AVL树

　　今天想复习一下AVL树和红黑树，想写出来，没想到太难了，我太难了 ：（

　　AVL树的左旋：左节点成为根，右节点接管原根节点，原根节点接管左节点的右节点。

　　只写了AVL树的插入：

　　

template <typename T>
class AVLNode
{
public:
    T value;
    AVLNode* left;
    AVLNode* right;
    int height;
    bool valid;
    AVLNode():value(0),left(nullptr),right(nullptr),height(0){}
    AVLNode(const T& v, AVLNode* l=nullptr, AVLNode* r=nullptr, int h=0,bool varg=true) :value(v), left(l), right(r), height(h),valid(varg){}
};


class AVLTree
{
public:
    using EleType = int;
    using NodeType = AVLNode<EleType>;
    AVLTree();
    void insert(const EleType& val);
private:
    NodeType* _head;
    void insert(const EleType& val, NodeType*& cur);
    void leftRotate(NodeType*& k2);
    void rightRotate(NodeType*& k2);
    void rightLeftRotate(NodeType*& k3);
    void leftRightRotate(NodeType*& k3);
    void balance(NodeType*& cur);
    const int MAX_DIFF_HEIGHT = 1;
    int height(const NodeType* cur)const;
};

AVLTree::AVLTree()
{
    _head = nullptr;
}

void AVLTree::insert(const EleType& val)
{
    insert(val, _head);
}

void AVLTree::insert(const EleType& val,NodeType*& cur)
{
    if (_head == nullptr)
    {
        NodeType* n = new NodeType(val);
        _head = n;
        return;
    }
    if (cur == nullptr)
    {
        cur = new NodeType(val);
    }
    else if (val <= cur->value)
    {
        insert(val, cur->left);
    }
    else if (val > cur->value)
    {
        insert(val, cur->right);
    }
    balance(cur);
}

void AVLTree::leftRotate(NodeType*& k2)
{
    NodeType* k1 = k2->left;
    k2->left = k1->right;
    k1->right = k2;
    k2->height = std::max(height(k2->left), height(k2->right)) + 1;
    k1->height = std::max(height(k1->left), k2->height) + 1;
    k2 = k1;
}

void AVLTree::rightRotate(NodeType*& k1)
{
    NodeType* k2 = k1->right;
    k1->right = k2->left;
    k2->left = k1;
    k1 = k2;
    k2->height = std::max(height(k2->left), height(k2->right)) + 1;
    k1->height = std::max(height(k1->left), height(k1->right)) + 1;
}

void AVLTree::rightLeftRotate(NodeType*& k3)
{
    rightRotate(k3->left);
    leftRotate(k3);
}

void AVLTree::leftRightRotate(NodeType*& k3)
{
    leftRotate(k3->right);
    rightRotate(k3);
}

void AVLTree::balance(NodeType*& cur)
{
    if (cur == nullptr) return;
    int lefthight = height(cur->left);
    int rightheight = height(cur->right);
    if ((lefthight-rightheight)>MAX_DIFF_HEIGHT)
    {
        if (height(cur->left->left) >= height(cur->left->right))
        {
            leftRotate(cur);
        }
        else
        {
            rightLeftRotate(cur);
        }
    }
    else if ((rightheight - lefthight) > MAX_DIFF_HEIGHT)
    {
        if (height(cur->right->right) >= height(cur->right->left))
        {
            rightRotate(cur);
        }
        else
        {
            leftRightRotate(cur);
        }
    }
    cur->height = std::max(lefthight, rightheight) + 1;
}

int AVLTree::height(const NodeType* cur) const
{
    return cur == nullptr ? -1 : cur->height;
}