伸展树，感觉对我这种菜鸟还是有些吃力，主要也是旋转的时候吧，把要查询的节点旋转到根节点，看网上是有两种方法，一是从上到下，一是从下到上。从上到下，是把树拆分成中树，左树和右树，始终保证目标节点在中树，不断向下把中树的节点添到右树或者左树，直到目标节点为中树的根，再将三树合并起来。另外一种从下到上，旋转操作类似AVL树中的旋转，但是判断好像不是很好写，我写的是从上到下的，另外删除也很巧妙，先把目标节点旋转到根，若此时左子树为空直接删除，否则找到左子树最右的节点当头，利用伸展树的特殊旋转就可以一步删除，太牛叉了，还有就是一个元素和指向它的指针的巧妙运用，真是涨了不少知识啊，，，，
1 #include <stdio.h> 2 #include <string.h> 3 #include <stdlib.h> 4 5 typedef struct _spaly 6 { 7 int key; 8 struct _spaly* left; 9 struct _spaly* right; 10 }*Pspaly; 11 12 Pspaly splay(Pspaly tree,int k); 13 void Destory(Pspaly tree); 14 void Printf(Pspaly tree); 15 Pspaly Insert(Pspaly tree,int k); 16 Pspaly Node(int k); 17 Pspaly Delete(Pspaly tree,int k); 18 Pspaly Search(Pspaly tree,int k); 19 20 int main() 21 { 22 Pspaly tree=NULL; 23 tree = Insert(tree,3); 24 tree = Insert(tree,6); 25 tree = Insert(tree,1); 26 tree = Insert(tree,5); 27 tree = Insert(tree,7); 28 tree = Insert(tree,0); 29 tree = Insert(tree,11); 30 Printf(tree); 31 printf(" "); 32 tree=splay(tree,2); 33 Printf(tree); 34 printf(" "); 35 // tree = splay(tree,6); 36 tree = Delete(tree,3); 37 Printf(tree); 38 printf(" "); 39 tree = splay(tree,11); 40 Printf(tree); 41 return 0; 42 } 43 44 Pspaly Node(int k) 45 { 46 Pspaly node = (Pspaly)malloc(sizeof(_spaly)); 47 node->key = k; 48 node->left = NULL; 49 node->right = NULL; 50 return node; 51 } 52 53 Pspaly Insert(Pspaly tree,int k) 54 { 55 Pspaly node = Node(k); 56 if(tree==NULL) 57 { 58 tree = node; 59 return tree; 60 } 61 if(k<tree->key) 62 { 63 tree->left = Insert(tree->left,k); 64 } 65 else if(k>tree->key) 66 { 67 tree->right = Insert(tree->right,k); 68 } 69 return tree; 70 } 71 72 //销毁伸展树 73 void Destory(Pspaly tree) 74 { 75 if(tree==NULL)return; 76 Destory(tree->left); 77 Destory(tree->right); 78 free(tree); 79 } 80 81 //核心，旋转操作 82 Pspaly splay(Pspaly tree,int k) 83 { 84 Pspaly l,r; 85 _spaly N; 86 l = r = &N; // 87 while(true) 88 { 89 if(k<tree->key) 90 { 91 if(tree->left==NULL) 92 break;//当目标节点不在树上时，在删除时有大用 93 if(k<tree->left->key) 94 { 95 Pspaly tem = tree->left; 96 tree->left = tem->right; 97 tem->right = tree; 98 tree = tem; 99 } 100 //将节点加到右树 101 r->left = tree; 102 r = tree; 103 tree = tree->left; 104 } 105 else if(k>tree->key) 106 { 107 if(tree->right==NULL)break; 108 if(k>tree->right->key) 109 { 110 Pspaly tem = tree->right; 111 tree->right = tem->left; 112 tem->left = tree; 113 tree = tem; 114 } 115 l->right = tree; 116 l = tree; 117 tree = tree->right; 118 } 119 else 120 { 121 break; 122 } 123 124 } 125 126 //合并三课树 127 l->right = tree->left; 128 r->left = tree->right; 129 tree->left = N.right; 130 tree->right = N.left; 131 return tree; 132 } 133 134 //打印函数 135 void Printf(Pspaly tree) 136 { 137 if(tree==NULL)return; 138 printf("父亲结点是:%d",tree->key); 139 printf(" 左儿子是:"); 140 if(tree->left==NULL)printf("NULL"); 141 else printf("%d",tree->left->key); 142 printf(" 右儿子是:"); 143 if(tree->right==NULL)printf("NULL "); 144 else printf("%d ",tree->right->key); 145 Printf(tree->left); 146 Printf(tree->right); 147 } 148 149 Pspaly Delete(Pspaly tree,int k) 150 { 151 Pspaly tem; 152 if(Search(tree,k)==NULL) 153 { 154 printf("无 "); 155 return NULL; 156 } 157 tree = splay(tree,k); 158 if(tree->left==NULL) 159 return tree->right; 160 else 161 { 162 //将tree->left的最右子树当做根 163 tem = splay(tree->left,k); 164 tem->right = tree->right; 165 } 166 free(tree); 167 return tem; 168 } 169 170 Pspaly Search(Pspaly tree,int k) 171 { 172 if(tree==NULL)return NULL; 173 if(k<tree->key)Search(tree->left,k); 174 else if(k>tree->key)Search(tree->right,k); 175 else 176 return tree; 177 }
再贴个C++的
