二叉查找樹的結構和普通二叉樹相同。它要麽是空樹，要麽滿足：對任意結點，如果左子樹不為空，則左子樹上所有結點的權值都小於該結點的權值；如果右子樹不為空，則右子樹上所有結點的權值都大於該結點的權值。在二叉查找樹中，任意結點的左子樹和右子樹都是一棵二叉查找樹。一般而言，二叉樹上結點的權值都是唯一的。

基本操作：

  1 //二叉查找樹
  2 //結點定義
  3 template <typename Type> class Node {
  4 public:
  5     Type data;
  6     Node *lchild,*rchild,*parent;
  7     //parent is NULL by default
 

  8     Node(Type _data, Node<Type> *_parent=NULL) {
  9         data=_data;
 10         lchild=NULL;
 11         rchild=NULL;
 12         parent=_parent;
 13     }
 14     //no need to delete parent because all nodes are already deleted by delete method recursively
 15     ~Node() {
 16         if
 
(lchild!=NULL){
 17             delete lchild;
 18         }
 19         if(rchild!=NULL){
 20             delete rchild;
 21         }
 22     }
 23 
 24 
 25     void insert(Type value) {
 26         //do not allow repeated element
 27         if(data==value){
 28             return;
 29         }
 30
 
         else if(value>data){
 31             if(rchild==NULL){
 32                 rchild=new Node<Type>(value,this);
 33             }
 34             else{
 35                 rchild->insert(value);
 36             }
 37         }
 38         //value<data
 39         else{
 40             if(lchild==NULL){
 41                 lchild=new Node<Type>(value,this);
 42             }
 43             else{
 44                 lchild->insert(value);
 45             }
 46         }
 47     }
 48 
 49 
 50     Node* search(Type value) {
 51         if(data==value){
 52             return this;
 53         }
 54         else if(value>data){
 55             if(rchild==NULL){
 56                 return NULL;
 57             }
 58             else{
 59                 rchild->search(value);
 60             }
 61         }
 62         //value<data
 63         else{
 64             if(lchild==NULL){
 65                 return NULL;
 66             }
 67             else{
 68                 lchild->search(value);
 69             }
 70         }
 71     }
 72 
 73     //inorder_print
 74     void print() {
 75         if(lchild!=NULL){
 76             lchild->print();
 77         }
 78         cout<<data<<" ";
 79         if(rchild!=NULL){
 80             rchild->print();
 81         }
 82     }
 83 
　　　　 //only for nodes with children
 84     Node<Type> * predecessor() {
 85         Node<Type> *temp = lchild;
 86         //the most right element in its left child tree
 87         while (temp != NULL && temp->rchild != NULL) {
 88             temp = temp->rchild;
 89         }
 90         return temp;
 91     }
 92 
　　　　　//only for nodes with children
 93     Node<Type> * successor() {
 94         Node<Type> *temp = rchild;
 95         //the most left elemnent in its right child tree
 96         while (temp != NULL && temp->lchild != NULL) {
 97             temp = temp->lchild;
 98         }
 99         return temp;
100     }
101 
102     //remove_node for leaf nodes or nodes with only one child
103     void remove_node(Node<Type> *delete_node) {
104         Node<Type> *temp = NULL;
105         if (delete_node->lchild != NULL) {
106             temp = delete_node->lchild;
107             //the successor of delete_node is the father of delete_node
108             temp->father = delete_node->father;
109         }
110         if (delete_node->rchild != NULL) {
111             temp = delete_node->rchild;
112             //the predecessor of delete_node is the father of delete_node
113             temp->father = delete_node->father;
114         }
115         //if delete_node is the left child
116         if (delete_node->father->lchild == delete_node) {
117             delete_node->father->lchild = temp;
118         } else {
119             delete_node->father->rchild = temp;
120         }
121         //set them to NULL to prevent deleting the entire tree
122         delete_node->lchild = NULL;
123         delete_node->rchild = NULL;
124         delete delete_node;
125     }
126 
127     //the complete version of deleting a node
128     //make use of the remove_node method
129     bool delete_node(Type value){
130         Node<Type> *delete_node,*current_node;
131         //find the target node
132         current_node=search(value);
133         if(current_node==NULL){
134             return false;
135         }
136         //replacing the current_node with either its predecessor or successor
137         if(current_node->lchild!=NULL){
138             delete_node=current_node->predecessor();
139         }
140         else if(current_node->rchild!=NULL){
141             delete_node=current_node->successor();
142         }
143         //else it must be a leaf node, which we can just remove it using remove_node
144         else{
145             delete_node=current_node;
146         }
147         //replace value and delete the predecessor/successor
148         current_node->data=delete_node->data;
149         remove_node(delete_node);
150         return true;
151     }
152 };
153 
154 
155 template <typename Type> class BinaryTree {
156 private:
157     Node<Type> *root;
158 public:
159     BinaryTree() {
160         root=NULL;
161     }
162     ~BinaryTree() {
163         delete root;
164     }
165     void insert(Type value) {
166         if(root==NULL){
167             root=new Node<Type>(value);
168         }
169         else root->insert(value);
170     }
171     bool find(Type value) {
172         if(root==NULL){
173             return false;
174         }
175         else{
176             if(root->search(value)==NULL){
177                 return false;
178             }
179             else{
180                 return true;
181             }
182         }
183     }
184     void print() {
185         if(root!=NULL){
186             root->print();
187         }
188     }
189 
190     bool delete_node(Type value){
191         if(root==NULL){
192             return false;
193         }
194         return root->delete_node(value);
195     }
196 };

二叉查找樹