我正在尝试创建一个balance_bst（bstNode root）函数，但我正在努力实现。
我正在将该函数实现为模板函数，因为我的bstNode类是模板类。
以下是（部分）我的代码：
template<class Item, class Key>
class bstNode{
public:
//Constructor
bstNode(const Item& init_data = Item(), const Key& init_key = Key(), bstNode<Item, Key>* l_child = NULL, bstNode<Item, Key>* r_child = NULL){
data_field = init_data;
key_field = init_key;
l_ptr = l_child;
r_ptr = r_child;
}
//Destructor
~bstNode(){
data_field = 0;
key_field = 0;
l_ptr = r_ptr = NULL;
}
//Basic Member Functions
bstNode<Item, Key>*& left( ) { return l_ptr; } //returns left child pointer by reference
bstNode<Item, Key>*& right( ) { return r_ptr; } //returns right child pointer by reference
bstNode<Item, Key>* left( ) const { return l_ptr; } //returns left child pointer by reference
bstNode<Item, Key>* right( ) const { return r_ptr; } //returns right child pointer by reference
const Item& data() const{ return data_field; } //returns reference to data_field
const Key& key()const { return key_field; }
Item& data() { return data_field; } //returns reference to data_field
Key& key() { return key_field; }
void set_data(const Item& new_data){ data_field = new_data; } //sets data_field to new_data
void set_key(const Key& new_key){ key_field = new_key; } //sets key_field to new_key
void set_left(bstNode* new_left){ l_ptr = new_left; } //sets left child pointer to new_left
void set_right(bstNode* new_right){ r_ptr = new_right; } //sets right child pointer to new_right
private:
bstNode<Item, Key> *l_ptr, //pointer to left child node
*r_ptr; //pointer to right child node
Item data_field;
Key key_field;
};
template<class Item, class Key>
void balance_bst(bstNode<Item, Key>*& root){ //unfinished
std::vector< bstNode<Item, Key>* > nodes;
sorter(root, nodes);
size_t i = nodes.size()/2; //size() divided by 2 will yield
//index of middle element of vector for
//odd-isized arrays and the greater of the
//middle two elements for an even-sized array
while(i>=0){
root->set_key(nodes[i]->key());
root->set_data(nodes[i]->data());
//.....MORE CODE HERE: recursive call??
}
}
template<class Item, class Key>
void sorter(bstNode<Item, Key>*& root, std::vector<bstNode<Item, Key>* >& tree_nodes){
if(root == NULL)
return;
sorter(root->left(), tree_nodes);
tree_nodes.push_back(root);
sorter(root->right(), tree_nodes);
}
我一直在搞乱实际的balance_bst函数，并认为递归是一个明显的解决方案，但我似乎无法绕过这个... ...
sorter基本上使用inorder处理算法将BST的元素插入到矢量中。因此，只要“root”是指向二叉搜索树的根的指针（即节点左子树的所有键值都小于节点的键值，并且节点右子树的所有键值都大于然后插入到向量中的节点将以升序方式进行分类。
然后，为了创建一个平衡的树，我将节点插入树的根处的向量的中心，然后应该能够递归地插入左和右子节点，然后它们位于向量的左半部分和向量的右半部分的中间。
注意：我知道这是使用整数除法，即7/2 = 3，这将是大小为7的数组的中间元素的索引。对于偶数大小的数组，上面实现的算法将找到向量中间两个元素中较大元素的索引。
无论如何，欢迎并鼓励任何建议或观察！提前致谢。
编辑：我要问的是如何实现一个平衡二叉搜索树的功能？ （平衡的BST是指给定节点数量的最小深度。）
答案 0 :(得分：7)
平衡二叉搜索树也称为AVL树
This wikipedia link 对解决平衡问题有很好的解释。
我发现在插入过程中平衡树的最简单方法。这是一个带有辅助函数的递归插入（用于各种旋转情况）和一个AVLNode类。
bool avl_insert(AVLNode*& subRoot, const int &newData, bool &taller)
{
bool result = true;
if(!subRoot){
subRoot = new AVLNode(newData);
taller = true;
}
else if(newData == subRoot->getData()){
result = false;
taller = false;
}
else if(newData < subRoot->getData()){
result = avl_insert(subRoot->getLeft(), newData, taller);
