头文件
1 typedef int ElementType; 2 3 #ifndef _AVLTREE_H_ 4 #define _AVLTREE_H_ 5 6 struct AvlNode; 7 typedef struct AvlNode *Position; 8 typedef struct AvlNode *AvlTree; 9 10 AvlTree MakeEmpty(AvlTree T); 11 Position Find(ElementType X, AvlTree T); 12 Position FindMin(AvlTree T); 13 Position FindMax(AvlTree T); 14 AvlTree Insert(ElementType X, AvlTree T); 15 AvlTree Delete(ElementType X, AvlTree T); 16 ElementType Retrieve(Position P); 17 void PrintTree(AvlTree T); 18 19 #endif
源文件
1 #include "fatal.h"
2 #include "avltree.h"
3 #include <malloc.h>
4
5 struct AvlNode
6 {
7 ElementType Element;
8 AvlTree Left;
9 AvlTree Right;
10 int Height;
11 };
12
13 AvlTree MakeEmpty(AvlTree T) // 同二叉查找树
14 {
15 if(T != NULL) // 递归终止
16 {
17 MakeEmpty(T->Left);
18 MakeEmpty(T->Right);
19 free(T);
20 }
21 return T;
22 }
23
24 Position Find(ElementType X, AvlTree T) // 同二叉查找树
25 {
26 if(T == NULL)
27 return NULL;
28 else if(X < T->Element)
29 {
30 return Find(X, T->Left);
31 }
32 else if(X > T->Element)
33 {
34 return Find(X, T->Right);
35 }
36 else
37 return T;
38 }
39
40 Position FindMin(AvlTree T) // 递归实现
41 {
42 if(T == NULL)
43 return NULL;
44 else if(T->Left == NULL)
45 return T;
46 else
47 return FindMin(T->Left);
48 }
49
50 Position FindMax(AvlTree T) // 非递归实现
51 {
52 if(T != NULL)
53 while(T->Right != NULL)
54 T = T->Right;
55
56 return T;
57 }
58
59 static int Height(Position P)
60 {
61 if(P == NULL)
62 return -1; // 空树高度为-1
63 else
64 return P->Height;
65 }
66
67 static int Max(int Left, int Right)
68 {
69 return Left > Right ? Left : Right;
70 }
71
72 /* This function can be called only if K2 has a left child */
73 /* Perform a rotate between a node (K2) and its left child */
74 /* Update heights, then return new root */
75 static Position SingleRotateWithLeft(Position K2)
76 {
77 Position K1;
78
79 K1 = K2->Left;
80 K2->Left = K1->Right;
81 K1->Right = K2;
82
83 K2->Height = Max(Height(K2->Left), Height(K2->Right)) + 1;
84 K1->Height = Max(Height(K1->Left), Height(K1->Right)) + 1;
85
86 return K1; /* New root */
87 }
88
89 /* This function can be called only if K1 has a right child */
90 /* Perform a rotate between a node (K1) and its right child */
91 /* Update heights, then return new root */
92 static Position SingleRotateWithRight(Position K1)
93 {
94 Position K2;
95
96 K2 = K1->Right;
97 K1->Right = K2->Left;
98 K2->Left = K1;
99
100 K1->Height = Max(Height(K1->Left), Height(K1->Right)) + 1;
101 K2->Height = Max(Height(K2->Left), Height(K2->Right)) + 1;
102
103 return K2; /* New root */
104 }
105
106 /* This function can be called only if K3 has a left */
107 /* child and K3‘s left child has a right child */
108 /* Do the left-right double rotation */
109 /* Update heights, then return new root */
110 static Position DoubleRotateWithLeft(Position K3)
111 {
112 /* Rotate between K1 and K2 */
113 K3->Left = SingleRotateWithRight(K3->Left);
114 /* Rotate between K3 and K2 */
115 return SingleRotateWithLeft(K3);
116 }
117
118 /* This function can be called only if K1 has a right */
119 /* child and K1‘s right child has a left child */
120 /* Do the right-left double rotation */
121 /* Update heights, then return new root */
122 static Position DoubleRotateWithRight(Position K1)
123 {
124 /* Rotate between K3 and K2 */
125 K1->Right = SingleRotateWithLeft(K1->Right);
126 /* Rotate between K1 and K2 */
127 return SingleRotateWithRight(K1);
128 }
129
130 // 1. 找位置; 2. 插入; 3. 平衡性; 4. 旋转
131 AvlTree Insert(ElementType X, AvlTree T)
132 {
133 if(T == NULL)
134 {
135 /* Create and return a one-node tree */
136 T = (AvlTree)malloc(sizeof(struct AvlNode));
137 if(T == NULL)
138 FatalError("Out of space!");
139 else
140 {
141 T->Left = T->Right = NULL;
142 T->Height = 0;
143 T->Element = X;
144 }
145 }
146 else if(X < T->Element)
147 {
148 T->Left = Insert(X, T->Left);
149 // 因为插到左边了, 所以肯定是左边比较高
150 if(Height(T->Left) - Height(T->Right) == 2)
151 {
152 if(X < T->Left->Element)
153 T = SingleRotateWithLeft(T);
154 else
155 T = DoubleRotateWithLeft(T);
156 }
157 }
158 else if(X > T->Element)
159 {
160 T->Right = Insert(X, T->Right);
161 // 插到右边了, 右边比较高
162 if(Height(T->Right) - Height(T->Left) == 2)
163 {
164 if(X > T->Right->Element)
165 T = SingleRotateWithRight(T);
166 else
167 T = DoubleRotateWithRight(T);
168 }
169 }
170 /* Else X is in the tree already; we‘ll do nothing */
171 T->Height = Max(Height(T->Left), Height(T->Right)) + 1;
172
173 return T;
174 }
175
176 AvlTree Delete(ElementType X, AvlTree T)
177 {
178 printf( "Sorry; Delete is unimplemented; %d remains\n", X );
179 return T;
180 }
181
182 ElementType Retrieve(Position P)
183 {
184 return P->Element;
185 }
186
187 void PrintTree(AvlTree T)
188 {
189 if( T != NULL)
190 {
191 PrintTree(T->Left);
192 printf("%d ", T->Element);
193 PrintTree(T->Right);
194 }
195 }
测试文件
1 #include "avltree.h"
2 #include <stdio.h>
3
4 main( )
5 {
6 AvlTree T;
7 Position P;
8 int i;
9 int j = 0;
10
11 T = MakeEmpty( NULL );
12 for( i = 0; i < 50; i++, j = ( j + 7 ) % 50 )
13 T = Insert( j, T );
14 for( i = 0; i < 50; i++ )
15 if( ( P = Find( i, T ) ) == NULL || Retrieve( P ) != i )
16 printf( "Error at %d\n", i );
17
18 /* for( i = 0; i < 50; i += 2 )
19 T = Delete( i, T );
20
21 for( i = 1; i < 50; i += 2 )
22 if( ( P = Find( i, T ) ) == NULL || Retrieve( P ) != i )
23 printf( "Error at %d\n", i );
24 for( i = 0; i < 50; i += 2 )
25 if( ( P = Find( i, T ) ) != NULL )
26 printf( "Error at %d\n", i );
27 */
28 printf( "Min is %d, Max is %d\n", Retrieve( FindMin( T ) ),
29 Retrieve( FindMax( T ) ) );
30 PrintTree(T);
31 return 0;
32 }
时间： 2024-10-13 17:24:23