[小明学算法]8.二叉平衡树

参考:http://www.cppblog.com/cxiaojia/archive/2014/03/02/187776.html

#include<iostream>
using namespace std;

template<class T>
class BTreeNode
{
public:
    //值
    T Data;
    //高度
    int Height;
    //左右节点
    BTreeNode* Left;
    BTreeNode* Right;
};

template<class T>
class BTree
{

public:
    //构造
    BTree() :Root(NULL){};
    //插入
    void Insert(BTreeNode<T>* &node, T data);
    //查找
    void Search(T data);
    //删除
    //TODO
    //中序遍历
    void Show(BTreeNode<T> *node);
    void Show1(BTreeNode<T> *node);
    //根节点
    BTreeNode<T>* Root;
private:

    //左旋
    BTreeNode<T>* RotateLeft(BTreeNode<T>* node);
    BTreeNode<T>* DoubleRotateLeft(BTreeNode<T>* node);
    //右旋
    BTreeNode<T>* RotateRight(BTreeNode<T>* node);
    BTreeNode<T>* DoubleRotateRight(BTreeNode<T>* node);
    //高度
    int GetHeight(BTreeNode<T>* node);
    //大值
    int Max(int a, int b)
    {
        return a > b ? a : b;
    }
};
template<class T>
void BTree<T>::Show(BTreeNode<T> *node)
{
    if (node == NULL)
        return;
    
    printf("Data:%d Height:%d
", node->Data, node->Height);
    Show(node->Left);
    Show(node->Right);
}
template<class T>
void BTree<T>::Show1(BTreeNode<T> *node)
{
    if (node == NULL)
        return;
    Show1(node->Left);
    printf("Data:%d Height:%d
", node->Data, node->Height);
    
    Show1(node->Right);
}

template<class T>
void BTree<T>::Insert(BTreeNode<T>* &node, T data)
{
    
    if (node == NULL)
    {
        node = new BTreeNode<T>();
        node->Data = data;
        node->Height = 1;
        return ;
        
    }

    //如果已经插入过了
    if (node->Data == data)
    {
        return;
    }

    if (node->Data > data)
    {
        //插入到左侧了
        Insert(node->Left, data);
        if (GetHeight(node->Left) - GetHeight(node->Right) > 1)
        {
            //左侧的左侧 即LL
            if (data < node->Left->Data)
                node = RotateRight(node);
            else// 左侧的右侧 LR
                node = DoubleRotateRight(node);
        }
    }

    if (node->Data < data)
    {
        Insert(node->Right, data);
        //插入后,若右侧不平衡了
        if (GetHeight(node->Right) - GetHeight(node->Left)>1)
        {
            //RR
            if (data > node->Right->Data)
                node = RotateLeft(node);
            else
                node = DoubleRotateLeft(node);
        }
    }
    if (node->Left!=NULL)
    node->Left->Height = Max(GetHeight(node->Left->Left), GetHeight(node->Left->Right)) + 1;
    if (node->Right != NULL)
    node->Right->Height = Max(GetHeight(node->Right->Left), GetHeight(node->Right->Right)) + 1;
    node->Height = Max(GetHeight(node->Left), GetHeight(node->Right))+1;
}

template<class T>
int BTree<T>::GetHeight(BTreeNode<T>* node)
{
    if (node != NULL)
        return node->Height;

    return 0;
}

template<class T>
BTreeNode<T>* BTree<T>::RotateLeft(BTreeNode<T>* node)
{
    BTreeNode<T>* rightChild = node->Right;
    if (rightChild != NULL)
    node->Right = rightChild->Left;
    rightChild->Left = node;

    return rightChild;
}

template<class T>
BTreeNode<T>* BTree<T>::DoubleRotateLeft(BTreeNode<T>* node)
{
    //先右旋子节点
    return RotateLeft(RotateRight(node->Right));
}

template<class T>
BTreeNode<T>* BTree<T>::RotateRight(BTreeNode<T>* node)
{
    BTreeNode<T>* leftChild = node->Left;

    if (leftChild!=NULL)
    node->Left = leftChild->Right;
    leftChild->Right = node;

    return leftChild;
}

template<class T>
BTreeNode<T>* BTree<T>::DoubleRotateRight(BTreeNode<T>* node)
{    
    return RotateRight(RotateLeft(node->Left));
}



void main()
{
    BTree<int> tree;
    for (int i = 0; i < 13; i++)
    {
        tree.Insert(tree.Root, rand()%100);
    }

    tree.Show(tree.Root);

    int a;
    cin >> a;
}