if(taller)
switch(subRoot->getBalance()){
case -1:
left_balance(subRoot);
taller = false;
break;
case 0:
subRoot->setBalance(-1);
break;
case 1:
subRoot->setBalance(0);
taller = false;
break;
}
}
else{
result = avl_insert(subRoot->getRight(), newData, taller);
if(taller)
switch(subRoot->getBalance()){
case -1:
subRoot->setBalance(0);
taller = false;
break;
case 0:
subRoot->setBalance(1);
break;
case 1:
right_balance(subRoot);
taller = false;
break;
}
}
return result;
}
辅助函数
void right_balance(AVLNode *&subRoot)
{
AVLNode *&right_tree = subRoot->getRight();
switch(right_tree->getBalance()){
case 1:
subRoot->setBalance(0);
right_tree->setBalance(0);
rotate_left(subRoot); break;
case 0:
cout<<"WARNING: program error in right_balance"<<endl; break;
case -1:
AVLNode *subTree = right_tree->getLeft();
switch(subTree->getBalance()){
case 0:
subRoot->setBalance(0);
right_tree->setBalance(0);break;
case -1:
subRoot->setBalance(0);
right_tree->setBalance(1); break;
case 1:
subRoot->setBalance(-1);
right_tree->setBalance(0);break;
}
subTree->setBalance(0);
rotate_right(right_tree);
rotate_left(subRoot); break;
}
}
void left_balance(AVLNode *&subRoot)
{
AVLNode *&left_tree = subRoot->getLeft();
switch(left_tree->getBalance()){
case -1:
subRoot->setBalance(0);
left_tree->setBalance(0);
rotate_right(subRoot); break;
case 0:
cout<<"WARNING: program error in left_balance"<<endl; break;
case 1:
AVLNode *subTree = left_tree->getRight();
switch(subTree->getBalance()){
case 0:
subRoot->setBalance(0);
left_tree->setBalance(0);break;
case -1:
subRoot->setBalance(0);
left_tree->setBalance(1); break;
case 1:
subRoot->setBalance(-1);
left_tree->setBalance(0);break;
}
subTree->setBalance(0);
rotate_left(left_tree);
rotate_right(subRoot); break;
}
}
void rotate_left(AVLNode *&subRoot)
{
if(subRoot == NULL || subRoot->getRight() == NULL)
cout<<"WARNING: program error detected in rotate_left"<<endl;
else{
AVLNode *right_tree = subRoot->getRight();
subRoot->setRight(right_tree->getLeft());
right_tree->setLeft(subRoot);
subRoot = right_tree;
}
}
void rotate_right(AVLNode *&subRoot)
{
if(subRoot == NULL || subRoot->getLeft() == NULL)
cout<<"WARNING: program error detected in rotate_left"<<endl;
else{
AVLNode *left_tree = subRoot->getLeft();
subRoot->setLeft(left_tree->getRight());
left_tree->setRight(subRoot);
subRoot = left_tree;
}
}
AVLNode类
class AVLNode
{
public:
AVLNode()
{
previous = NULL;
next = NULL;
}
AVLNode(int newData){
data = newData;
previous = NULL;
balance=0;
next = NULL;
}
~AVLNode(){}
void setBalance(int b){balance = b;}
int getBalance(){return balance;}
void setRight(AVLNode* newNext){next = newNext;}
void setLeft(AVLNode* newPrevious){previous = newPrevious;}
AVLNode* getRight() const{return next;}
AVLNode* getLeft() const{return previous;}
AVLNode*& getRight(){return next;}
AVLNode*& getLeft(){return previous;}
int getData() const{return data;}
int& getData(){return data;}
void setData(int newData){data = newData;}
void setHeight(int newHeight){ height = newHeight;}
int getHeight(){return height;}
private:
AVLNode* next;
AVLNode* previous;
int balance;
int height;
int data;
};
希望这有帮助！