叉查找树的平均深度是O(logN)。

二叉查找树的删除操作：

  1. 如果节点是一片树叶，可以立即删除。
  2. 如果有一个儿子，调节父节点指针绕过该节点后被删除。
  3. 如果有两个儿子，用右子树的最小数据代替该节点的数据，并递归地删除那个节点（现在它是空的）。因为右子树的最小节点不可能有左儿子，所以第二次删除更容易。
  1 #ifndef _Tree_H
  2 
  3 struct TreeNode;
  4 typedef struct TreeNode *Position;
  5 typedef struct TreeNode *SearchTree;
  6 
  7 SearchTree MakeEmpty(SearchTree T);
  8 Position Find(ElementType X, SearchTree T);
  9 Position FindMin(SearchTree T);
 10 Position FindMax(SearchTree T);
 11 SearchTree Insert(ElementType X, SearchTree T);
 12 SearcgTree Delete(ElementType X, SearchTree T);
 13 ElementType Retrieve(Position P);
 14 
 15 #endif
 16 
 17 struct TreeNode
 18 {
 19     ElementType Element;
 20     SearchTree Left;
 21     SearchTree Right;
 22 }
 23 
 24 
 25 SearchTree MakeEmpty(SearchTree T)
 26 {
 27     if (T != NULL)
 28     {
 29         MakeEmpty(T->Left);
 30         MakeEmpty(T->Right);
 31         free(T);
 32     }
 33     return NULL;
 34 }
 35 
 36 
 37 Position Find(ElementType X, SearchTree T)
 38 {
 39     if (T == NULL)
 40         return NULL;
 41     if (X < T->Element)
 42         return Find(X, T->Left);
 43     else if (X > T->Element)
 44         return Find(X, T->Right);
 45     else
 46         return T;
 47 }
 48 
 49 
 50 Position FindMin(SearchTree T)
 51 {
 52     if (T == NULL)
 53         return NULL;
 54     else if (T->Left == NULL)
 55         return T;
 56     else
 57         return FindMin(T->Left);
 58 }
 59 
 60 Position FindMax(SearchTree T)
 61 {
 62     if (T != NULL)
 63         while (T->Right != NULL)
 64             T = T->Right;
 65     return T;
 66 }
 67 
 68 
 69 SearchTree Insert(ElementType X, SearchTree T)
 70 {
 71     if (T == NULL)
 72     {
 73         T = malloc(sizeof(struct TreeNode));
 74         if (T = NULL)
 75             perror("Out of Space");
 76         else
 77         {
 78             T->Element = X;
 79             T->Left = T->Right = NULL;
 80         }
 81     }
 82     else if (X < T->Element)
 83         T->Left = Insert(X, T->Left);
 84     else
 85         T->Right = Insert(X, T->Right);
 86 
 87     return T;
 88 }
 89 
 90 
 91 SearchTree Delete(ElementType X, SearchTree T)
 92 {
 93     Position TmpCell;
 94 
 95     if (T == NULL)
 96         perror("Element not found");
 97     // Found the element to be deleted
 98     else if (X < T->Left)
 99         T->Left = Delete(X, T->Left);
100     else if(X > T-Right)
101         T->Right = Delete(X, T->Right);
102 
103     // Two children
104     else if (T->Left && T->Right)
105     {
106         TmpCell = FindMin(T->Right);
107         T->Element = TmpCell->Element;
108         T->Right = Delete(T->Element, T->Right);
109     }
110     // One or zero children
111     else
112     {
113         TmpCell = T;
114         if (T->Left == NULL)
115             T = T->Right;
116         else if (T->Right == NULL)
117             T = T->Left;
118         free(TmpCell);
119     }
120 
121     return T;
122 }

 

posted @ 2015-03-31 22:43  bournet  阅读(227)  评论(0)  编辑  收藏  举报