数据结构--AVLTree(平衡二叉搜索树)【菜鸟学习日记】

之前写完了二叉搜索树,今天打算写一下AVL树,对之前的二叉搜索树进行平衡优化

AVL树(使不平衡的树,变平衡)

AVL树又称为高度平衡的二叉搜索树,它能保持二叉树的高度平衡,尽量降低二叉树的高度,减少树的平均搜索长度

AVL树的性质
  1. 左子树和右子树的高度之差的绝对值不超过1 (衡量是否平衡的标准)
  2. 树中的每个左子树和右子树都是AVL树
  3. 每个节点都有一个平衡因子(balance factor–bf),任一节点的平衡因子是-1,0,1。(每个节点的平衡因子等于右子树的高度减去左子树的高度 )

《数据结构--AVLTree(平衡二叉搜索树)【菜鸟学习日记】》

通过旋转,使树平衡

左单旋&右单旋
左右双旋&右左双旋

《数据结构--AVLTree(平衡二叉搜索树)【菜鸟学习日记】》

//左旋
    void RotateL(Node* parent)
    {
        Node* subR = parent->_right;
        Node* subRL = subR->_left;

        parent->_right = subRL;
        if (subRL)
            subRL->_parent = parent;

        subR->_left = parent;
        Node* ppNode = parent->_parent;
        parent->_parent = subR;

        if (ppNode == NULL)
        {
            _root = subR;
            subR->_parent = NULL;
        }
        else  //(ppNode!=NULL)
        {
            if (parent = ppNode->_left)
            {
                ppNode->_left = subR;
                subR->_parent = ppNode;
            }
            else
            {
                ppNode->_right = subR;
                subR->_parent = ppNode;
            }
        }
        parent->_num = subR->_num = 0;
    }
//右旋
    void RotateR(Node* parent)
    {
        Node* subL = parent->_left;
        Node* subLR = subL->_right;

        parent->_left= subLR;
        if (subLR)
            subLR->_parent = parent;

        subL->_right = parent;
        Node* ppNode = parent->_parent;
        parent->_parent = subL;

        if(ppNode == NULL)
        {
            _root = subL;
            _root->_parent = NULL; 
        }
       else
        {
            if (parent == ppNode->_left)
            {
                ppNode->_left = subL;
                subL->_parent = ppNode;
            }
            else
            {
                ppNode->_right = subL;
                subL->_parent = ppNode;
            }
        }
        parent->_num = subL->_num = 0;
    }
    //左右旋
    void RotateLR(Node* parent)
    {
        RotateL(parent->_left);
        RotateR(parent);
    }
    //右左旋
    void RotateRL(Node* parent)
    {
        RotateR(parent->_right);
        RotateL(parent);
    }
bool Insert(const K& key, V value)
    {
        if (_root == NULL)
        {
            _root = new Node(key, value);
            return true;
        }
        //找位置
        Node* cur = _root;
        Node* parent = NULL;
        while (cur)
        {
            if (key < cur->_key)
            {
                parent = cur;
                cur = cur->_left;
            }
            else if (key>cur->_key)
            {
                parent = cur;
                cur = cur->_right;
            }
            else
            {
                break;
            }
        }
        //插入,左插/右插
        cur = new Node(key, value);
        if (key < parent->_key)
        {
            parent->_left = cur;
            cur->_parent = parent;
        }
        else if (key>parent->_key)
        {
            parent->_right = cur;
            cur->_parent = parent;
        }
        else
        {
            return false;
        }

        //更新平衡因子
        while (cur != _root)
        {
            //如果左插--,右插++
            if (cur == parent->_left)
                parent->_num--;
            else
                parent->_num++;
            //判断平衡因子
            if (parent->_num == 0)
            {
                return true;
            }
            //|p|=1,子树的高度改变,继续向更新
            else if (parent->_num == 1 || parent->_num == -1)
            {
                cur = parent;
                parent = parent->_parent;
            }
            //|p|=2,进行平衡调整
            else if (parent->_num == 2 || parent->_num == -2)
            {
                if (parent->_num == 2 && cur->_num == 1)
                {
                    RotateL(parent);
                }
                if (parent->_num == -2 && cur->_num == -1)
                {
                    RotateR(parent);
                }
                if (parent->_num == 2 && cur->_num == -1)
                {
                    RotateRL(parent);
                }
                if (parent->_num == -2 && cur->_num == 1)
                {
                    RotateLR(parent);
                }   
                return true;
            }
        }
    }
    原文作者:平衡二叉树
    原文地址: https://blog.csdn.net/lindaxym/article/details/79640601
    本文转自网络文章,转载此文章仅为分享知识,如有侵权,请联系博主进行删除。
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