1 #include <cstdio> 2 #include <iostream> 3 #include <cstring> 4 5 using namespace std; 6 7 template<class T> 8 class SplayNode 9 { 10 public: 11 T key; 12 SplayNode* left; 13 SplayNode* right; 14 15 SplayNode():left(NULL),right(NULL){} 16 SplayNode(T value,SplayNode* l,SplayNode* r):key(value),left(l),right(r){} 17 18 /*SplayNode() 19 { 20 left = NULL; 21 right = NULL; 22 } 23 SplayNode(T value,SplayNode* l,SplayNode* r) 24 { 25 key = value; 26 left = l; 27 right = r; 28 }*/ 29 }; 30 31 template <class T> 32 class SplayTree 33 { 34 private: 35 SplayNode<T>* mroot; 36 public: 37 SplayTree(); 38 ~SplayTree(); 39 SplayNode<T>* splay(SplayNode<T>* tree,T k); 40 void Destory(SplayNode<T>* tree); 41 void Printf(SplayNode<T>* tree); 42 void Insert(T k); 43 SplayNode<T>* Node(T k); 44 SplayNode<T>* Delete(SplayNode<T>* tree,T k); 45 SplayNode<T>* Insert_into(SplayNode<T>* Tree,T k); 46 SplayNode<T>* Search(T k); 47 void Printf(SplayTree<T>* tree); 48 void _printf(); 49 }; 50 51 template <class T> 52 SplayTree<T>::SplayTree() 53 { 54 mroot = NULL; 55 } 56 57 template <class T> 58 SplayTree<T>::~SplayTree() 59 { 60 Destory(mroot); 61 } 62 63 template <class T> 64 void SplayTree<T>::Destory(SplayNode<T>* tree) 65 { 66 if(tree==NULL)return; 67 Destory(tree->left); 68 Destory(tree->right); 69 delete tree; 70 } 71 72 template <class T> 73 SplayNode<T>* SplayTree<T>::Node(T k) 74 { 75 SplayNode<T>* node = new SplayNode<T>(k,NULL,NULL); 76 /* node->key = k; 77 node->left = NULL; 78 node->right = NULL;*/ 79 return node; 80 } 81 82 template <class T> 83 void SplayTree<T>::Insert(T k) 84 { 85 mroot = Insert_into(mroot,k); 86 } 87 88 template <class T> 89 void SplayTree<T>::_printf() 90 { 91 SplayTree::Printf(mroot); 92 } 93 94 template <class T> 95 void SplayTree<T>::Printf(SplayNode<T>* tree) 96 { 97 if(tree==NULL)return; 98 printf("父亲节点是:%d",tree->key); 99 printf(" 左儿子是:"); 100 if(tree->left==NULL)printf("NULL"); 101 else printf("%d",tree->left->key); 102 printf(" 右儿子是:"); 103 if(tree->right==NULL)printf("NULL "); 104 else printf("%d ",tree->right->key); 105 Printf(tree->left); 106 Printf(tree->right); 107 } 108 template <class T> 109 SplayNode<T>* SplayTree<T>::Insert_into(SplayNode<T>* tree,T k) 110 { 111 SplayNode<T>* node = SplayTree<T>::Node(k); 112 if(tree==NULL) 113 { 114 tree = node; 115 return tree; 116 } 117 if(k<tree->key) 118 { 119 tree->left = Insert_into(tree->left,k); 120 } 121 else if(k>tree->key) 122 { 123 tree->right = Insert_into(tree->right,k); 124 } 125 return tree; 126 } 127 128 template <class T> 129 SplayNode<T>* SplayTree<T>::splay(SplayNode<T>* tree,T k) 130 { 131 SplayNode<T> N,*r,*l; 132 N.left = N.right = NULL; 133 l = r = &N; 134 while(true) 135 { 136 if(k<tree->key) 137 { 138 if(tree->left==NULL)break; 139 if(k<tree->left->key) 140 { 141 SplayNode<T>* tem = tree->left; 142 tree->left = tem->right; 143 tem->right = tree; 144 tree = tem; 145 } 146 r->left = tree; 147 r = tree; 148 tree = tree->left; 149 } 150 if(k>tree->key) 151 { 152 if(tree->right==NULL)break; 153 if(k>tree->right->key) 154 { 155 SplayNode<T>* tem = tree->right; 156 tree->right = tem->left; 157 tem->left = tree; 158 tree = tem; 159 } 160 l->right = tree; 161 l = tree; 162 tree = tree->right; 163 } 164 else 165 { 166 break; 167 } 168 } 169 l->right = tree->left; 170 r->left = tree->right; 171 tree->left = N.right; 172 tree->right = N.left; 173 return tree; 174 } 175 176 template <class T> 177 SplayNode<T>* SplayTree<T>::Search(T k) 178 { 179 mroot = SplayTree<T>::splay(mroot,k); 180 } 181 int main() 182 { 183 SplayTree<int>* tree = new SplayTree<int>(); 184 tree->Insert(3); 185 tree->Insert(6); 186 tree->Insert(1); 187 tree->Insert(5); 188 tree->Insert(7); 189 tree->Insert(0); 190 tree->Insert(11); 191 tree->_printf(); 192 printf(" "); 193 tree->Search(11); 194 tree->_printf(); 195 return 0; 196 }