我正在尝试制作一个balance_bst(bstNode root)函数,但我在实现上遇到了困难。
我将该函数实现为模板函数,因为我的 bstNode 类是模板类。
这是我的(一些)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,并认为递归是明显的解决方案,但我似乎无法理解这个......
排序器基本上使用中序处理算法将 BST 的元素插入到向量中。 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该节点的键值并且该节点右子树的所有键值都大于该节点的键值)节点),那么插入到向量中的节点将以升序方式排序。
然后,为了创建平衡树,我将节点插入树根处向量的中心,然后应该能够递归地插入左右子节点,然后这些子节点将位于左侧的中间向量的一半和向量右半部分的中间。
注意:我知道这是使用整数除法,也就是说,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者的索引。
无论如何,欢迎和鼓励任何建议或意见! 提前致谢。
编辑:我要问的是如何实现平衡二叉搜索树的功能? (平衡 BST 是在给定节点数量的情况下具有最小深度的 BST。)
平衡二叉搜索树也称为 AVL 树 .
这个维基百科链接 对解决平衡问题有很好的解释。
我发现平衡树的最简单方法是在插入过程中。这是带有辅助函数(针对各种旋转情况)和 AVLNode 类的递归插入。
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;
}
辅助功能
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!
请遵循此更好的编码实践指南代码来获取解决方案:
https://leetcode.com/problems/balance-a-binary-search-tree/editorial/comments/2479284
解决方案采用Python,具有更高效和逻辑的解决方案方法。