二叉搜索树

• 结点定义：

struct Node{
        char val;
        Node *l = NULL, *r = NULL, *p = NULL;
};

• 建树:

Node* build(Node *p /*...根据实际情况而定*/)
{
        Node *root = new Node;
        root->val = data;
        root->p = p;
        root->l = build(root /*...根据实际情况而定*/);
        root->r = build(root /*...根据实际情况而定*/);
        return root;
}

• 遍历

1. 递归实现
   • 先序遍历

   void pre_order(Node* root)
   {
           if(root != NULL){
               cout<<root->val;
               pre_order(root->l);
               pre_order(root->r);
           }
   }
   

   • 中序遍历

   void in_order(Node* root)
   {
           if(root != NULL){
               in_order(root->l);
               cout<<root->val;
               in_order(root->r);
           }
   }
   

   • 后序遍历

   void post_order(Node* root)
   {
           if(root != NULL){
               post_order(root->l);
               post_order(root->r);
               cout<<root->val;
           }
   }
   

2. 非递归实现
   • 先序遍历

   void pre_order2(Node* root)
   {
           Node *pre = NULL;
           Node *node = root;
           while(node != NULL){
               if(pre == node->p){
                   cout<<node->val;
                   if(node->l != NULL){
                       pre = node;
                       node = node->l;
                   }
                   else{
                       if(node->r != NULL){
                           pre = node;
                           node = node->r;
                       }
                       else{
                           pre = node;
                           node = node->p;
                       }
                   }
               }
               else if(pre == node->l){
                   if(node->r != NULL){
                       pre = node;
                       node = node->r;
                   }
                   else{
                       pre = node;
                       node = node->p;
                   }
               }
               else if(pre == node->r){
                   pre = node;
                   node = node->p;
               }
           }
   }
   

   • 中序遍历

   void in_order2(Node* root)
   {
           Node *pre = NULL;
           Node *node = root;
           while(node != NULL){
               if(pre == node->p){
                   if(node->l != NULL){
                       pre = node;
                       node = node->l;
                   }
                   else{
                       cout<<node->val;
                       if(node->r != NULL){
                           pre = node;
                           node = node->r;
                       }
                       else{
                           pre = node;
                           node = node->p;
                       }
                   }
               }
               else if(pre == node->l){
                   cout<<node->val;
                   if(node->r != NULL){
                       pre = node;
                       node = node->r;
                   }
                   else{
                       pre = node;
                       node = node->p;
                   }
               }
               else if(pre == node->r){
                   pre = node;
                   node = node->p;
               }
           }
   }
   

   • 后序遍历

   void post_order2(Node* root)
   {
           Node *pre = NULL;
           Node *node = root;
           while(node != NULL){
               if(pre == node->p){
                   if(node->l != NULL){
                       pre = node;
                       node = node->l;
                   }
                   else{
                       if(node->r != NULL){
                           pre = node;
                           node = node->r;
                       }
                       else{
                           cout<<node->val;
                           pre = node;
                           node = node->p;
                       }
                   }
               }
               else if(pre == node->l){
                   if(node->r != NULL){
                       pre = node;
                       node = node->r;
                   }
                   else{
                       cout<<node->val;
                       pre = node;
                       node = node->p;
                   }
               }
               else if(pre == node->r){
                   cout<<node->val;
                   pre = node;
                   node = node->p;
               }
           }
   }
   

• 查找

1. 递归实现

   Node* tree_search(Node *x, char k)
   {
       if(x == NULL || k == x.val)
           return x;
       if(k < x.val)
           return tree_search(x->l, k);
       else
           return tree_search(x->r, k);
   }
   
   

2. 非递归实现

   Node* tree_search2(Node *x, char k)
   {
       while(x != NULL && k != x->val){
           if(k < x->val)
               x = x->l;
           else
               x = x->r;
       }
       return x;
   }
   
   

• 最值元素

1. 最小关键字元素

   Node* tree_minimum(Node *x)
   {
       while(x->l != NULL)
           x = x->l;
       return x;
   }
   

2. 最大关键字元素

   Node* tree_maximum(Node *x)
   {
       while(x->r != NULL)
           x = x->r;
       return x;
   }
   

• 后继和前驱（中序遍历）

1. 后继

   Node* tree_successor(Node *x)
   {
       if(x->r != NULL)
           return tree_minimum(x->r);
       Node *y = x->p;
       while(y != NULL && x == y->r){
           x = y;
           y = y->p;
       }
       return y;
   }
   

2. 前驱

   Node* tree_predecessor(Node *x)
   {
       if(x->l != NULL)
           return tree_maximum(x->l);
       Node *y = x->p;
       while(y != NULL && x == y->l){
           x = y;
           y = y->p;
       }
       return y;
   }
   

• 插入和删除

1. 插入

   Node* tree_insert(Node *root, Node *z)  //插入结点z
   {
       Node *x = root;
       Node *y = NULL;
       while(x != NULL){
           y = x;
           if(z->val < x->val)
               x = x->l;
           else
               x = x->r;
       }
       z->p = y;
       if(y == NULL){
           //树为空，此时z为根节点
       }
       else if(z->val <　y->val)
           y->l = z;
       else
           y->r = z;
   }
   
   

2. 删除
   待续。。。