平衡二叉搜索树（BST）(Balancing a Binary Search Tree (BST))

2019-06-24 03:48发布

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我试图做一个balance_bst（bstNode根）函数，但我与实施挣扎。

我执行的功能为模板的功能，因为我的bstNode类是一个模板类。

这里是（一些）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); 
}

我一直在搞乱与实际balance_bst功能，并认为递归是显而易见的解决办法，但我似乎无法环绕这一个我的头......

分拣机基本上插入BST的元素复制到使用中序处理算法的载体。 所以只要“根”是一个指向二叉搜索树的根部（即左子树一个节点的所有关键值小于节点的键值和节点的右子树的所有键值比更大插入到载体中的节点），那么节点将处于升序方式分拣机。

然后，建立一个平衡的树，我插入节点的载体在树的根部的中心，然后应该能够递归插入左，右子节点那么这将是在左半边的中间向量，向量的右半部分的中间。

注意：我明白，这是使用整数除法，并且说，7/2 = 3，这将是尺寸7而对于偶数大小的数组的数组的中间元素的索引，上述实施的算法会发现在矢量中间的两个元素中的较大指数。

不管怎样，任何建议或意见，欢迎和鼓励！ 提前致谢。

编辑：我问什么是如何实现的功能，以平衡二叉搜索树？ （A平衡BST是具有可以使用给定的节点的数目的最小深度。）

Answer 1:

一个平衡二叉搜索树也被称为AVL树。

此维基百科的链接 ，对解决平衡问题一个很好的解释。

我找到平衡树插入过程中最简单的方法。 下面是辅助功能的递归接插件（适用于各种旋转的情况下）和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;
};

希望这可以帮助！



文章来源: Balancing a Binary Search Tree (BST)
标签： c++ binary-search-tree
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