04-课堂笔记

Posted 2020-10-28 biankun

　　二叉搜索树基本操作：

 1 #include <stdio.h>
 2 #include <stdlib.h>
 3 
 4 typedef struct TreeNode *BinTree;
 5 struct TreeNode{
 6     BinTree Left;
 7     BinTree Right;
 8     ElementType Data;
 9 };
10 BinTree BST;
11 
12 Position Find(ElementType X, BinTree BST)
13 {
14     if(!BST)
15         return NULL;
16     if(X > BST->Data)
17         return Find(X, BST->Right);
18     else if(X < BST->Data)
19         return Find(X, BST->Left);
20     else
21         return BST;
22 }
23 
24 //将尾递归函数改为迭代函数
25 Position IterFind(ElementType X, BinTree BST)
26 {
27     while(BST){
28         if(X > BST->Data);
29             BST = BST->Right;
30         else if(X < BST->Data);
31             BST = BST->Left;
32         else
33             return BST;
34     }
35     return NULL;
36 }
37 
38 Position FindMin(BinTree BST)
39 {
40     if(!BST)
41         return NULL;
42     else if(!BST->Left)
43         return BST;
44     else
45         return FindMin(BST->Left);
46 }
47 
48 Position FindMax(BinTree BST)
49 {
50     if(BST){
51         while(BST->Right)
52             BST = BST->Right;
53     }
54     return BST;
55 }
56 
57 BinTree Insert(ElementType X, BinTree BST)
58 {
59     if(!BST){
60         BST = (BinTree)malloc(sizeof(struct TreeNode));
61         BST->Data = X;
62         BST->Left = NULL;
63         BST->Right = NULL;
64     }else{
65         if(X > BST->Data)
66             BST->Right = Insert(X, BST->Right);
67         if(X < BST->Data)
68             BST->Left = Insert(X, BST->Left);
69     }
70     return BST;
71 }
72 
73 BinTree Delete(ElementType X, BinTree BST)
74 {
75     Position Tmp;
76     if(!BST)
77         printf("要删除的元素未找到\n");
78     else if(X < BST->Data)
79         BST->Left = Delete(X, BST->Left);
80     else if(X > BST->Data)
81         BST->Right = Delete(X, BST->Right);
82     else{
83         if(BST->Left && BST->Right){
84             Tmp = FindMin(BST->Right);
85             BST->Data = Tmp->Data;
86             BST = Delete(BST->Data, BST->Right);
87             free(Tmp);
88         }else{
89             Tmp = BST;
90             if(!BST->Left)
91                 BST = BST->Right;
92             if(!BST->Right)
93                 BST = BST->Left;
94             free(Tmp);
95         }
96     }
97     return BST;
98 }

 

　　平衡二叉树基本操作：

 1 #include <stdio.h>
 2 #include <stdlib.h>
 3 
 4 typedef struct AVLNode *AVLTree;
 5 struct AVLNode{
 6     AVLTree Left;
 7     AVLTree Right;
 8     ElementType Data;
 9     int Height;
10 };
11 BinTree BST;
12 
13 int Max(int a, int b)
14 {
15     return a > b ? a : b;
16 }
17 
18 AVLTree SingleLeftRotation(AVLTree A)
19 {   //A必须有一个左子节点B
20     //将A与B做单左旋，更新A与B的高度，返回新的根节点B
21     AVLTree B = A->Left;
22     B->Right = A;
23     A->Height = Max(GetHeight(A->Left), GetHeight(A->Right)) + 1;
24     B->Height = Max(GetHeight(B->Left), A->Height) + 1;
25     return B;
26 }
27 
28 AVLTree DoubleLeftRightRotation(AVLTree A)
29 {    //A必须有一个左子节点B，且B必须有一个右子节点C
30     //将A、B与C做两次单旋，返回新的根节点C
31     A->Left = SingleRightRotation(A->Left)  //B与C做右单旋，C被返回
32     return SingleLeftRotation(A);  //A与C做左单旋，C被返回
33 }
34 
35 AVLTree Insert(AVLTree T, ElementType X)
36 {
37     if(!T){  //插入空树，新建包含一个结点的树
38         T = (AVLTree)malloc(sizeof(struct AVLNode));
39         T->Data = X;
40         T->Height = 0;
41         T->Left = T->Right = NULL;
42     }
43 
44     else if(X < T->Data){  //插入T的左子树
45         T->Left = Insert(T->Left, X);
46         //如果需要左旋
47         if(GetHeight(T->Left) - GetHeight(T->Right) == 2)
48             if(X < T->Left->Data)  //X在“左左上”
49                 T = SingleLeftRotation(T);  //左单旋
50             else  //X在“左右”上，LR旋
51                 T = DoubleLeftRightRotation(T);
52     }
53 
54     else if(X > T->Data){
55         T->Right = Insert(T->Right, X);
56         if(GetHeight(T->Left) - GetHeight(T->Right) == 2)
57             if(X > T->Right->Data)
58                 T = SingleRightRotation(T);
59             else
60                 T = DoubleRightLeftRotation(T);
61     }
62 
63     //else X == T->Data ，无需插入
64 
65     //更新树高
66     T->Height = Max(GetHeight(T->Left), GetHeight(T->Right)) + 1;
67     
68     return T;
69 }